Physics Question bank
February 18, 2017 | Author: Roberto De La Paz | Category: N/A
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Chapter 23—Electric Fields MULTIPLE CHOICE 1. Each of two small non-conducting spheres is charged positively, the combined charge being 40 C. When the two spheres are 50 cm apart, each sphere is repelled from the other by a force of magnitude 2.0 N. Determine the magnitude of the smaller of the two charges. a. 1.4 C b. 1.1 C c. 2.0 C d. 3.3 C e. 17 C ANS: A
PTS: 3
DIF: Challenging
2. A particle (charge = +40 C) is located on the x axis at the point x = 20 cm, and a second particle (charge = 50 C) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = 4.0 C) placed at the origin (x = 0)? a. 41 N b. 16 N c. 56 N d. 35 N e. 72 N ANS: C
PTS: 2
DIF: Average
3. In the figure, if Q = 30 C, q = 5.0 C, and d = 30 cm, what is the magnitude of the electrostatic force on q?
a. b. c. d. e.
15 N 23 N zero 7.5 N 38 N
ANS: D
PTS: 2
DIF: Average
4. A charge of +80 C is placed on the x axis at x = 0. A second charge of 50 C is placed on the x axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 C placed on the x axis at x = 30 cm? a. 13 N b. 77 N c. 39 N d. 25 N e. 45 N ANS: B
PTS: 2
DIF: Average
5. Three point charges are positioned on the x axis. If the charges and corresponding positions are +32 C at x = 0, +20 C at x = 40 cm, and 60 C at x = 60 cm, what is the magnitude of the electrostatic force on the +32-C charge? a. 84 N b. 12 N c. 36 N d. 50 N e. 48 N ANS: B
PTS: 2
DIF: Average
6. A particle (m = 50 g, q = 5.0 C) is released from rest when it is 50 cm from a second particle (Q = 20 C). Determine the magnitude of the initial acceleration of the 50-g particle. a. 54 m/s2 b. 90 m/s2 c. 72 m/s2 d. 65 m/s2 e. 36 m/s2 ANS: C
PTS: 2
DIF: Average
7. A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, Q, is placed at x = 3.0 m. If Q = 40 C, what is the magnitude of the electrostatic force on a 30-C charge placed at the origin? a. 7.2 N b. 3.9 N c. 1.5 N d. 14 N e. 8.1 N ANS: C
PTS: 2
DIF: Average
8. A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, Q, is placed at x = 1.0 m. If Q = 60 C, what is the magnitude of the electrostatic force on a 40-C charge placed at the origin? a. 16 N b. 27 N c. 32 N d. 11 N e. 3.0 N ANS: B
PTS: 2
DIF: Average
9. A point charge Q is placed on the x axis at the origin. An identical point charge is placed on the x axis at x = 1.0 m and another at x = +1.0 m. If Q = 40 C, what is the magnitude of the electrostatic force on the charge at x = +1.0 m? a. 29 N b. 14 N c. 11 N d. 18 N e. 7.0 N ANS: D
PTS: 2
DIF: Average
10. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 36 nC in the figure, what is the magnitude of the electric force on q?
a. b. c. d. e.
5.0 N 4.4 N 3.8 N 5.7 N 0.60 N
ANS: C
PTS: 2
DIF: Average
11. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 30 nC in the figure, what is the magnitude of the electric force on q?
a. b. c. d. e.
1.4 N 1.0 N 1.7 N 2.0 N 0.50 N
ANS: B
PTS: 2
DIF: Average
12. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 24 nC in the figure, what is the magnitude of the electric force on q?
a. b. c. d. e.
2.7 N 1.9 N 2.3 N 1.5 N 0.52 N
ANS: D
PTS: 2
DIF: Average
13. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 32 nC in the figure, what is the magnitude of the electric force on q?
a. b. c. d. e.
1.6 N 1.3 N 1.9 N 2.2 N 0.040 N
ANS: B
PTS: 2
DIF: Average
14. Three point charges, two positive and one negative, each having a magnitude of 20 C are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on the negative charge? a. 80 N b. 40 N c. 69 N d. 57 N e. 75 N ANS: C
PTS: 2
DIF: Average
15. Three point charges, two positive and one negative, each having a magnitude of 20 C are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on one of the positive charges? a. 69 N b. 40 N c. 80 N d. 57 N e. 20 N ANS: B
PTS: 2
DIF: Average
16. A point charge Q is placed at the origin. A second charge, 2Q, is placed on the x axis at x = 3.0 m. If Q = 50 C, what is the magnitude of the electrostatic force on a third point charge, Q, placed on the y axis at y = +4.0 m? a. 2.5 N b. 3.0 N c. 3.7 N d. 4.4 N e. 1.8 N ANS: B
PTS: 3
DIF: Challenging
17. Three identical point charges Q are placed at the vertices of an equilateral triangle (length of each side = 2.0 m). If Q = 60 C, what is the magnitude of the electrostatic force on any one of the charges? a. 25 N
b. c. d. e.
19 N 14 N 22 N 16 N
ANS: C
PTS: 2
DIF: Average
18. Identical point charges Q are placed at each of the four corners of a 3.0 m 4.0 m rectangle. If Q = 40 C, what is the magnitude of the electrostatic force on any one of the charges? a. 3.0 N b. 2.4 N c. 1.8 N d. 3.7 N e. 2.0 N ANS: B
PTS: 3
DIF: Challenging
19. A point charge (5.0 C) is placed on the x axis at x = 4.0 cm, and a second charge (+5.0 C) is placed on the x axis at x = 4.0 cm. What is the magnitude of the electric force on a third charge (+2.5 C) placed on the y axis at y = 3.0 cm? a. 90 N b. 45 N c. 54 N d. 72 N e. 36 N ANS: D
PTS: 2
DIF: Average
20. If Q = 25 C, q = 10 C, and L = 40 cm in the figure, what is the magnitude of the electrostatic force on q?
a. b. c. d. e.
28 N 22 N 20 N 14 N 10 N
ANS: C
PTS: 2
DIF: Average
21. If Q = 20 C and L = 60 cm, what is the magnitude of the electrostatic force on any one of the charges shown?
a. b. c. d. e.
25 N 19 N 15 N 9.1 N 14 N
ANS: D
PTS: 3
DIF: Challenging
22. If a = 60 cm, b = 80 cm, Q = 4.0 nC, and q = 1.5 nC, what is the magnitude of the electric field at point P?
a. b. c. d. e.
68 N/C 72 N/C 77 N/C 82 N/C 120 N/C
ANS: A
PTS: 2
DIF: Average
23. If a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 4.0 nC, what is the magnitude of the electric field at point P?
a. b. c. d.
35 N/C 42 N/C 52 N/C 64 N/C
e. 104 N/C ANS: A
PTS: 2
DIF: Average
24. If a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 6.0 nC, what is the magnitude of the electric field at point P in the figure?
a. b. c. d. e.
65 N/C 55 N/C 60 N/C 52 N/C 67 N/C
ANS: D
PTS: 2
DIF: Average
25. If a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 3.0 nC in the figure, what is the magnitude of the electric field at point P?
a. b. c. d. e.
71 N/C 56 N/C 60 N/C 53 N/C 67 N/C
ANS: D
PTS: 2
DIF: Average
26. If Q = 16 nC, a = 3.0 m, and b = 4.0 m, what is the magnitude of the electric field at point P?
a. b. c. d. e.
33 N/C 31 N/C 24 N/C 19 N/C 13 N/C
ANS: C
PTS: 2
DIF: Average
27. If Q = 80 nC, a = 3.0 m, and b = 4.0 m in the figure, what is the magnitude of the electric field at point P?
a. b. c. d. e.
45 N/C 70 N/C 29 N/C 47 N/C 92 N/C
ANS: D
PTS: 2
DIF: Average
28. A +2.0-nC point charge is placed at one corner of a square (1.5 m on a side), and a 3.0-nC charge is placed on a corner diagonally away from the first charge. What is the magnitude of the electric field at either of the two unoccupied corners? a. 20 N/C b. 14 N/C c. 4.0 N/C d. 12 N/C e. 8.0 N/C ANS: B
PTS: 2
DIF: Average
29. A +15-nC point charge is placed on the x axis at x = 1.5 m, and a 20-nC charge is placed on the y axis at y = 2.0m. What is the magnitude of the electric field at the origin?
a. b. c. d. e.
105 N/C 15 N/C 75 N/C 45 N/C 60 N/C
ANS: C
PTS: 2
DIF: Average
30. A +20-nC point charge is placed on the x axis at x = 2.0 m, and a 25-nC point charge is placed on the y axis at y = 3.0 m. What is the direction of the electric field at the origin? a. 209 b. 61 c. 29 d. 241 e. 151 ANS: A
PTS: 2
DIF: Average
31. A charge Q is placed on the x axis at x = +4.0 m. A second charge q is located at the origin. If Q = +75 nC and q = 8.0 nC, what is the magnitude of the electric field on the y axis at y = +3.0 m? a. 19 N/C b. 23 N/C c. 32 N/C d. 35 N/C e. 21 N/C ANS: B
PTS: 3
DIF: Challenging
32. A 40-C charge is positioned on the x axis at x = 4.0 cm. Where should a 60-C charge be placed to produce a net electric field of zero at the origin? a. 5.3 cm b. 5.7 cm c. 4.9 cm d. 6.0 cm e. +6.0 cm ANS: C
PTS: 2
DIF: Average
33. A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m. a. 30 N/C b. 15 N/C c. 48 N/C d. 90 N/C e. 60 N/C ANS: B
PTS: 3
DIF: Challenging
34. A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m. a. 81 N/C b. 74 N/C c. 61 N/C d. 88 N/C e. 20 N/C
ANS: C
PTS: 2
DIF: Average
35. A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle. What is the magnitude of the electric field at the center of the circle along which the arc lies? a. 81 N/C b. 61 N/C c. 71 N/C d. 51 N/C e. 25 N/C ANS: D
PTS: 3
DIF: Challenging
36. Charge of uniform density 4.0 nC/m is distributed along the x axis from x = 2.0 m to x = +3.0 m. What is the magnitude of the electric field at the point x = +5.0 m on the x axis? a. 16 N/C b. 13 N/C c. 19 N/C d. 26 N/C e. 5.0 N/C ANS: B
PTS: 2
DIF: Average
37. A uniformly charged rod (length = 2.0 m, charge per unit length = 5.0 nC/m) is bent to form one quadrant of a circle. What is the magnitude of the electric field at the center of the circle? a. 62 N/C b. 56 N/C c. 50 N/C d. 44 N/C e. 25 N/C ANS: C
PTS: 3
DIF: Challenging
38. A uniformly charged rod (length = 2.0 m, charge per unit length = 3.0 nC/m) is bent to form a semicircle. What is the magnitude of the electric field at the center of the circle? a. 64 N/C b. 133 N/C c. 48 N/C d. 85 N/C e. 34 N/C ANS: D
PTS: 3
DIF: Challenging
39. A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +10 m on the x axis? a. b. c.
d. e. none of these ANS: A
PTS: 2
DIF: Average
40. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the y component of the electric field at y = 4 m on the y axis? a. b. c. d. e. none of these ANS: A
PTS: 2
DIF: Average
41. A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis? a. b. c. d. e. none of these ANS: B
PTS: 2
DIF: Average
42. A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = 3 m to y = 2m. Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis? a. b. c. d. e. none of these
ANS: A
PTS: 2
DIF: Average
43. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis? a. b. c. d. e. none of these ANS: A
PTS: 3
DIF: Challenging
44. A rod (length = 2.0 m) is uniformly charged and has a total charge of 40 nC. What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod? a. 40 N/C b. 45 N/C c. 24 N/C d. 90 N/C e. 36 N/C ANS: B
PTS: 2
DIF: Average
45. A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m. What is the magnitude of the electric field at the origin? a. 18 N/C b. 50 N/C c. 30 N/C d. 15 N/C e. 90 N/C ANS: C
PTS: 2
DIF: Average
46. A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +8 m on the x axis? a. b. c. d. e. none of these ANS: A
PTS: 2
DIF: Average
47. A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y = 5 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at y = 0 on the y axis? a. b. c. d. e. none of these ANS: A
PTS: 2
DIF: Average
48. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. What is the x component of the electric field at y = 2 m on the y axis? a. 5.0 N/C b. 4.0 N/C c. 5.7 N/C d. 6.2 N/C e. 9.0 N/C ANS: B
PTS: 3
DIF: Challenging
49. A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vx = 80 m/s, vy = vz = 0, what is the speed of the particle at t = 2.0 s? a. 40 m/s b. 20 m/s c. 60 m/s d. 80 m/s e. 180 m/s ANS: B
PTS: 2
DIF: Average
50. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vy = 50 m/s, vx = vz = 0, what is the speed of the particle at t = 2.0 s? a. 81 m/s b. 72 m/s c. 64 m/s d. 89 m/s e. 25 m/s ANS: C
PTS: 2
DIF: Average
51. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 5.5 N/C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and vx = 50 m/s, vy = vz = 0, what is the distance from the origin to the particle at t = 2.0 s? a. 60 m b. 28 m c. 44 m d. 12 m e. 88 m ANS: D
PTS: 2
DIF: Average
52. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.3 N/C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and vz = 20 m/s, vx = vy = 0, what is the distance from the origin to the particle at t = 2.0 s? a. 60 m b. 54 m c. 69 m d. 78 m e. 3.2 m ANS: B
PTS: 2
DIF: Average
53. A particle (q = 3.0 mC, m = 20 g) has a speed of 20 m/s when it enters a region where the electric field has a constant magnitude of 80 N/C and a direction which is the same as the velocity of the particle. What is the speed of the particle 3.0 s after it enters this region? a. 68 m/s b. 44 m/s c. 56 m/s d. 80 m/s e. 36 m/s ANS: C
PTS: 2
DIF: Average
54. A particle (q = 4.0 mC, m = 50 g) has a velocity of 25 m/s in the positive x direction when it first enters a region where the electric field is uniform (60 N/C in the positive y direction). What is the speed of the particle 5.0 s after it enters this region? a. 49 m/s b. 35 m/s c. 32 m/s d. 44 m/s e. 24 m/s ANS: B
PTS: 2
DIF: Average
55. A charge of 50-C is placed on the y axis at y = 3.0 cm and a 77-C charge is placed on the x axis at x = 4.0 cm. If both charges are held fixed, what is the magnitude of the initial acceleration of an electron released from rest at the origin? a. 1.2 1020 m/s2 b. 1.5 1020 m/s2 c. 1.0 1020 m/s2 d. 1.8 1020 m/s2 e. 2.0 1020 m/s2
ANS: A
PTS: 3
DIF: Challenging
56. The velocity of a particle (m = 10 mg, q = 4.0 C) at t = 0 is 20 m/s in the positive x direction. If the particle moves in a uniform electric field of 20 N/C in the positive x direction, what is the particle's speed at t = 5.0 s? a. 60 m/s b. 20 m/s c. 45 m/s d. 40 m/s e. 70 m/s ANS: B
PTS: 2
DIF: Average
57. A particle (m = 20 mg, q = 5.0 C) moves in a uniform electric field of 60 N/C in the positive x direction. At t = 0, the particle is moving 25 m/s in the positive x direction and is passing through the origin. How far is the particle from the origin at t = 2.0 s? a. 80 m b. 20 m c. 58 m d. 10 m e. 30 m ANS: B
PTS: 2
DIF: Average
58. A particle (m = 20 mg, q = 5.0 C) moves in a uniform electric field of 60 N/C in the positive x direction. At t = 0, the particle is moving 30 m/s in the positive x direction and is passing through the origin. Determine the maximum distance beyond x = 0 the particle travels in the positive x direction. a. 25 m b. 20 m c. 15 m d. 30 m e. 60 m ANS: D
PTS: 2
DIF: Average
59. Charge Q is distributed uniformly along a semicircle of radius a. Which formula below gives the correct magnitude of the electric field at the center of the circle? a. . b. c.
. .
d. e.
ANS: D
. . PTS: 2
DIF: Average
60. Charge Q is distributed uniformly along a semicircle of radius a. Which formula below gives the correct magnitude of the force on a particle of charge q located at the center of the circle?
a. b. c. d. e.
. . . . .
ANS: D
PTS: 2
DIF: Average
61. Charge Q is uniformly distributed over a line segment of length 2L, as shown below. When the xcoordinate of point P is x, the magnitude of the y-component of the electric field at point P is
a. 0. b. c. d. e.
ANS: A
. . . . PTS: 1
DIF: Easy
62. When gravitational, magnetic and any forces other than static electric forces are not present, electric field lines in the space surrounding a charge distribution show a. the directions of the forces that exist in space at all times. b. only the directions in which static charges would accelerate when at points on those lines c. only the directions in which moving charges would accelerate when at points on those lines. d. tangents to the directions in which either static or moving charges would accelerate when passing through points on those lines. e. the paths static or moving charges would take. ANS: D
PTS: 1
DIF: Easy
63. When a positive charge q is placed in the field created by two other charges Q1 and Q2, each a distance r away from q, the acceleration of q is a. in the direction of the charge Q1 or Q2 of smaller magnitude. b. in the direction of the charge Q1 or Q2 of greater magnitude. c. in the direction of the negative charge if Q1 and Q2 are of opposite sign. d. in the direction of the positive charge if Q1 and Q2 are of opposite sign. e. in a direction determined by the vector sum of the electric fields of Q1 and Q2. ANS: E
PTS: 1
DIF: Easy
64. Two charged particles, Q1 and Q2, are a distance r apart with Q2 = 5Q1. Compare the forces they exert on one another when is the force Q2 exerts on Q1 and is the force Q1 exerts on Q2. a. =5 . b.
= 5
c.
=
d.
=
.
=
.
e. 5 ANS: D
. .
PTS: 1
DIF: Easy
65. Rubber rods charged by rubbing with cat fur repel each other. Glass rods charged by rubbing with silk repel each other. A rubber rod and a glass rod charged respectively as above attract each other. A possible explanation is that a. Any two rubber rods charged this way have opposite charges on them. b. Any two glass rods charged this way have opposite charges on them. c. A rubber rod and a glass rod charged this way have opposite charges on them. d. All rubber rods always have an excess of positive charge on them. e. All glass rods always have an excess of negative charge on them. ANS: C
PTS: 1
DIF: Easy
66. Which one of the diagrams below is not a possible electric field configuration for a region of space which does not contain any charges? a. b. c. d. e.
ANS: D
PTS: 1
DIF: Easy
67. A positively charged particle is moving in the +y-direction when it enters a region with a uniform electric field pointing in the +x-direction. Which of the diagrams below shows its path while it is in the region where the electric field exists. The region with the field is the region between the plates bounding each figure. The field lines always point to the right. The x-direction is to the right; the ydirection is up. a. b. c. d. e.
ANS: D
PTS: 1
DIF: Easy
68. A negatively charged particle is moving in the +x-direction when it enters a region with a uniform electric field pointing in the +x-direction. Which graph gives its position as a function of time correctly? (Its initial position is x = 0 at t = 0.) a. b. c. d. e.
ANS: C 69. The symbol a. b. c. d. e.
PTS: 1
DIF: Easy
appears in Coulomb's law because we use independently defined units for
force and distance. charge and distance. distance and force. force, distance and electric charge. charge.
ANS: D
PTS: 1
DIF: Easy
70. Three pith balls supported by insulating threads hang from a support. We know that ball X is positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that a. Y has a negative charge. b. Z has a negative charge. c. Y has a positive charge. d. Z has a positive charge. e. Z is neutral (has no net charge.) ANS: D
PTS: 1
DIF: Easy
71. Three pith balls supported by insulating threads hang from a support. We know that ball X is positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that a. Y has a negative charge. b. Z has a negative charge. c. Y has a positive charge. d. Z is neutral (has no net charge.) e. Y is negatively charged or neutral (has no net charge.) ANS: E
PTS: 1
DIF: Easy
72. Two identical pith balls supported by insulating threads hang side by side and close together, as shown below.
One is positively charged; the other is neutral. We can conclude that a. all field lines leaving the positively charged pith ball end on the neutral pith ball.
b. c. d. e.
some of the field lines leaving the positively charged pith ball end on the neutral pith ball. none of the field lines leaving the positively charged pith ball end on the neutral pith ball. positive charge is transferred along the field lines until both balls have equal charges. positive charge is transferred along the field lines until both balls hang along vertical lines.
ANS: B
PTS: 1
DIF: Easy
73. Two imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the concentric spheres. When compared to the number of field lines N1 going through the sphere of radius R, the number of electric field lines N2 going through the sphere of radius 2R is a. . b.
.
c. N2 = N1. d. N2 = 2N1. e. N2 = 4N1. ANS: C
PTS: 1
DIF: Easy
74. Two tiny metal spheres are fixed to the ends of a non-conducting string of length . Equal charges, +q, are placed on the metal spheres. Randall says that the force on the string has magnitude Tilden says that the tension in the string has magnitude
.
. Which one, if either, is correct?
a. Randall, because both charges exert forces on the string, but the tension is
.
Tilden, because both charges exert forces on the string, but the net force is
.
b. c. Both are correct, because both charges exert forces on the string. d. Neither is correct, because both the tension and the force have magnitude
.
e. Neither is correct, because the tension is ANS: E
PTS: 1
, but the net force is 0. DIF: Easy
75. Enrico says that positive charge is created when you rub a glass rod with silk, and that negative charge is simply the absence of positive charge. Rosetta says that negative charge is created and that positive charge is the absence of positive charge. (She has heard that Ben Franklin should have reversed the signs he associated with the charges.) Which one, if either, is correct? a. Enrico, because there really is only one kind of charge. b. Rosetta, because there really is only one kind of charge. c. Neither: although no charge is present originally, both types of charge are created through friction. d. Both: only one type of charge is created by friction at any one time. e. Neither: both negative and positive charge are present simultaneously in all solid materials on Earth and the process described involves a transfer of charge, not the creation of charge.
ANS: E
PTS: 1
DIF: Easy
76. Three 2.50 C charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120 angles as shown below. The magnitude, in N, of the force on any one of the charges is
a. b. c. d. e.
1.88 102. 3.25 102. 3.73 102. 6.50 102. 7.50 102.
ANS: B
PTS: 3
DIF: Challenging
77. Three 2.50 C charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120 angles as shown below. The magnitude, in N, of the tension in any one of the strings is
a. b. c. d. e.
1.88 102. 3.25 102. 3.75 102. 6.50 102. 7.50 102.
ANS: B
PTS: 3
DIF: Challenging
78. Three 2.50 C charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120 angles as shown below. The magnitude, in N, of the force on the knot at the center is
a. b. c. d. e.
0. 3.75 102. 5.63 102. 6.50 102. 7.50 102.
ANS: A
PTS: 1
DIF: Easy
79. Suppose a uniform electric field of 4 N/C is in the positive x direction. When a charge is placed at and fixed to the origin, the resulting electric field on the x axis at x = 2 m becomes zero. What is the magnitude of the electric field at x = 4 m on the x axis at this time? a. 0 b. 1 N/C c. 2 N/C d. 4 N/C e. More information is needed to find the resulting field magnitude at this position. ANS: C
PTS: 2
DIF: Average
80. In a diagram of charges and electric field lines charge has twelve field lines going outward from it and charge has three field lines going into it. If one of the charges is 100 nC, what is the other one? a. 25 nC b. 100 nC c. –25 nC d. –100 nC e. Both answers b and c can be correct. ANS: C
PTS: 1
DIF: Easy
81. Two uniform rods, each of length 2.0 m, are bent to form semicircles. One rod has a charger per unit lent of 1.5 nC/m, and the other has a charge per unit length of –1.5 nC/m. The semicircles are joined to make a circle. What is the magnitude of the electric field at the center of the circle? a. 42 N/C b. 84 N/C c. 34 N/C d. 68 N/C e. 0 ANS: B
PTS: 3
DIF: Challenging
PROBLEM 82. The electron gun in a television tube accelerates electrons (mass = 9.11 1031 kg, charge = 1.60 1019 C) from rest to 3.00 107 m/s within a distance of 2.00 cm. What electric field is required?
ANS: 128 000 N/C PTS: 2
DIF: Average
83. An alpha particle (charge = +2e) is sent at high speed toward a gold nucleus (charge +79e). What is the electrical force acting on the alpha particle when it is at a distance of 2 1014 m away from the gold nucleus? (e = 1.6 1019 C) ANS: 91 N PTS: 2
DIF: Average
84. A proton moving at 3 104 m/s is projected at an angle of 30 above a horizontal plane. If an electric field of 400 N/C is directed downwards, how long does it take the proton to return to the horizontal plane? (HINT: Ignore gravity.) [mProton = 1.67 1027 kg, qProton = +1.6 1019 C.] ANS: 7.8 107 s PTS: 2
DIF: Average
85. Imagine for a minute that the Moon is held in its orbit about the Earth by electrical forces rather than by gravitation. What electrical charges Q on the Earth and +Q on the Moon are necessary to hold the Moon in a circular orbit with a period of 27.3 days? The Earth-Moon distance is 384 000 km and the mass of the Moon is 7.35 1022 kg. ANS: Q = 5.73 1013 C PTS: 3
DIF: Challenging
Chapter 24—Gauss's Law MULTIPLE CHOICE 1. Two charges of 15 pC and 40 pC are inside a cube with sides that are of 0.40-m length. Determine the net electric flux through the surface of the cube. a. +2.8 N m2/C b. 1.1 N m2/C c. +1.1 N m2/C d. 2.8 N m2/C e. 0.47 N m2/C ANS: D
PTS: 2
DIF: Average
2. The total electric flux through a closed cylindrical (length = 1.2 m, diameter = 0.20 m) surface is equal to 5.0 N m2/C. Determine the net charge within the cylinder. a. 62 pC b. 53 pC c. 44 pC
d. 71 pC e. 16 pC ANS: C
PTS: 2
DIF: Average
3. Charges q and Q are placed on the x axis at x = 0 and x = 2.0 m, respectively. If q = 40 pC and Q = +30 pC, determine the net flux through a spherical surface (radius = 1.0 m) centered on the origin. a. 9.6 N m2/C b. 6.8 N m2/C c. 8.5 N m2/C d. 4.5 N m2/C e. 1.1 N m2/C ANS: D
PTS: 2
DIF: Average
4. A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin. Determine the electric flux through this surface. a. 68 N m2/C b. 62 N m2/C c. 45 N m2/C d. 79 N m2/C e. 23 N m2/C ANS: C
PTS: 2
DIF: Average
5. A uniform charge density of 500 nC/m3 is distributed throughout a spherical volume (radius = 16 cm). Consider a cubical (4.0 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface. a. 7.1 N m2/C b. 3.6 N m2/C c. 12 N m2/C d. 19 N m2/C e. 970 N m2/C ANS: B
PTS: 2
DIF: Average
6. A point charge +Q is located on the x axis at x = a, and a second point charge Q is located on the x axis at x = a. A Gaussian surface with radius r = 2a is centered at the origin. The flux through this Gaussian surface is a. zero because the negative flux over one hemisphere is equal to the positive flux over the other. b. greater than zero. c. zero because at every point on the surface the electric field has no component perpendicular to the surface. d. zero because the electric field is zero at every point on the surface. e. none of the above. ANS: A
PTS: 1
DIF: Easy
7. The xy plane is "painted" with a uniform surface charge density which is equal to 40 nC/m2. Consider a spherical surface with a 4.0-cm radius that has a point in the xy plane as its center. What is the electric flux through that part of the spherical surface for which z > 0? a. 14 N m2/C b. 11 N m2/C
c. 17 N m2/C d. 20 N m2/C e. 23 N m2/C ANS: B
PTS: 2
DIF: Average
8. A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a uniform charge density of 1.3 C/m3. Determine the electric flux through a spherical surface (radius = 2.0 cm) which has a point on the axis of the cylinder as its center. a. 5.7 N m2/C b. 4.9 N m2/C c. 6.4 N m2/C d. 7.2 N m2/C e. 15 N m2/C ANS: B
PTS: 2
DIF: Average
9. Charge of uniform surface density (4.0 nC/m2) is distributed on a spherical surface (radius = 2.0 cm). What is the total electric flux through a concentric spherical surface with a radius of 4.0 cm? a. 2.8 N m2/C b. 1.7 N m2/C c. 2.3 N m2/C d. 4.0 N m2/C e. 9.1 N m2/C ANS: C
PTS: 2
DIF: Average
10. A charge of uniform volume density (40 nC/m3) fills a cube with 8.0-cm edges. What is the total electric flux through the surface of this cube? a. 2.9 N m2/C b. 2.0 N m2/C c. 2.6 N m2/C d. 2.3 N m2/C e. 1.8 N m2/C ANS: D
PTS: 2
DIF: Average
11. A charge of 0.80 nC is placed at the center of a cube that measures 4.0 m along each edge. What is the electric flux through one face of the cube? a. 90 N m2/C b. 15 N m2/C c. 45 N m2/C d. 23 N m2/C e. 64 N m2/C ANS: B
PTS: 2
DIF: Average
12. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface? a. R2E b. 4R2E/3 c. 2R2E/3 d. R2E/2
e. R2E/3 ANS: A
PTS: 1
DIF: Easy
13. The electric field in the region of space shown is given by N/C where y is in m. What is the magnitude of the electric flux through the top face of the cube shown?
a. b. c. d. e.
90 N m2/C 6.0 N m2/C 54 N m2/C 12 N m2/C 126 N m2/C
ANS: C
PTS: 2
DIF: Average
14. Charge of uniform surface density (0.20 nC/m2) is distributed over the entire xy plane. Determine the magnitude of the electric field at any point having z = 2.0 m. a. 17 N/C b. 11 N/C c. 23 N/C d. 28 N/C e. 40 N/C ANS: B
PTS: 2
DIF: Average
15. Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m2 and 0.60 nC/m2. What is the magnitude of the electric field at a point between the two surfaces? a. 34 N/C b. 23 N/C c. 45 N/C d. 17 N/C e. 90 N/C ANS: C
PTS: 2
DIF: Average
16. Two infinite, uniformly charged, flat surfaces are mutually perpendicular. One of the sheets has a charge density of +60 pC/m2, and the other carries a charge density of 80 pC/m2. What is the magnitude of the electric field at any point not on either surface? a. 1.1 N/C b. 5.6 N/C c. 7.9 N/C
d. 3.8 N/C e. 4.0 N/C ANS: B
PTS: 2
DIF: Average
17. Charge of a uniform density (8.0 nC/m2) is distributed over the entire xy plane. A charge of uniform density (3.0 nC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m. a. 0.79 kN/C b. 0.17 kN/C c. 0.62 kN/C d. 0.34 kN/C e. 0.28 kN/C ANS: C
PTS: 2
DIF: Average
18. Charge of a uniform density (8.0 nC/m2) is distributed over the entire xy plane. A charge of uniform density (5.0 nC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 1.0 m. a. 0.45 kN/C b. 0.17 kN/C c. 0.28 kN/C d. 0.73 kN/C e. 0.62 kN/C ANS: B
PTS: 2
DIF: Average
19. Charge of uniform density (0.30 nC/m2) is distributed over the xy plane, and charge of uniform density (0.40 nC/m2) is distributed over the yz plane. What is the magnitude of the resulting electric field at any point not in either of the two charged planes? a. 40 N/C b. 34 N/C c. 28 N/C d. 46 N/C e. 6.0 N/C ANS: C
PTS: 2
DIF: Average
20. A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m3) distributed throughout its column. Determine the magnitude of the electric field 5.0 cm from the axis of the cylinder. a. 25 N/C b. 20 N/C c. 14 N/C d. 31 N/C e. 34 N/C ANS: C
PTS: 2
DIF: Average
21. A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m3) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the axis of the cylinder. a. 20 N/C b. 27 N/C c. 16 N/C
d. 12 N/C e. 54 N/C ANS: B
PTS: 2
DIF: Average
22. Each 2.0-m length of a long cylinder (radius = 4.0 mm) has a charge of 4.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point 5.0 mm from the axis of the cylinder? a. 9.9 kN/C b. 8.1 kN/C c. 9.0 kN/C d. 7.2 kN/C e. 18 kN/C ANS: D
PTS: 2
DIF: Average
23. A long nonconducting cylinder (radius = 6.0 mm) has a nonuniform volume charge density given by r2, where = 6.2 mC/m5 and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis? a. 1.4 N/C b. 1.6 N/C c. 1.8 N/C d. 2.0 N/C e. 5.4 N/C ANS: A
PTS: 3
DIF: Challenging
24. A long cylindrical shell (radius = 2.0 cm) has a charge uniformly distributed on its surface. If the magnitude of the electric field at a point 8.0 cm radially outward from the axis of the shell is 85 N/C, how much charge is distributed on a 2.0-m length of the charged cylindrical surface? a. 0.38 nC b. 0.76 nC c. 0.19 nC d. 0.57 nC e. 0.98 nC ANS: B
PTS: 2
DIF: Average
25. Charge of uniform linear density (4.0 nC/m) is distributed along the entire x axis. Determine the magnitude of the electric field on the y axis at y = 2.5 m. a. 36 N/C b. 29 N/C c. 43 N/C d. 50 N/C e. 58 N/C ANS: B
PTS: 2
DIF: Average
26. Charge of uniform density (80 nC/m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 2.0 mm from the symmetry axis. a. 7.9 N/C b. 9.0 N/C c. 5.9 N/C d. 6.8 N/C
e. 18 N/C ANS: D
PTS: 3
DIF: Challenging
27. Charge of uniform density (80 nC/m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 4.0 mm from the symmetry axis. a. 7.9 N/C b. 10 N/C c. 9.0 N/C d. 8.9 N/C e. 17 N/C ANS: C
PTS: 3
DIF: Challenging
28. Charge of uniform density (20 nC/m2) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of 12 nC/m2. Determine the magnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces. a. 2.3 kN/C b. 1.1 kN/C c. 1.7 kN/C d. 3.4 kN/C e. 4.5 kN/C ANS: B
PTS: 3
DIF: Challenging
29. Charge of uniform density (20 nC/m2) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of 12 nC/m2. Determine the magnitude of the electric field at a point 4.0 cm from the symmetry axis of the two surfaces. a. 0.45 kN/C b. 1.0 kN/C c. 0.73 kN/C d. 0.56 kN/C e. 2.3 kN/C ANS: A
PTS: 3
DIF: Challenging
30. Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m2. What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces? a. 3.8 N/C b. 4.1 N/C c. 3.5 N/C d. 3.2 N/C e. 0.28 N/C ANS: B
PTS: 3
DIF: Challenging
31. A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m3) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the center of the sphere. a. 22 N/C b. 49 N/C c. 31 N/C d. 87 N/C
e. 26 N/C ANS: D
PTS: 2
DIF: Average
32. A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of 8.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere? a. 1.8 105 N/C b. 9.0 104 N/C c. 3.6 105 N/C d. 2.7 105 N/C e. 7.2 105 N/C ANS: C
PTS: 2
DIF: Average
33. A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of 2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces. a. 30 N/C b. 50 N/C c. 40 N/C d. 20 N/C e. 70 N/C ANS: B
PTS: 2
DIF: Average
34. A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of 3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces. a. 14 N/C b. 11 N/C c. 22 N/C d. 18 N/C e. 40 N/C ANS: D
PTS: 2
DIF: Average
35. A point charge (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm), and a charge of 3.0 pC is spread uniformly upon this surface. Determine the magnitude of the electric field 1.0 cm from the point charge. a. 0.72 kN/C b. 0.45 kN/C c. 0.63 kN/C d. 0.90 kN/C e. 0.18 kN/C ANS: B
PTS: 2
DIF: Average
36. Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m2. What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces? a. 1.1 N/C b. 4.5 N/C c. 1.4 N/C d. 5.6 N/C
e. 0.50 N/C ANS: A
PTS: 2
DIF: Average
37. A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm, outer radius = 4.0 cm) conducting sphere which has a net charge of 4.0 pC. Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge. a. 35 N/C b. 25 N/C c. 30 N/C d. 20 N/C e. 10 N/C ANS: D
PTS: 2
DIF: Average
38. The axis of a long hollow metallic cylinder (inner radius = 1.0 cm, outer radius = 2.0 cm) coincides with a long wire. The wire has a linear charge density of 8.0 pC/m, and the cylinder has a net charge per unit length of 4.0 pC/m. Determine the magnitude of the electric field 3.0 cm from the axis. a. 5.4 N/C b. 7.2 N/C c. 4.3 N/C d. 3.6 N/C e. 2.4 N/C ANS: B
PTS: 2
DIF: Average
39. A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m2. Determine the magnitude of the electric field 3.0 mm from the axis. a. 18 N/C b. 23 N/C c. 30 N/C d. 15 N/C e. 60 N/C ANS: C
PTS: 2
DIF: Average
40. If the electric field just outside a thin conducting sheet is equal to 1.5 N/C, determine the surface charge density on the conductor. a. 53 pC/m2 b. 27 pC/m2 c. 35 pC/m2 d. 13 pC/m2 e. 6.6 pC/m2 ANS: D
PTS: 2
DIF: Average
41. The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C. What is the charge density on the surface of the cylinder? a. 2.7 nC/m2 b. 1.8 nC/m2 c. 3.5 nC/m2 d. 4.4 nC/m2 e. 0.90 nC/m2 ANS: B
PTS: 2
DIF: Average
42. A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm, outer radius = 4.0 cm) which has a total charge of 3.0 pC. What is the magnitude of the electric field 2.0 cm from the center of these conductors? a. 23 N/C b. zero c. 45 N/C d. 90 N/C e. 110 N/C ANS: C
PTS: 2
DIF: Average
43. A long cylindrical conductor (radius = 1.0 mm) carries a charge density of 4.0 pC/m and is inside a coaxial, hollow, cylindrical conductor (inner radius = 3.0 mm, outer radius = 4.0 mm) that has a total charge of 8.0 pC/m. What is the magnitude of the electric field 2.0 mm from the axis of these conductors? a. 24 N/C b. 18 N/C c. zero d. 36 N/C e. 226 N/C ANS: D
PTS: 2
DIF: Average
44. The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has a magnitude of 500 N/C and is directed outward. An unknown charge Q is introduced into the center of the sphere and it is noted that the electric field is still directed outward but has decreased to 100 N/C. What is the magnitude of the charge Q? a. 1.5 nC b. 1.8 nC c. 1.3 nC d. 1.1 nC e. 2.7 nC ANS: B
PTS: 2
DIF: Average
45. A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm, outer radius = 2.0 cm) which has a net charge of 4.0 nC. Determine the resulting charge density on the inner surface of the conducting sphere. a. +4.8 C/m2 b. 4.8 C/m2 c. 9.5 C/m2 d. +9.5 C/m2 e. 8.0 C/m2 ANS: B
PTS: 2
DIF: Average
46. An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station. Which statement is correct? a. The astronaut must abandon the chamber immediately to avoid being electrocuted. b. The astronaut will be safe only if she is wearing a spacesuit made of non-conducting materials. c. The astronaut does not need to worry: the charge will remain on the outside surface. d. The astronaut must abandon the chamber if the electric field on the outside surface
becomes greater than the breakdown field of air. e. The astronaut must abandon the chamber immediately because the electric field inside the chamber is non-uniform. ANS: C
PTS: 1
DIF: Easy
47. A small metal sphere is suspended from the conducting cover of a conducting metal ice bucket by a non-conducting thread. The sphere is given a negative charge before the cover is placed on the bucket. The bucket is tilted by means of a non-conducting material so that the charged sphere touches the inside of the bucket. Which statement is correct? a. The negative charge remains on the metal sphere. b. The negative charge spreads over the outside surface of the bucket and cover. c. The negative charge spreads over the inside surface of the bucket and cover. d. The negative charge spreads equally over the inside and outside surfaces of the bucket and cover. e. The negative charge spreads equally over the sphere and the inside and outside surfaces of the bucket and cover. ANS: B
PTS: 1
DIF: Easy
48. A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown. Where is the induced charge density greatest in magnitude and what is its sign?
a. b. c. d. e.
A; negative. A; positive. B; negative. B; positive. C; negative.
ANS: A
PTS: 1
DIF: Easy
49. A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground. The outside of the sphere is then grounded as shown. Then the ground wire is removed. A is the inner surface and B is the outer surface. Which statement is correct?
a. The charge on A is q; that on B is +q. b. The charge on B is q; that on A is +q. c. The charge is on A and on B. d. There is no charge on either A or B. e. The charge on A is q; there is no charge on B.
ANS: E
PTS: 1
DIF: Easy
50. An uncharged metal sphere is placed on an insulating puck on a frictionless table. While being held parallel to the table, a rod with a charge q is brought close to the sphere, but does not touch it. As the rod is brought in, the sphere a. remains at rest. b. moves toward the rod. c. moves away from the rod. d. moves perpendicular to the velocity vector of the rod. e. moves upward off the puck. ANS: B
PTS: 1
DIF: Easy
51. Three originally uncharged infinite parallel planes are arranged as shown. Then the upper plate has surface charge density placed on it while the lower plate receives surface charge density . The net charge induced on the center plate is
a. b. c. d. e.
0. /2. +/2. . +.
ANS: A
PTS: 1
DIF: Easy
52. Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces. When compared to the electric flux 1 through the surface of radius R, the electric flux 2 through the surface of radius 2R is a. . b.
.
c. 2 = 1. d. 2 = 21. e. 2 = 41. ANS: C
PTS: 1
DIF: Easy
53. Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces. When compared to the electric flux 1 through the surface of radius R, the electric flux 2 through the surface of radius 2R is a. . b. c. 2 = 1.
.
d. 2 = 21. e. 2 = 41. ANS: C
PTS: 1
DIF: Easy
54. When a cube is inscribed in a sphere of radius r, the length L of a side of the cube is
. If a
positive point charge Q is placed at the center of the spherical surface, the ratio of the electric flux sphere at the spherical surface to the flux cube at the surface of the cube is a. . b. . c. 1. d. . e.
.
ANS: C
PTS: 1
DIF: Easy
55. The electric flux through the two adjacent spherical surfaces shown below is known to be the same.
It is also known that there is no charge inside either spherical surface. We can conclude that a. there is no electric field present in this region of space. b. there is a constant E field present in this region of space. c. the electric flux has a constant value of zero. d. any of the above may be correct. e. only (a) and (b) above may be correct. ANS: D
PTS: 1
DIF: Easy
56. Which one of the following cannot be a statement of Gauss's Law for some physical situation? a. 4r20E = Q. b. 2rL0E = Q. c. . d.
.
e.
.
ANS: D
PTS: 1
DIF: Easy
57. Which one of the following is not an expression for electric charge? a.
b. c. d. e.
ANS: D
PTS: 1
DIF: Easy
58. An uncharged spherical conducting shell surrounds a charge q at the center of the shell. The charges on the inner and outer surfaces of the shell are respectively a. q, q. b. q, +q. c. +q, q. d. +q, +q. e. +q, 0. ANS: C
PTS: 1
DIF: Easy
59. An uncharged spherical conducting shell surrounds a charge q at the center of the shell. Then charge +3q is placed on the outside of the shell. When static equilibrium is reached, the charges on the inner and outer surfaces of the shell are respectively a. +q, q. b. q, +q. c. +q, +2q. d. +2q, +q. e. +3q, 0. ANS: C
PTS: 1
60. A constant electric field
DIF: Easy is present throughout a region of space that includes the plane
bounded by the x and y axes and the lines x = 30 cm and y = 50 cm. The electric flux through the plane's surface, in N m2/C, is a. 0. b. 0.25. c. 25. d. 50. e. 100. ANS: A
PTS: 1
61. A constant electric field
DIF: Easy is present throughout a region of space that includes the plane
bounded by the y and z axes and the lines y = 50 cm and z = 50 cm. The electric flux through the plane's surface, in N m2/C, is a. 0. b. 0.25. c. 25. d. 50.
e. 100. ANS: C
PTS: 2
DIF: Average
62. A spaceship encounters a single plane of charged particles, with the charge per unit area equal to . The electric field a short distance above the plane has magnitude ____ and is directed ____ to the plane. a. , parallel b. c. d. e.
, perpendicular , parallel , perpendicular , parallel
ANS: B
PTS: 1
63. You are told that to
DIF: Easy
summed over both the surface areas of sphere A and sphere B below totals
. You can conclude that
a. Sphere A contains charge qin = Q. b. Sphere B contains charge qin = Q. c. Sphere B contains charge qin = +Q. d. Each sphere contains charge
.
e. The sum of the charges contained in both spheres is Q. ANS: E
PTS: 1
DIF: Easy
64. If we define the gravitational field for gravity is a.
.
b.
.
c.
.
d.
.
e.
, where
.
is a unit radial vector, then Gauss's Law
ANS: C
PTS: 2
DIF: Average
65. Gino says that the analog of Gauss's law for the flow of an incompressible fluid of density at constant velocity is for an imaginary surface within the fluid. Lorenzo says that it is true only if the area where the fluid enters the surface and the area where it leaves the surface are both perpendicular to the velocity of the fluid. Which one, if either, is correct? a. Gino, because as much fluid leaves as enters. b. Lorenzo, because is not equal to zero if the fluid enters or exits at angles other than 90. c. Lorenzo, because this is true only when the fluid executes rotational motion. d. Gino, because it is true only when the fluid is enclosed on all sides, not when it is flowing. e. Lorenzo, because it is true only when the fluid is enclosed on all sides, not when it is flowing. ANS: A
PTS: 1
66. A beam of electrons moves at velocity
DIF: Easy . The number of particles per unit volume in the beam of
area A is . If we imagine a cylindrical Gaussian surface of radius r and length beam, the electron flux through the surface is a. 0. b. vfA. c. vfA. d. vf(A+2r ). e. vf(A+r ). ANS: A
PTS: 1
centered on the
DIF: Easy
67. A student has made the statement that the electric flux through one half of a Gaussian surface is always equal and opposite to the flux through the other half of the Gaussian surface. This is a. never true. b. never false. c. true whenever enclosed charge is symmetrically located at a center point, or on a center line or centrally placed plane. d. true whenever no charge is enclosed within the Gaussian surface. e. true only when no charge is enclosed within the Gaussian surface. ANS: E
PTS: 1
DIF: Easy
68. A student has made the statement that the electric flux through one half of a Gaussian surface is always equal to the flux through the other half of the Gaussian surface. This is a. never true. b. never false. c. true whenever enclosed charge is symmetrically located at a center point, on a center line, or on a centrally placed plane. d. true whenever no charge is enclosed within the Gaussian surface. e. true only when no charge is enclosed within the Gaussian surface. ANS: C
PTS: 1
DIF: Easy
69. Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in the region between the two planes has magnitude
. The electric field in the region to the left of A and
the electric field in the region to the right of B may have the magnitudes a. 0, 0. b. , . c.
,
.
d. given in any answer above. e. given only in answer (a) or (b) above. ANS: D
PTS: 2
DIF: Average
70. Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in region I to the left of plane A has magnitude right of B has magnitude planes has magnitude
and points to the left. The electric field in the region to the
and points to the right. The electric field in the region between the two and points to the right. The surface charge density on planes A and B
respectively is a. , . b.
,
c.
,
.
d.
,
.
e. 2, . ANS: E
PTS: 2
DIF: Average
71. Whitney says that Gauss's Law can be used to find the electric field of a sufficiently symmetrical distribution of charge as long as over the whole Gaussian surface. Algie says that the electric field must be a constant vector over the entire Gaussian surface. Which one, if either, is correct? a. Whitney, because that means no charge is enclosed within the Gaussian surface. b. Algie, because a constant electric field means that . c. Both, because the conditions in (a) and (b) are equivalent. d. Neither, because the electric field can be found from Gauss's law only if holds only over a portion of the Gaussian surface. e. Neither, because the charge distribution must be symmetric if anywhere on the surface. ANS: D
PTS: 2
DIF: Average
72. A uniform electric field
is present in the region between the infinite parallel planes of charge A and
B, and a uniform electric field is present in the region between the infinite parallel planes of charge B and C. When the planes are vertical and the fields are both non-zero, a. and are both directed to the right. b. and are both directed to the left. c.
points to the right and
to the left.
d.
points to the left and to the right. e. Any one of the above is possible. ANS: E
PTS: 1
73. A uniform electric field uniform electric field
DIF: Easy
is present in the region between infinite parallel plane plates A and B and a is present in the region between infinite parallel plane plates B and C. When
the plates are vertical, is directed to the right and A, B and C may be a. , , . b. +, , . c. +, , +. d. +, +, +. e. any one of the above. ANS: E
PTS: 1
to the left. The signs of the charges on plates
DIF: Easy
74. Three infinite planes of charge, A, B and C, are vertical and parallel to one another. There is a uniform electric field to the left of plane A and a uniform electric field to the right of plane C. The field points to the left and the field may be a. , , . b. +, , . c. +, , +. d. +, +, +. e. any one of the above. ANS: E
PTS: 1
points to the right. The signs of the charges on plates A, B and C
DIF: Easy
75. An constant electric field, N/C, goes through a surface with area m2. 2 (This surface can also be expressed as an area of 10 m with the direction of the unit vector ( ). What is the magnitude of the electric flux through this area? a. 24 N m2/C b. 48 N m2/C c. 0.24 N m2/C d. 0.48 N m2/C e. 0 ANS: A
PTS: 2
DIF: Average
76. A point charge is located at the origin. Centered along the x axis is a cylindrical closed surface of radius 10 cm with one end surface located at x = 2 m and the other end surface located at x = 4 m. If the magnitude of the electric flux through the surface at x = 2 m is 4 N m2/C, what is the magnitude of the electric flux through the surface at x = 4 m? a. 1 N m2/C b. 2 N m2/C c. 4 N m2/C d. 16 N m2/C e. The correct value is not given. ANS: A
PTS: 2
DIF: Average
PROBLEM 77. The nucleus of lead-208, , has 82 protons within a sphere of radius 6.34 1015. Each electric charge has a value of 1.60 1019 C. Assuming that the protons create a spherically symmetric distribution of charge, calculate the electric field at the surface of the nucleus. ANS: 2.94 1021 N/C PTS: 2
DIF: Average
78. At the point of fission, a nucleus of U-238, with 92 protons is divided into two smaller spheres each with 46 protons and a radius of 5.9 1015 m. What is the repulsive force pushing the two spheres apart when they are just touching one another? (The mass of the U-238 nucleus is 3.98 1025 kg.) ANS: 3 500 N PTS: 2
DIF: Average
79. The nucleus of a hydrogen atom, a proton, sets up an electric field. The distance between the proton and electron is about 5.1 1011 m. What is the magnitude of the electric field at this distance from the proton? [The charge on the proton is +1.6 1019 C.] ANS: 5.5 1011 N/C PTS: 2
DIF: Average
80. A Geiger counter is like an electroscope that discharges whenever ions formed by a radioactive particle produce a conducting path. A typical Geiger counter consists of a thin conducting wire of radius 0.002 cm stretched along the axis of a conducting cylinder of radius 2.0 cm. The wire and the cylinder carry equal and opposites charges of 8.0 1010 C all along their length of 10.0 cm. What is the magnitude of the electric field at the surface of the wire? ANS: 7.2 106 N/C PTS: 2
DIF: Average
Chapter 25—Electric Potential MULTIPLE CHOICE 1. A charged particle (q = 8.0 mC), which moves in a region where the only force acting on the particle is an electric force, is released from rest at point A. At point B the kinetic energy of the particle is equal to 4.8 J. What is the electric potential difference VB VA? a. 0.60 kV b. +0.60 kV c. +0.80 kV d. 0.80 kV e. +0.48 kV ANS: B
PTS: 2
DIF: Average
2. A particle (charge = 50 C) moves in a region where the only force on it is an electric force. As the particle moves 25 cm from point A to point B, its kinetic energy increases by 1.5 mJ. Determine the electric potential difference, VB VA. a. 50 V b. 40 V c. 30 V d. 60 V e. +15 V ANS: C
PTS: 2
DIF: Average
3. Points A [at (2, 3) m] and B [at (5, 7) m] are in a region where the electric field is uniform and given by N/C. What is the potential difference VA VB? a. 33 V b. 27 V c. 30 V d. 24 V e. 11 V ANS: D
PTS: 2
DIF: Average
4. A particle (charge = +2.0 mC) moving in a region where only electric forces act on it has a kinetic energy of 5.0 J at point A. The particle subsequently passes through point B which has an electric potential of +1.5 kV relative to point A. Determine the kinetic energy of the particle as it moves through point B. a. 3.0 J b. 2.0 J c. 5.0 J d. 8.0 J e. 10.0 J ANS: B
PTS: 2
DIF: Average
5. A particle (mass = 6.7 1027 kg, charge = 3.2 1019 C) moves along the positive x axis with a speed of 4.8 105 m/s. It enters a region of uniform electric field parallel to its motion and comes to rest after moving 2.0 m into the field. What is the magnitude of the electric field? a. 2.0 kN/C b. 1.5 kN/C
c. 1.2 kN/C d. 3.5 kN/C e. 2.4 kN/C ANS: C
PTS: 2
DIF: Average
6. A proton (mass = 1.67 1027 kg, charge = 1.60 1019 C) moves from point A to point B under the influence of an electrostatic force only. At point A the proton moves with a speed of 50 km/s. At point B the speed of the proton is 80 km/s. Determine the potential difference VB VA. a. +20 V b. 20 V c. 27 V d. +27 V e. 40 V ANS: B
PTS: 2
DIF: Average
7. A proton (mass = 1.67 1027 kg, charge = 1.60 1019 C) moves from point A to point B under the influence of an electrostatic force only. At point A the proton moves with a speed of 60 km/s. At point B the speed of the proton is 80 km/s. Determine the potential difference VB VA. a. +15 V b. 15 V c. 33 V d. +33 V e. 20 V ANS: B
PTS: 2
DIF: Average
8. What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV? a. 1.1 106 m/s b. 9.8 105 m/s c. 8.8 105 m/s d. 1.2 106 m/s e. 6.2 105 m/s ANS: C
PTS: 2
DIF: Average
9. An electron (m = 9.1 1031 kg, q = 1.6 1019 C) starts from rest at point A and has a speed of 5.0 106 m/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference VA VB. a. 71 V b. +71 V c. 26 V d. +26 V e. 140 V ANS: A
PTS: 2
DIF: Average
10. A proton (m = 1.7 1027 kg, q = +1.6 1019 C) starts from rest at point A and has a speed of 40 km/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference VB VA. a. +8.5 V b. 8.5 V
c. 4.8 V d. +4.8 V e. 17 V ANS: B
PTS: 2
DIF: Average
11. A particle (m = 2.0 g, q = 5.0 C) has a speed of 30 m/s at point A and moves (with only electric forces acting on it) to point B where its speed is 80 m/s. Determine the electric potential difference VA VB. a. 2.2 kV b. +1.1 kV c. 1.1 kV d. +2.2 kV e. +1.3 kV ANS: C
PTS: 2
DIF: Average
12. An alpha particle (m = 6.7 1027 kg, q = +3.2 1019 C) has a speed of 20 km/s at point A and moves to point B where it momentarily stops. Only electric forces act on the particle during this motion. Determine the electric potential difference VA VB. a. +4.2 V b. 4.2 V c. 9.4 V d. +9.4 V e. 8.4 V ANS: B
PTS: 2
DIF: Average
13. Points A [at (3, 6) m] and B [at (8, 3) m] are in a region where the electric field is uniform and given by N/C. What is the electric potential difference VA VB? a. +60 V b. 60 V c. +80 V d. 80 V e. +50 V ANS: A
PTS: 2
DIF: Average
14. If a = 30 cm, b = 20 cm, q = +2.0 nC, and Q = 3.0 nC in the figure, what is the potential difference VA VB?
a. b. c. d. e.
+60 V +72 V +84 V +96 V +48 V
ANS: A
PTS: 2
DIF: Average
15. Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity) and an electric field of N/C at point P. Determine the work required of an external agent to move a 3.0-C charge along the x axis from infinity to point P without any net change in the kinetic energy of the particle. a. 21 mJ b. 18 mJ c. 24 mJ d. 27 mJ e. 12 mJ ANS: B
PTS: 2
DIF: Average
16. Point charges q and Q are positioned as shown. If q = +2.0 nC, Q = 2.0 nC, a = 3.0 m, and b = 4.0 m, what is the electric potential difference, VA VB?
a. b. c. d. e.
8.4 V 6.0 V 7.2 V 4.8 V 0V
ANS: D
PTS: 2
DIF: Average
17. Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 m on the y axis, a 80nC charge at x = 4 m on the x axis, and a 70-nc charge at y = 6 m on the y axis. What is the electric potential (relative to a zero at infinity) at the point x = 8 m on the x axis? a. +81 V b. +48 V c. +5.8 V d. 72 V e. 18 V ANS: B
PTS: 2
DIF: Average
18. Point charges of equal magnitudes (25 nC) and opposite signs are placed on (diagonally) opposite corners of a 60-cm 80-cm rectangle. If point A is the corner of this rectangle nearest the positive charge and point B is located at the intersection of the diagonals of the rectangle, determine the potential difference, VB VA. a. 47 V b. +94 V c. zero d. 94 V e. +47 V ANS: D
PTS: 2
DIF: Average
19. Identical 2.0-C charges are located on the vertices of a square with sides that are 2.0 m in length. Determine the electric potential (relative to zero at infinity) at the center of the square. a. 38 kV b. 51 kV c. 76 kV d. 64 kV e. 13 kV ANS: B
PTS: 2
DIF: Average
20. A +4.0-C charge is placed on the x axis at x = +3.0 m, and a 2.0-C charge is located on the y axis at y = 1.0 m. Point A is on the y axis at y = +4.0 m. Determine the electric potential at point A (relative to zero at the origin). a. 6.0 kV b. 8.4 kV c. 9.6 kV d. 4.8 kV e. 3.6 kV ANS: C
PTS: 2
DIF: Average
21. Identical 4.0-C charges are placed on the y axis at y = 4.0 m. Point A is on the x axis at x = +3.0 m. Determine the electric potential of point A (relative to zero at the origin). a. 4.5 kV b. 2.7 kV c. 1.8 kV d. 3.6 kV e. 14 kV ANS: D
PTS: 2
DIF: Average
22. Four identical point charges (+6.0 nC) are placed at the corners of a rectangle which measures 6.0 m 8.0 m. If the electric potential is taken to be zero at infinity, what is the potential at the geometric center of this rectangle? a. 58 V b. 63 V c. 43 V d. 84 V e. 11 V ANS: C
PTS: 2
DIF: Average
23. Three identical point charges (+2.0 nC) are placed at the corners of an equilateral triangle with sides of 2.0-m length. If the electric potential is taken to be zero at infinity, what is the potential at the midpoint of any one of the sides of the triangle? a. 16 V b. 10 V c. 70 V d. 46 V e. 44 V ANS: D
PTS: 2
DIF: Average
24. A particle (charge = Q) is kept in a fixed position at point P, and a second particle (charge = q) is released from rest when it is a distance R from P. If Q = +2.0 mC, q = 1.5 mC, and R = 30 cm, what is the kinetic energy of the moving particle after it has moved a distance of 10 cm? a. 60 kJ b. 45 kJ c. 75 kJ d. 90 kJ e. 230 kJ ANS: B
PTS: 2
DIF: Average
25. Particle A (mass = m, charge = Q) and B (mass = m, charge = 5 Q) are released from rest with the distance between them equal to 1.0 m. If Q = 12 C, what is the kinetic energy of particle B at the instant when the particles are 3.0 m apart? a. 8.6 J b. 3.8 J c. 6.0 J d. 2.2 J e. 4.3 J ANS: D
PTS: 3
DIF: Challenging
26. A particle (charge = 40 C) moves directly toward a second particle (charge = 80 C) which is held in a fixed position. At an instant when the distance between the two particles is 2.0 m, the kinetic energy of the moving particle is 16 J. Determine the distance separating the two particles when the moving particle is momentarily stopped. a. 0.75 m b. 0.84 m c. 0.95 m d. 0.68 m e. 0.56 m ANS: C
PTS: 3
DIF: Challenging
27. A particle (charge 7.5 C) is released from rest at a point on the x axis, x = 10 cm. It begins to move due to the presence of a 2.0-C charge which remains fixed at the origin. What is the kinetic energy of the particle at the instant it passes the point x = 1.0 m? a. 3.0 J b. 1.8 J c. 2.4 J d. 1.2 J e. 1.4 J ANS: D
PTS: 2
DIF: Average
28. A particle (charge = 5.0 C) is released from rest at a point x = 10 cm. If a 5.0-C charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 90 cm? a. 1.6 J b. 2.0 J c. 2.4 J d. 1.2 J e. 1.8 J ANS: B
PTS: 2
DIF: Average
29. A 60-C charge is held fixed at the origin and a 20-C charge is held fixed on the x axis at a point x = 1.0 m. If a 10-C charge is released from rest at a point x = 40 cm, what is its kinetic energy the instant it passes the point x = 70 cm? a. 9.8 J b. 7.8 J c. 8.8 J d. 6.9 J e. 2.8 J ANS: C
PTS: 2
DIF: Average
30. Two identical particles, each with a mass of 2.0 g and a charge of 25 nC, are released simultaneously from rest when the two are 4.0 cm apart. What is the speed of either particle at the instant when the two are separated by 10 cm? a. 7.3 m/s b. 9.8 m/s c. 9.2 m/s d. 6.5 m/s e. 4.6 m/s ANS: D
PTS: 2
DIF: Average
31. Two particles, each having a mass of 3.0 g and having equal but opposite charges of magnitude 5.0 nC, are released simultaneously from rest when the two are 5.0 cm apart. What is the speed of either particle at the instant when the two are separated by 2.0 cm? a. 2.1 m/s b. 1.5 m/s c. 1.8 m/s d. 2.4 m/s e. 3.2 m/s ANS: B
PTS: 2
DIF: Average
32. Two identical particles, each with a mass of 4.5 g and a charge of 30 nC, are moving directly toward each other with equal speeds of 4.0 m/s at an instant when the distance separating the two is equal to 25 cm. How far apart will they be when closest to one another? a. 9.8 cm b. 12 cm c. 7.8 cm d. 15 cm e. 20 cm ANS: C
PTS: 2
DIF: Average
33. Two particles, each having a mass of 3.0 g and having equal but opposite charges of magnitude of 6.0 nC, are released simultaneously from rest when they are a very large distance apart. What distance separates the two at the instant when each has a speed of 5.0 m/s? a. 4.3 mm b. 8.6 mm c. 7.3 mm d. 5.6 mm e. 2.2 mm ANS: A
PTS: 2
DIF: Average
34. A particle (q = +5.0 C) is released from rest when it is 2.0 m from a charged particle which is held at rest. After the positively charged particle has moved 1.0 m toward the fixed particle, it has a kinetic energy of 50 mJ. What is the charge on the fixed particle? a. 2.2 C b. +6.7 C c. 2.7 C d. +8.0 C e. 1.1 C ANS: A
PTS: 2
DIF: Average
35. Four identical point charges (+4.0 C) are placed at the corners of a square which has 20-cm sides. How much work is required to assemble this charge arrangement starting with each of the charges a very large distance from any of the other charges? a. +2.9 J b. +3.9 J c. +2.2 J d. +4.3 J e. +1.9 J ANS: B
PTS: 3
DIF: Challenging
36. Identical 8.0-C point charges are positioned on the x axis at x = 1.0 m and released from rest simultaneously. What is the kinetic energy of either of the charges after it has moved 2.0 m? a. 84 mJ b. 54 mJ c. 96 mJ d. 63 mJ e. 48 mJ ANS: C
PTS: 2
DIF: Average
37. Through what potential difference must an electron (starting from rest) be accelerated if it is to reach a speed of 3.0 107 m/s? a. 5.8 kV b. 2.6 kV c. 7.1 kV d. 8.6 kV e. 5.1 kV ANS: B
PTS: 2
DIF: Average
38. Identical point charges (+50 C) are placed at the corners of a square with sides of 2.0-m length. How much external energy is required to bring a fifth identical charge from infinity to the geometric center of the square? a. 41 J b. 16 J c. 64 J d. 10 J e. 80 J ANS: C
PTS: 2
DIF: Average
39. A charge of +3.0 C is distributed uniformly along the circumference of a circle with a radius of 20 cm. How much external energy is required to bring a charge of 25C from infinity to the center of the circle? a. 5.4 J b. 3.4 J c. 4.3 J d. 2.7 J e. 6.8 J ANS: B
PTS: 2
DIF: Average
40. Identical point charges (+20 C) are placed at the corners of an equilateral triangle with sides of 2.0-m length. How much external energy is required to bring a charge of 45 C from infinity to the midpoint of one side of the triangle? a. 26 J b. 16 J c. 23 J d. 21 J e. 12 J ANS: D
PTS: 2
DIF: Average
41. Identical point charges (+30 C) are placed at the corners of a rectangle (4.0 m 6.0 m). How much external energy is required to bring a charge of 55 C from infinity to the midpoint of one of the 6.0-m long sides of the rectangle? a. 22 J b. 16 J c. 13 J d. 19 J e. 8.0 J ANS: B
PTS: 2
DIF: Average
42. A charge per unit length given by (x) = bx, where b = 12 nC/m2, is distributed along the x axis from x = +9.0 cm to x = +16 cm. If the electric potential at infinity is taken to be zero, what is the electric potential at the point P on the y axis at y = 12 cm? a. 5.4 V b. 7.2 V c. 9.0 V d. 9.9 V e. 16 V ANS: A
PTS: 3
DIF: Challenging
43. A charge Q is uniformly distributed along the x axis from x = a to x = b. If Q = 45 nC, a = 3.0 m, and b = 2.0 m, what is the electric potential (relative to zero at infinity) at the point, x = 8.0 m, on the x axis? a. 71 V b. 60 V c. 49 V d. 82 V e. 150 V ANS: C
PTS: 3
DIF: Challenging
44. Charge of uniform density (3.5 nC/m) is distributed along the circular arc shown. Determine the electric potential (relative to zero at infinity) at point P.
a. b. c. d. e.
61 V 42 V 52 V 33 V 22 V
ANS: D
PTS: 2
DIF: Average
45. A charge of uniform density (0.80 nC/m) is distributed along the x axis from the origin to the point x = 10 cm. What is the electric potential (relative to zero at infinity) at a point, x = 18 cm, on the x axis? a. 7.1 V b. 5.8 V c. 9.0 V d. 13 V e. 16 V ANS: B
PTS: 2
DIF: Average
46. A charge of 20 nC is distributed uniformly along the x axis from x = 2.0 m to x = +2.0 m. What is the electric potential (relative to zero at infinity) at the point x = 5.0 m on the x axis? a. 57 V b. 48 V c. 38 V d. 67 V e. 100 V ANS: C
PTS: 2
DIF: Average
47. Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 m to x = 5.0 m. What is the electric potential (relative to zero at infinity) at the origin (x = 0)? a. 91 V b. 99 V c. 82 V d. 74 V e. 140 V ANS: B
PTS: 2
DIF: Average
48. A linear charge of nonuniform density = bx, where b = 2.1 nC/m2, is distributed along the x axis from x = 2.0 m to x = 3.0 m. Determine the electric potential (relative to zero at infinity) of the point y = 4.0 m on the y axis. a. 36 V
b. c. d. e.
95 V 10 V 17 V 15 V
ANS: C
PTS: 3
DIF: Challenging
49. A nonuniform linear charge distribution given by (x) = bx, where b is a constant, is distributed along the x axis from x = 0 to x = +L. If b = 40 nC/m2 and L = 0.20 m, what is the electric potential (relative to a potential of zero at infinity) at the point y = 2L on the y axis? a. 19 V b. 17 V c. 21 V d. 23 V e. 14 V ANS: B
PTS: 3
DIF: Challenging
50. A charge of 10 nC is distributed uniformly along the x axis from x = 2 m to x = +3 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +5 m on the x axis? a. b. c. d. e. ANS: D
PTS: 2
DIF: Average
51. Charge of uniform linear density 3.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +4 m on the x axis? a. b. c. d. e. ANS: C
PTS: 2
DIF: Average
52. A charge of 4.0 nC is distributed uniformly along the x axis from x = +4 m to x = +6 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the origin?
a. b. c. d. e. ANS: C
PTS: 2
DIF: Average
53. A charge of 20 nC is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +3 m on the x axis? a. b. c. d. e.
ANS: A
PTS: 2
DIF: Average
54. Charge of uniform linear density 6.0 nC/m is distributed along the x axis from x = 0 to x = +3 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point y = +4 m on the y axis? a. b. c. d. e.
ANS: A
PTS: 2
DIF: Average
55. A rod (length = 2.0 m) is uniformly charged and has a total charge of 5.0 nC. What is the electric potential (relative to zero at infinity) at a point which lies along the axis of the rod and is 3.0 m from the center of the rod? a. 22 V b. 19 V c. 16 V d. 25 V e. 12 V ANS: C
PTS: 2
DIF: Average
56. A charge of 18 nC is uniformly distributed along the y axis from y = 3 m to y = 5 m. Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point x = +2 m on the x axis? a. b. c. d. e.
ANS: A
PTS: 2
DIF: Average
57. Two large parallel conducting plates are 8.0 cm apart and carry equal but opposite charges on their facing surfaces. The magnitude of the surface charge density on either of the facing surfaces is 2.0 nC/m2. Determine the magnitude of the electric potential difference between the plates. a. 36 V b. 27 V c. 18 V d. 45 V e. 16 V ANS: C
PTS: 2
DIF: Average
58. A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformly on its surface. If point A is located at the center of the sphere and point B is 15 cm from the center, what is the magnitude of the electric potential difference between these two points? a. 23 V b. 30 V c. 15 V d. 45 V e. 60 V ANS: B
PTS: 2
DIF: Average
59. Charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a. 2.7 V b. 2.0 V c. 2.4 V d. 1.7 V e. 3.4 V ANS: D
PTS: 3
DIF: Challenging
60. Charge of uniform density 90 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 2.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a. 1.9 V b. 1.4 V c. 2.2 V d. 2.8 V e. 4.0 V ANS: B
PTS: 2
DIF: Average
61. A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3. What is the magnitude of the potential difference between the center and a point 4.0 cm away? a. 12 V b. 6.8 V c. 3.0 V d. 4.7 V e. 2.2 V ANS: C
PTS: 3
DIF: Challenging
62. A charge of 40 pC is distributed on an isolated spherical conductor that has a 4.0-cm radius. Point A is 1.0 cm from the center of the conductor and point B is 5.0 cm from the center of the conductor. Determine the electric potential difference VA VB. a. +1.8 V b. +29 V c. +27 V d. +7.2 V e. +9.0 V ANS: A
PTS: 2
DIF: Average
63. Two flat conductors are placed with their inner faces separated by 6.0 mm. If the surface charge density on one of the inner faces is 40 pC/m2, what is the magnitude of the electric potential differences between the two conductors? a. 36 mV b. 18 mV c. 32 mV d. 27 mV e. 14 mV ANS: D
PTS: 2
DIF: Average
64. The electric field in a region of space is given by Ex = (3.0x) N/C, Ey = Ez = 0, where x is in m. Points A and B are on the x axis at xA = 3.0 m and xB = 5.0 m. Determine the potential difference VB VA. a. 24 V b. +24 V c. 18 V d. +30 V e. 6.0 V ANS: A
PTS: 2
DIF: Average
65. Equipotentials are lines along which a. the electric field is constant in magnitude and direction. b. the electric charge is constant in magnitude and direction. c. maximum work against electrical forces is required to move a charge at constant speed. d. a charge may be moved at constant speed without work against electrical forces. e. charges move by themselves. ANS: D
PTS: 1
DIF: Easy
66. When a charged particle is moved along an electric field line, a. the electric field does no work on the charge. b. the electrical potential energy of the charge does not change. c. the electrical potential energy of the charge undergoes the maximum change in magnitude. d. the voltage changes, but there is no change in electrical potential energy. e. the electrical potential energy undergoes the maximum change, but there is no change in voltage. ANS: C
PTS: 1
DIF: Easy
67. When a positive charge is released and moves along an electric field line, it moves to a position of a. lower potential and lower potential energy. b. lower potential and higher potential energy. c. higher potential and lower potential energy. d. higher potential and higher potential energy. e. greater magnitude of the electric field. ANS: A
PTS: 1
DIF: Easy
68. When a negative charge is released and moves along an electric field line, it moves to a position of a. lower potential and lower potential energy. b. lower potential and higher potential energy. c. higher potential and lower potential energy. d. higher potential and higher potential energy. e. decreasing magnitude of the electric field. ANS: C
PTS: 1
DIF: Easy
69. A charge is placed on a spherical conductor of radius r1. This sphere is then connected to a distant sphere of radius r2 (not equal to r1) by a conducting wire. After the charges on the spheres are in equilibrium, a. the electric fields at the surfaces of the two spheres are equal. b. the amount of charge on each sphere is q/2. c. both spheres are at the same potential.
d. the potentials are in the ratio
.
the potentials are in the ratio
.
e.
ANS: C
PTS: 1
DIF: Easy
70. The electric potential inside a charged solid spherical conductor in equilibrium a. is always zero. b. is constant and equal to its value at the surface. c. decreases from its value at the surface to a value of zero at the center. d. increases from its value at the surface to a value at the center that is a multiple of the potential at the surface. e. is equal to the charge passing through the surface per unit time divided by the resistance. ANS: B
PTS: 1
DIF: Easy
71. Which statement is always correct when applied to a charge distribution located in a finite region of space? a. Electric potential is always zero at infinity. b. Electric potential is always zero at the origin. c. Electric potential is always zero at a boundary surface to a charge distribution. d. Electric potential is always infinite at a boundary surface to a charge distribution. e. The location where electric potential is zero may be chosen arbitrarily. ANS: E
PTS: 1
DIF: Easy
72. Which of the following represents the equipotential lines of a dipole? a.
b.
c.
d.
e.
ANS: E
PTS: 1
DIF: Easy
73. Can the lines in the figure below be equipotential lines?
a. b. c. d. e.
No, because there are sharp corners. No, because they are isolated lines. Yes, because any lines within a charge distribution are equipotential lines. Yes, they might be boundary lines of the two surfaces of a conductor. It is not possible to say without further information.
ANS: D
PTS: 1
DIF: Easy
74. A series of n uncharged concentric shells surround a small central charge q. The charge distributed on the outside of the nth shell is a. nq. b. (ln n)q. c. +q. d. +(ln n)q. e. +nq. ANS: C
PTS: 1
DIF: Easy
75. A series of 3 uncharged concentric shells surround a small central charge q. The charge distributed on the outside of the third shell is a. 3q. b. (ln 3)q. c. +q. d. +(ln 3)q. e. +3q. ANS: C
PTS: 1
DIF: Easy
76. A series of n uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the nth shell, at distance r from the center, and relative to V = 0 at , is a. . b. c.
. .
d. e.
. .
ANS: C
PTS: 1
DIF: Easy
77. A series of 3 uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the third shell, at distance r from the center, and relative to V = 0 at , is a. . b. c.
. .
d. e. ANS: C
. . PTS: 1
DIF: Easy
78. The electric field in the region defined by the y-z plane and the negative x axis is given by E = ax, where a is a constant. (There is no field for positive values of x.) As x increases in magnitude, relative to V = 0 at the origin, the electric potential in the region defined above is a. a decreasing function proportional to |x2|. b. a decreasing function proportional to |x|. c. constant. d. an increasing function proportional to +|x|. e. an increasing function proportional to +|x2|. ANS: E
PTS: 1
DIF: Easy
79. The electric field in the region defined by the y-z plane and the positive x axis is given by E = ax, where a is a constant. (There is no field for negative values of x.) As x increases in magnitude, relative to V = 0 at the origin, the electric potential in the region defined above is a. a decreasing function proportional to |x2|. b. a decreasing function proportional to |x|. c. constant. d. an increasing function proportional to +|x|. e. an increasing function proportional to +|x2|. ANS: A
PTS: 1
DIF: Easy
80. Two charges lie on the x axis, +3q at the origin, and 2q at x = 5.0 m. The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero) is a. 1.0 m. b. 2.0 m. c. 2.5 m. d. 3.0 m. e. 4.0 m. ANS: D
PTS: 2
DIF: Average
81. Two charges lie on the x axis, +2q at the origin, and 3q at x = 5.0 m. The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero) is a. 1.0 m. b. 2.0 m. c. 2.5 m. d. 3.0 m. e. 4.0 m. ANS: B
PTS: 2
DIF: Average
82. When introduced into a region where an electric field is present, an electron with initial velocity eventually move a. along an electric field line, in the positive direction of the line. b. along an electric field line, in the negative direction of the line. c. to a point of decreased potential. d. to a point of increased potential. e. as described in both (b) and (d). ANS: D
PTS: 1
DIF: Easy
83. When introduced into a region where an electric field is present, a proton with initial velocity eventually move a. along an electric field line, in the positive direction of the line. b. along an electric field line, in the negative direction of the line. c. to a point of decreased potential. d. to a point of decreased potential. e. as described in both (a) and (c). ANS: C
PTS: 1
DIF: Easy
84. A system consisting of a positively-charged particle and an electric field a. loses potential difference and kinetic energy when the charged particle moves in the direction of the field. b. loses electric potential energy when the charged particle moves in the direction of the field. c. loses kinetic energy when the charged particle moves in the direction of the field. d. gains electric potential energy when the charged particle moves in the direction of the field. e. gains potential difference and electric potential energy when the charged particle moves in the direction of the field. ANS: B
PTS: 1
will
DIF: Easy
85. A system consisting of a negatively-charged particle and an electric field a. gains potential difference and kinetic energy when the charged particle moves in the direction of the field. b. loses electric potential energy when the charged particle moves in the direction of the field. c. gains kinetic energy when the charged particle moves in the direction of the field. d. gains electric potential energy when the charged particle moves in the direction of the field. e. gains potential difference and electric potential energy when the charged particle moves in the direction of the field.
will
ANS: D
PTS: 1
DIF: Easy
86. The Bohr model pictures a hydrogen atom in its ground state as a proton and an electron separated by the distance a0 = 0.529 1010 m. The electric potential created by the proton at the position of the electron is a. 13.6 V. b. +13.6 V. c. 27.2 V. d. +27.2 V. e. +5.12 109 V. ANS: D
PTS: 2
DIF: Average
87. The Bohr model pictures a hydrogen atom in its ground state as a proton and an electron separated by the distance a0 = 0.529 1010 m. The electric potential created by the electron at the position of the proton is a. 13.6 V. b. +13.6 V. c. 27.2 V. d. +27.2 V. e. +5.12 109 V. ANS: C
PTS: 2
DIF: Average
88. The electric potential at the surface of a charged conductor a. is always zero. b. is always independent of the magnitude of the charge on the surface. c. may be set equal to zero by adding an appropriate constant to the potential at all points of space. d. is always such that the potential is zero at all points inside the conductor. e. is always such that the potential is always zero within a hollow space inside the conductor. ANS: C
PTS: 1
DIF: Easy
89. An electron is released form rest in a region of space where a uniform electric field is present. Joanna claims that its kinetic and potential energies both increase as it moves from its initial position to its final position. Sonya claims that they both decrease. Which one, if either, is correct? a. Joanna, because the electron moves opposite to the direction of the field. b. Sonya, because the electron moves opposite to the direction of the field. c. Joanna, because the electron moves in the direction of the field. d. Sonya, because the electron moves in the direction of the field. e. Neither, because the kinetic energy increases while the electron moves to a point at a higher potential. ANS: E
PTS: 2
DIF: Average
90. Four electrons move from point A to point B in a uniform electric field as shown below. Rank the electrons in diagrams I through IV by the changes in potential energy from most positive to most negative when traveling from A to B.
a. b. c. d. e.
I = II = III = IV. II = III > I > IV. III > I = IV > II. II > I = IV > III. I > II = III > IV.
ANS: D
PTS: 2
DIF: Average
91. Four electrons move from point A to point B in a uniform electric field as shown below. Rank the electrons in diagrams I through IV by the changes in potential from most positive to most negative when traveling from A to B.
a. b. c. d. e.
I = II = III = IV. II = III > I > IV. III > I = IV > II. II > I = IV > III. I > II = III > IV.
ANS: C
PTS: 2
92. An infinite plane of charge with
DIF: Average is tilted at a 45 angle to the vertical direction as
shown below. The potential difference, VB VA, in volts, between points A and B, a 4.50 m distance apart, is
a. b. c. d. e.
7.06. 9.98. 14.11. +7.06. +9.98.
ANS: B
PTS: 2
93. An infinite plane of charge with
DIF: Average is tilted at a 45 angle to the vertical direction as
shown below. The potential difference, VA VB, in volts, between points A and B, a 4.50 m distance apart, is
a. b. c. d. e.
7.06. 9.98. 14.11. +7.06. +9.98.
ANS: E
PTS: 2
DIF: Average
94. For the potential , what is the corresponding electric field at the point (2,2,2)? a. b. c. d. e. The correct answer is not given. ANS: A
PTS: 3
DIF: Challenging
PROBLEM 95. How much electrical charge is needed to raise an isolated metal sphere of radius 1.0 m to a potential of 1.0 106 V? ANS: 1.1 104 C PTS: 2
DIF: Average
96. In the Bohr model of the hydrogen atom, the electron circles the proton at a distance of 0.529 1010 m. Find the potential at the position of the electron. ANS: 27.2 Volts PTS: 2
DIF: Average
97. The gap between electrodes in a spark plug is 0.06 cm. In order to produce an electric spark in a gasoline-air mixture, the electric field must reach a value of 3 106 V/m. What minimum voltage must be supplied by the ignition circuit when starting the car? ANS: 1 800 V PTS: 2
DIF: Average
98. To recharge a 12-V battery, a battery charger must move 3.6 105 C of charge from the negative to the positive terminal. What amount of work is done by the battery charger? How many kilowatt hours is this? ANS: 4.3 MJ, 1.2 kWh PTS: 2
DIF: Average
Chapter 26—Capacitance and Dielectrics MULTIPLE CHOICE 1. Determine the equivalent capacitance of the combination shown when C = 12 pF.
a. b. c. d. e.
48 pF 12 pF 24 pF 6.0 pF 59 pF
ANS: D
PTS: 2
DIF: Average
2. Determine the equivalent capacitance of the combination shown when C = 15 mF.
a. b. c. d. e.
20 mF 16 mF 12 mF 24 mF 75 mF
ANS: C
PTS: 2
DIF: Average
3. Determine the equivalent capacitance of the combination shown when C = 12 nF.
a. b. c. d. e.
34 nF 17 nF 51 nF 68 nF 21 nF
ANS: B
PTS: 2
DIF: Average
4. Determine the equivalent capacitance of the combination shown when C = 45 F.
a. b. c. d. e.
36 F 32 F 34 F 30 F 38 F
ANS: D
PTS: 2
DIF: Average
5. If C = 10 F, what is the equivalent capacitance for the combination shown?
a. b. c. d. e.
7.5 F 6.5 F 7.0 F 5.8 F 13 F
ANS: D
PTS: 2
DIF: Average
6. What is the equivalent capacitance of the combination shown?
a. b. c. d. e.
29 F 10 F 40 F 25 F 6.0 F
ANS: B
PTS: 2
DIF: Average
7. What is the equivalent capacitance of the combination shown?
a. b. c. d. e.
20 F 90 F 22 F 4.6 F 67 F
ANS: A
PTS: 2
DIF: Average
8. Determine the equivalent capacitance of the combination shown when C = 45 F.
a. b. c. d. e.
28 F 36 F 52 F 44 F 23 F
ANS: B
PTS: 2
DIF: Average
9. Determine the equivalent capacitance of the combination shown when C = 24 F.
a. b. c. d. e.
20 F 36 F 16 F 45 F 27 F
ANS: C
PTS: 2
DIF: Average
10. Determine the energy stored in C2 when C1 = 15 F, C2 = 10 F, C3 = 20 F, and V0 = 18 V.
a. b. c. d. e.
0.72 mJ 0.32 mJ 0.50 mJ 0.18 mJ 1.60 mJ
ANS: D
PTS: 3
DIF: Challenging
11. Determine the energy stored in C1 when C1 = 10 F, C2 = 12 F, C3 = 15 F, and V0 = 70 V.
a. b. c. d. e.
6.5 mJ 5.1 mJ 3.9 mJ 8.0 mJ 9.8 mJ
ANS: C
PTS: 2
DIF: Average
12. Determine the energy stored by C4 when C1 = 20 F, C2 = 10 F, C3 = 14 F, C4 = 30 F, and V0 = 45 V.
a. b. c. d. e.
3.8 mJ 2.7 mJ 3.2 mJ 2.2 mJ 8.1 mJ
ANS: D
PTS: 2
DIF: Average
13. Determine the charge stored by C1 when C1 = 20 F, C2 = 10 F, C3 = 30 F, and V0 = 18 V.
a. b. c. d. e.
0.37 mC 0.24 mC 0.32 mC 0.40 mC 0.50 mC
ANS: B
PTS: 2
DIF: Average
14. What is the total energy stored by C3 when C1 = 50 F, C2 = 30 F, C3 = 36 F, C4 = 12 F, and V0 = 30 V?
a. b. c. d. e.
6.3 mJ 25 mJ 57 mJ 1.6 mJ 14 mJ
ANS: A
PTS: 3
DIF: Challenging
15. How much energy is stored in the 50-F capacitor when Va Vb = 22V?
a. b. c. d. e.
0.78 mJ 0.58 mJ 0.68 mJ 0.48 mJ 0.22 mJ
ANS: D
PTS: 2
DIF: Average
16. What is the total energy stored in the group of capacitors shown if the charge on the 30-F capacitor is 0.90 mC?
a. b. c. d. e.
29 mJ 61 mJ 21 mJ 66 mJ 32 mJ
ANS: D
PTS: 3
DIF: Challenging
17. What is the potential difference across C2 when C1 = 5.0 F, C2 = 15 F, C3 = 30 F, and V0 = 24 V?
a. 21 V
b. c. d. e.
19 V 16 V 24 V 8.0 V
ANS: C
PTS: 2
DIF: Average
18. What total energy is stored in the group of capacitors shown if the potential difference Vab is equal to 50 V?
a. b. c. d. e.
48 mJ 27 mJ 37 mJ 19 mJ 10 mJ
ANS: D
PTS: 2
DIF: Average
19. Determine the energy stored in the 60-F capacitor.
a. b. c. d. e.
2.4 mJ 3.0 mJ 3.6 mJ 4.3 mJ 6.0 mJ
ANS: B
PTS: 2
DIF: Average
20. Determine the energy stored in the 40-F capacitor.
a. b. c. d. e.
2.4 mJ 1.6 mJ 2.0 mJ 2.9 mJ 4.0 mJ
ANS: C
PTS: 2
DIF: Average
21. If VA VB = 50 V, how much energy is stored in the 36-F capacitor?
a. b. c. d. e.
50 mJ 28 mJ 13 mJ 8.9 mJ 17 mJ
ANS: D
PTS: 2
DIF: Average
22. If VA VB = 50 V, how much energy is stored in the 54-F capacitor?
a. b. c. d. e.
50 mJ 13 mJ 28 mJ 8.9 mJ 17 mJ
ANS: B
PTS: 2
DIF: Average
23. A 3.0-F capacitor charged to 40 V and a 5.0-F capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 3.0-F capacitor? a. 11 C b. 15 C c. 19 C d. 26 C e. 79 C ANS: A
PTS: 3
DIF: Challenging
24. A 6.0-F capacitor charged to 50 V and a 4.0-F capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected. What is the total energy stored in the 6.0-F capacitor at equilibrium? a. 6.1 mJ b. 5.7 mJ c. 6.6 mJ d. 7.0 mJ e. 3.8 mJ ANS: B
PTS: 3
DIF: Challenging
25. A 25-F capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other, with the two positive plates connected and the two negative plates connected. The final potential difference across the 25-F capacitor is 36 V. What is the value of the capacitance of C? a. 43 F b. 29 F c. 22 F d. 58 F e. 63 F ANS: C
PTS: 2
DIF: Challenging
26. A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other. What is the final charge on the 6.0-mF capacitor? a. 20 mC b. 8.0 mC c. 10 mC d. 12 mC e. 230 mC ANS: D
PTS: 3
DIF: Challenging
27. When a capacitor has a charge of magnitude 80 C on each plate the potential difference across the plates is 16 V. How much energy is stored in this capacitor when the potential difference across its plates is 42 V? a. 1.0 mJ b. 4.4 mJ c. 3.2 mJ d. 1.4 mJ e. 1.7 mJ ANS: B
PTS: 2
DIF: Average
28. A 15-F capacitor and a 30-F capacitor are connected in series, and charged to a potential difference of 50 V. What is the resulting charge on the 30-F capacitor? a. 0.70 mC b. 0.80 mC c. 0.50 mC d. 0.60 mC e. 0.40 mC ANS: C
PTS: 2
DIF: Average
29. A 15-F capacitor and a 25-F capacitor are connected in parallel, and charged to a potential difference of 60 V. How much energy is then stored in this capacitor combination? a. 50 mJ b. 18 mJ c. 32 mJ d. 72 mJ e. 45 mJ ANS: D
PTS: 2
DIF: Average
30. A 20-F capacitor charged to 2.0 kV and a 40-F capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 20-F capacitor after the two are so connected? a. 53 mC b. 27 mC c. 40 mC d. 80 mC e. 39 mC ANS: B
PTS: 2
DIF: Average
31. A 15-F capacitor is charged to 40 V and then connected across an initially uncharged 25-F capacitor. What is the final potential difference across the 25-F capacitor? a. 12 V b. 18 V c. 15 V d. 21 V e. 24 V ANS: C
PTS: 2
DIF: Average
32. A 30-F capacitor is charged to 40 V and then connected across an initially uncharged 20-F capacitor. What is the final potential difference across the 30-F capacitor? a. 15 V b. 24 V c. 18 V d. 21 V e. 40 V ANS: B
PTS: 2
DIF: Average
33. A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60-F capacitor. If the final potential difference across the 60-F capacitor is 40 V, determine C. a. 49 F b. 32 F c. 40 F d. 90 F e. 16 F ANS: C
PTS: 2
DIF: Average
34. A 30-F capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C. If the final potential difference across the 30-F capacitor is 20 V, determine C. a. 60 F b. 75 F c. 45 F d. 90 F e. 24 F ANS: D
PTS: 2
DIF: Average
35. A 30-F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10-F capacitor. If the final potential difference across the 10-F capacitor is 20 V, determine V0. a. 13 V b. 27 V c. 20 V d. 29 V e. 60 V ANS: B
PTS: 2
DIF: Average
36. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are a. Q0, V0 b.
Q0,
V0
c. Q0, V0 d. Q0, 2V0 e. 2Q0, 2V0 ANS: D
PTS: 2
DIF: Average
37. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the new capacitance and the potential difference between the plates are a. C0, V0 b. c.
C0, V0 C0, 2V0
d. C0, 2V0 e. 2C0, 2V0 ANS: C
PTS: 2
DIF: Average
38. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are a. Q0, V0 b.
Q0, V0
c. Q0, V0 d. 2Q0, V0 e. 2Q0, 2V0 ANS: B
PTS: 2
DIF: Average
39. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the capacitance of the capacitor and the magnitude of the charge on the plates are a. C0, Q0 b.
C0, Q0
c. C0, Q0 d. 2C0, Q0 e. 2C0, 2Q0 ANS: A
PTS: 2
DIF: Average
40. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. While it is connected to the battery the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the potential difference between them are a. Q0, V0 b.
Q0,
V0
c. Q0, V0 d. 3Q0, V0 e. 3Q0, 3V0 ANS: D
PTS: 2
DIF: Average
41. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. While it is connected to the battery, the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the new capacitance are a. Q0, C0 b.
Q0,
C0
c. Q0, C0 d. 3Q0, C0 e. 3Q0, 3C0
ANS: E
PTS: 2
DIF: Average
42. The equivalent capacitance of the circuit shown below is
a. b. c. d. e.
0.2 C. 0.4 C. 1 C. 4 C. 5 C.
ANS: D
PTS: 1
DIF: Easy
43. The equivalent capacitance of the circuit shown below is
a. b. c. d. e.
0.2 C. 0.4 C. 1 C. 4 C. 5 C.
ANS: B
PTS: 2
DIF: Average
44. The equivalent capacitance of the circuit shown below is
a. b. c. d. e.
0.50 C. 1.0 C. 1.5 C. 2.0 C. 2.5 C.
ANS: B
PTS: 1
DIF: Easy
45. Which of the following is not a capacitance? a. b.
c. d. e.
ANS: E
PTS: 1
DIF: Easy
46. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitudes of the charge on the plates and the potential difference between them are a. Q0, V0. b.
Q0,
V0.
c. Q0, V0. d. Q0, 3V0. e. 3Q0, 3V0. ANS: B
PTS: 1
DIF: Easy
47. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitudes of the capacitance and the potential difference between the plates are a. C0, V0. b.
C0,
V0.
c. C0, V0. d. 3C0, V0. e. 3C0, 3V0. ANS: D
PTS: 1
DIF: Easy
48. An initially uncharged parallel plate capacitor of capacitance C is charged to potential V by a battery. The battery is then disconnected. Which statement is correct? a. There is no charge on either plate of the capacitor. b. The capacitor can be discharged by grounding any one of its two plates. c. Charge is distributed evenly over both the inner and outer surfaces of the plates. d. The magnitude of the electric field outside the space between the plates is approximately zero. e. The capacitance increases when the distance between the plates increases. ANS: D
PTS: 1
DIF: Easy
49. A 0.120 pF parallel-plate capacitor is charged to a potential difference of 10.0 V and then disconnected from the battery. A cosmic ray burst creates 1.00 106 electrons and 1.00 106 positive charges between the plates. If the charges do not recombine, but reach the oppositely charged plates, by how much is the potential difference between the capacitor plates reduced? a. 1.33 V b. 7.34 V c. 8.67 V d. 1,330 V e. 8,670 V ANS: A
PTS: 3
DIF: Challenging
50. A 0.16 pF parallel-plate capacitor is charged to 10 V. Then the battery is disconnected from the capacitor. When 1.00 107 electrons are now placed on the negative plate of the capacitor, the voltage between the plates changes by a. 5.0 V. b. 1.1 V. c. 0 V. d. +1.1 V. e. +5.0 V. ANS: E
PTS: 3
DIF: Challenging
51. A 0.16 pF parallel-plate capacitor is charged to 10 V. Then the battery is disconnected from the capacitor. When 1.00 107 positive charges of magnitude |e| are now placed on the positive plate of the capacitor, the voltage between the plates changes by a. 5.0 V. b. 1.1 V. c. 0 V. d. +1.1 V. e. +5.0 V. ANS: E
PTS: 3
DIF: Challenging
52. A parallel plate capacitor is charged to voltage V and then disconnected from the battery. Leopold says that the voltage will decrease if the plates are pulled apart. Gerhardt says that the voltage will remain the same. Which one, if either, is correct, and why? a. Gerhardt, because the maximum voltage is determined by the battery. b. Gerhardt, because the charge per unit area on the plates does not change. c. Leopold, because charge is transferred from one plate to the other when the plates are separated. d. Leopold, because the force each plate exerts on the other decreases when the plates are pulled apart. e. Neither, because the voltage increases when the plates are pulled apart. ANS: E
PTS: 1
DIF: Easy
53. Addition of a metal slab of thickness a between the plates of a parallel plate capacitor of plate separation d is equivalent to introducing a dielectric with dielectric constant between the plates. The value of is a. . b. d. c. d a.
d. e.
. .
ANS: D
PTS: 2
DIF: Average
54. A parallel plate capacitor is connected to a battery and charged to voltage V. Leah says that the charge on the plates will decrease if the distance between the plates is increased while they are still connected to the battery. Gertie says that the charge will remain the same. Which one, if either, is correct, and why? a. Gertie, because the maximum voltage is determined by the battery. b. Gertie, because the capacitance of the capacitor does not change. c. Leah, because the capacitance decreases when the plate separation is increased. d. Leah, because the capacitance increases when the plate separation is increased. e. Neither, because the charge increases when the plate separation is increased. ANS: C
PTS: 1
DIF: Easy
55. Which of the following statements is incorrect? a. Capacitance is always positive. b. The symbol for potential difference between the plates of a capacitor is . c. Water is a polar molecule. d. When a dielectric is placed in a capacitor it serves to reduce the electric field. e. Nonpolar molecules cannot be used for dielectric material in a capacitor. ANS: E
PTS: 1
DIF: Easy
56. Two spheres are made of conducting material. Sphere #2 has twice the radius of Sphere #1. What is the ratio of the capacitance of Sphere #2 to the capacitance of sphere #1? a. 1, since all conducting spheres have the same capacitance. b. 2 c. 4 d. 8 e. A single sphere has no capacitance since a second concentric spherical shell is necessary to make a spherical capacitor. Thus, none of the answers above is correct. ANS: B
PTS: 2
DIF: Average
57. Which of the following materials has the highest dielectric constant? a. air b. Mylar c. paper d. Pyrex glass e. water ANS: E
PTS: 1
DIF: Easy
58. Into the gap between the plates of a parallel plate capacitor of capacitance a slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates. What is the resulting new capacitance? a. b.
c. d. e. ANS: B
PTS: 2
DIF: Average
59. The plates of a parallel plate capacitor of capacitance are horizontal. Into the gap a slab of dielectric material with is placed, filling the bottom half of the gap between the plates. What is the resulting new capacitance? a. b. c. d. e. ANS: E
PTS: 3
DIF: Challenging
60. An electric dipole having dipole moment of magnitude p is placed in a uniform electric field having magnitude E. What is the magnitude of the greatest change in potential energy that can happen for this dipole in this field? a. pE b. c. 4pE d. e. No answer given is correct. ANS: B
PTS: 1
DIF: Easy
PROBLEM 61. Is it feasible to construct an air-filled parallel-plate capacitor that has its two plates separated by 0.10 mm and has a capacitance of 1.0 F? Why or why not? ANS: No. Each plate would have an area of 1.1 107 m2 PTS: 2
DIF: Average
62. Regarding the Earth and a cloud layer 800 m above the Earth as the "plates" of a capacitor, calculate the capacitance if the cloud layer has an area of 1.0 km2. If an electric field of 2.0 106 N/C makes the air break down and conduct electricity (lightning), what is the maximum charge the cloud can hold? ANS: 11.1 nF, 17.7 C PTS: 2
DIF: Average
63. An electron is released from rest at the negative plate of a parallel plate capacitor. If the distance between the plates is 5 mm and the potential difference across the plates is 5 V, with what velocity does the electron hit the positive plate? (me = 9.1 1031 kg, qe = 1.6 1019 C.) ANS: 1.33 106 m/s PTS: 2
DIF: Average
64. A 200-volt battery is connected to a 0.50-microfarad parallel-plate, air-filled capacitor. Now the battery is disconnected, with care taken not to discharge the plates. Some Pyrex glass is then inserted between the plates, completely filling up the space. What is the final potential difference between the plates? (The dielectric constant for Pyrex is = 5.6.) ANS: 36 V PTS: 2
DIF: Average
Chapter 27—Current and Resistance MULTIPLE CHOICE 1. A rod of 2.0-m length and a square (2.0 mm 2.0 mm) cross section is made of a material with a resistivity of 6.0 108 m. If a potential difference of 0.50 V is placed across the ends of the rod, at what rate is heat generated in the rod? a. 3.0 W b. 5.3 W c. 8.3 W d. 1.3 W e. 17 W ANS: C
PTS: 2
DIF: Average
2. An electric device, which heats water by immersing a resistance wire in the water, generates 50 cal of heat per second when an electric potential difference of 12 V is placed across its leads. What is the resistance of the heater wire? (Note: 1 cal = 4.186 J) a. 0.94 b. 0.81 c. 0.58 d. 0.69 e. 1.5 ANS: D
PTS: 2
DIF: Average
3. A light bulb is rated at 30 W when operated at 120 V. How much charge enters (and leaves) the light bulb in 1.0 min? a. 17 C b. 15 C c. 14 C d. 13 C e. 60 C ANS: B
PTS: 2
DIF: Average
4. What maximum power can be generated from an 18-V emf using any combination of a 6.0- resistor and a 9.0- resistor? a. 54 W b. 71 W c. 90 W d. 80 W e. 22 W ANS: C
PTS: 2
DIF: Average
5. An electric heater is constructed by applying a potential difference of 110 V across a wire with a resistance of 5.0 . What is the power rating of the heater? a. 2.0 kW b. 2.4 kW c. 1.7 kW d. 1.5 kW e. 60 kW ANS: B
PTS: 2
DIF: Average
6. How much energy is dissipated as heat during a two-minute time interval by a 1.5-k resistor which has a constant 20-V potential difference across its leads? a. 58 J b. 46 J c. 32 J d. 72 J e. 16 J ANS: C
PTS: 2
DIF: Average
7. A 4.0- resistor has a current of 3.0 A in it for 5.0 min. How many electrons pass through the resistor during this time interval? a. 7.5 1021 b. 5.6 1021 c. 6.6 1021 d. 8.4 1021 e. 2.1 1021 ANS: B
PTS: 2
DIF: Average
8. If 5.0 1021 electrons pass through a 20- resistor in 10 min, what is the potential difference across the resistor? a. 21 V b. 32 V c. 27 V d. 37 V e. 54 V ANS: C
PTS: 2
DIF: Average
9. How many electrons pass through a 20- resistor in 10 min if there is a potential drop of 30 volts across it? a. 5.6 1021
b. c. d. e.
7.5 1021 9.4 1021 1.1 1021 3.8 1021
ANS: A
PTS: 2
DIF: Average
10. A wire (length = 2.0 m, diameter = 1.0 mm) has a resistance of 0.45. What is the resistivity of the material used to make the wire? a. 5.6 107 m b. 1.2 107 m c. 1.8 107 m d. 2.3 107 m e. 7.1 107 m ANS: C
PTS: 2
DIF: Average
11. What is the resistance of a wire made of a material with a resistivity of 3.2 108 m if its length is 2.5 m and its diameter is 0.50 mm? a. 0.16 b. 0.10 c. 1.28 d. 0.41 e. 0.81 ANS: D
PTS: 3
DIF: Challenging
12. A rod (length = 80 cm) with a rectangular cross section (1.5 mm 2.0 mm) has a resistance of 0.20 . What is the resistivity of the material used to make the rod? a. 6.0 107 m b. 3.8 107 m c. 7.5 107 m d. 3.0 107 m e. 4.8 107 m ANS: C
PTS: 2
DIF: Average
13. Most telephone cables are made of copper wire of either 24 or 26 gauge. If the resistance of 24-gauge wire is 137 /mile and the resistance of 26-gauge wire is 220 /mile, what is the ratio of the diameter of 24-gauge wire to that of 26-gauge wire? a. 1.6 b. 1.3 c. 0.62 d. 0.79 e. 0.88 ANS: B
PTS: 3
DIF: Challenging
14. If a mile of 24-gauge copper wire has a resistance of 0.14 k and the resistivity of copper is 1.7 108 m, what is the diameter of the wire? (1 mile = 1.6 km) a. 0.40 mm b. 0.50 mm c. 0.63 mm d. 0.80 mm
e. 0.25 mm ANS: B
PTS: 3
DIF: Challenging
15. A conductor of radius r, length and resistivity has resistance R. What is the new resistance if it is stretched to 4 times its original length? a. R b.
R
c. R d. 4R e. 16R ANS: E
PTS: 2
DIF: Average
16. A small bulb is rated at 7.5 W when operated at 125 V. Its resistance (in ohms) is a. 0.45. b. 7.5. c. 17. d. 940. e. 2 100. ANS: E
PTS: 2
DIF: Average
17. A small bulb is rated at 7.50 W when operated at 125 V. The tungsten filament has a temperature coefficient of resistivity = 4.50 103 / C. When the filament is hot and glowing, its temperature is seven times room temperature (20 C). What is the resistance of the filament (in ohms) at room temperature? a. 234 b. 1 350 c. 2 080 d. 4 530 e. 5 630 ANS: A
PTS: 3
DIF: Challenging
18. The temperature coefficient of resistivity of iron is 5.0 103 / C; that of carbon is 0.50 103 / C. When an iron wire and a carbon rod, each having the same 10 resistance at 20C, are cooled from that temperature to 80C, the new ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature is a. 0.10. b. +1.9. c. +2.1. d. 10. e. +10. ANS: C
PTS: 3
DIF: Challenging
19. A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately. (Al = 2.82 108 m; Al = 3.9 103 / C; nichrome = 1.50 106 m; nichrome = 0.40 103 / C.) The ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire is a. 0.019.
b. c. d. e.
0.10. 0.18. 9.8. 53.
ANS: D
PTS: 2
DIF: Average
20. The electron density in copper is 8.49 1028 electrons/m3. The electron charge is e = 1.60 1019 C. When a 1.00 A current is present in a copper wire with a 0.40 cm2 cross-section, the electron drift velocity, in m/s, with direction defined relative to the current density, is a. 1.84 106. b. +1.84 106. c. 1.84. d. 5.43 10. e. +5.43 10. ANS: A
PTS: 2
DIF: Average
21. In the Drude model of electrical conduction, the current density is directly proportional to a. the average time interval between successive collisions. b. the number of charge carriers per unit volume. c. the square of the electron charge. d. the electric field present in the wire. e. the product of all four quantities listed above. ANS: E
PTS: 1
DIF: Easy
22. In the Drude model of electrical conduction, the current density is NOT directly proportional to a. the average time interval between successive collisions. b. the number of charge carriers per unit volume. c. the square of the electron charge. d. the electric field present in the wire. e. the resistivity of the wire. ANS: E
PTS: 1
DIF: Easy
23. A conductor of radius r, length and resistivity has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. The resistance of the new conductor is a. R b.
R
c. R d. 4R e. 16R ANS: A
PTS: 2
DIF: Average
24. Light bulb A is rated at 60 W and light bulb B is rated at 100 W. Both are designed to operate at 110 V. Which statement is correct? a. The 60 W bulb has a greater resistance and greater current than the 100 W bulb. b. The 60 W bulb has a greater resistance and smaller current than the 100 W bulb. c. The 60 W bulb has a smaller resistance and smaller current than the 100 W bulb. d. The 60 W bulb has a smaller resistance and greater current than the 100 W bulb.
e. We need to know the resistivities of the filaments to answer this question. ANS: B
PTS: 3
DIF: Challenging
25. Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why? a. Arnell, because the conductivity of the wire increases when it is heated. b. Arnell, because the conductivity of the wire decreases when it is heated. c. Jadeen, because the conductivity of a wire is directly proportional to its area and inversely proportional to its length. d. Jadeen, because the conductivity of a copper wire does not increase when it is hammered. e. Both are correct because (b) and (d) are both correct. ANS: E
PTS: 1
DIF: Easy
26. Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why? a. Arnell, because the resistivity of the wire increases when it is heated. b. Arnell, because the resistivity of the wire decreases when it is heated. c. Jadeen, because the resistivity of a wire is inversely proportional to its area and directly proportional to its length. d. Jadeen, because the resistivity of a copper wire does not decrease when it is hammered. e. Both are correct because (a) and (d) are both correct. ANS: E
PTS: 1
DIF: Easy
27. A cook plugs a 500 W crockpot and a 1 000 W kettle into a 240 V power supply, all operating on direct current. When we compare the two, we find that a. Icrockpot < Ikettle and Rcrockpot < Rkettle. b. Icrockpot < Ikettle and Rcrockpot > Rkettle. c. Icrockpot = Ikettle and Rcrockpot = Rkettle. d. Icrockpot > Ikettle and Rcrockpot < Rkettle. e. Icrockpot > Ikettle and Rcrockpot > Rkettle. ANS: B
PTS: 2
DIF: Average
28. To increase the current density in a wire of length and diameter D, you can a. decrease the potential difference between the two ends of the wire. b. increase the potential difference between the two ends of the wire. c. decrease the magnitude of the electric field in the wire. d. heat the wire to a higher temperature. e. combine both (b) and (d). ANS: B
PTS: 1
DIF: Easy
29. A high-resistance material is used as an insulator between the conductors of a length of coaxial cable. The resistance material, which forms a hollow tube, has an inner radius a and an outer radius b, and the insulator provides a resistance R between the conductors. If a second insulator, made of the same material and having the same length, is made with double both the inner radius and the outer radius of the first, what resistance would it provide between the conductors? a. R b. 2 R c. 4 R
d. (ln2)R e. R/(ln2) ANS: A
PTS: 3
DIF: Challenging
PROBLEM 30. What is the resistance of 1 000 m of 4-mm diameter copper wire? (Cu = 1.7 10-8 m) ANS: 1.35 ohm PTS: 2
DIF: Average
31. A high-voltage transmission line carries 1 000 A at 700 kV for a distance of 100 miles. If the resistance per length in the wire is 0.5 /mile, what is the power loss due to resistive losses? ANS: 50 MW PTS: 2
DIF: Average
32. The heating coil of a hot water heater has a resistance of 20 ohms and operates at 210 V. If electrical energy costs 5.5 cents per kW-hr, what does it cost to raise the 200 kg of water in the tank from 15C to 80C? (The specific heat of water is 4 186 J/kgC) ANS: 83 cents PTS: 2
DIF: Average
33. A copper cable is to be designed to carry a current of 300 A with a power loss of only 2.0 watts per meter. What is the required radius of the copper cable? (The resistivity of copper is 1.7 108 m.) ANS: 1.6 cm PTS: 2
DIF: Average
34. An aluminum wire of cross-sectional area 4.0 mm2 is carrying a current of 8.0 A. The density of aluminum is 2.7 g/cm3, and its molar mass is 27 g. Assuming one free electron per aluminum atom, what is the drift speed of the electrons in this wire? ANS:
PTS: 2
DIF: Average
Chapter 28—Direct-Current Circuits MULTIPLE CHOICE
1. At what rate is thermal energy being generated in the 2R-resistor when = 12 V and R = 3.0 ?
a. b. c. d. e.
12 W 24 W 6.0 W 3.0 W 1.5 W
ANS: C
PTS: 2
DIF: Average
2. At what rate is thermal energy generated in the 30- resistor?
a. b. c. d. e.
20 W 27 W 60 W 13 W 30 W
ANS: D
PTS: 2
DIF: Average
3. What is the magnitude of the potential difference across the 20- resistor?
a. 3.2 V b. 7.8 V c. 11 V
d. 5.0 V e. 8.6 V ANS: B
PTS: 2
DIF: Average
4. What is the current in the 10- resistor ?
a. b. c. d. e.
0.60 A 3.0 A 1.2 A 2.4 A 0.30 A
ANS: A
PTS: 2
DIF: Average
5. At what rate is thermal energy generated in the 20- resistor when = 20 V?
a. b. c. d. e.
6.5 W 1.6 W 15 W 26 W 5.7 W
ANS: B
PTS: 2
DIF: Average
6. At what rate is thermal energy generated in the 5- resistor when = 24 V?
a. 13 W b. 3.2 W c. 23 W
d. 39 W e. 51 W ANS: B
PTS: 2
DIF: Average
7. When a 20-V emf is placed across two resistors in series, a current of 2.0 A is present in each of the resistors. When the same emf is placed across the same two resistors in parallel, the current through the emf is 10 A. What is the magnitude of the greater of the two resistances? a. 7.2 b. 7.6 c. 6.9 d. 8.0 e. 2.8 ANS: A
PTS: 3
DIF: Challenging
8. A resistor of unknown resistance and a 15- resistor are connected across a 20-V emf in such a way that a 2.0 A current is observed in the emf. What is the value of the unknown resistance? a. 75 b. 12 c. 7.5 d. 30 e. 5.0 ANS: D
PTS: 2
DIF: Average
9. What is the current in the 15- resistor when = 9.0 V?
a. b. c. d. e.
0.20 A 0.30 A 0.10 A 0.26 A 0.60 A
ANS: A
PTS: 2
DIF: Average
10. How much heat is produced in the 10- resistor in 5.0 s when = 18 V?
a. 72 J
b. c. d. e.
32 J 50 J 18 J 90 J
ANS: D
PTS: 2
DIF: Average
11. Determine when I = 0.50 A and R = 12 .
a. b. c. d. e.
12 V 24 V 30 V 15 V 6.0 V
ANS: B
PTS: 2
DIF: Average
12. Determine R when I = 0.20 A and = 18 V.
a. b. c. d. e.
50 8.0 10 20 30
ANS: D
PTS: 2
13. Determine the current in the 10-V emf.
DIF: Average
a. b. c. d. e.
2.3 A 2.7 A 1.3 A 0.30 A 2.5 A
ANS: A
PTS: 3
DIF: Challenging
14. What is the magnitude of the current in the 20- resistor?
a. b. c. d. e.
0.75 A 0.00 A 0.25 A 0.50 A 1.00 A
ANS: D
PTS: 3
DIF: Challenging
15. Determine the potential difference Va Vb shown in the circuit below.
a. b. c. d. e.
5.0 V +5.0 V 10 V +10 V 0V
ANS: B
PTS: 3
DIF: Challenging
16. What is the potential difference Vb Va shown in the circuit below.
a. b. c. d. e.
8.0 V +8.0 V 18 V +18 V 12 V
ANS: A
PTS: 3
DIF: Challenging
17. At what rate is power supplied by the 10-V emf shown below?
a. b. c. d. e.
10 W +10 W zero +20 W 20 W
ANS: B
PTS: 3
DIF: Challenging
18. If = 8.0 V, at what rate is that emf providing energy to the circuit shown below?
a. b. c. d. e.
8.4 W 7.6 W 5.6 W 11 W 2.0 W
ANS: C
PTS: 3
DIF: Challenging
19. Determine the magnitude and sense (direction) of the current in the 500- resistor when I = 30 mA.
a. b. c. d. e.
56 mA left to right 56 mA right to left 48 mA left to right 48 mA right to left 26 mA left to right
ANS: A
PTS: 2
DIF: Average
20. Determine the magnitude and sense (direction) of the current in the 10- resistor when I = 1.8 A.
a. b. c. d. e.
1.6 A right to left 1.6 A left to right 1.2 A right to left 1.2 A left to right 1.8 A left to right
ANS: A
PTS: 2
21. Determine the resistance R when I = 1.5 A.
DIF: Average
a. b. c. d. e.
40 8.0 85 28 32
ANS: B
PTS: 2
DIF: Average
22. What is the potential difference VB VA when the I = 1.5 A in the circuit segment below?
a. b. c. d. e.
+22 V 22 V 38 V +38 V +2.0 V
ANS: B
PTS: 2
DIF: Average
23. What is the potential difference VB VA when I = 0.50 A in the circuit segment shown below?
a. b. c. d. e.
+28 V +2.0 V 28 V 2.0 V +18 V
ANS: A
PTS: 2
DIF: Average
24. If R = 2.0 k, C = 4.0 mF, = 8.0 V, Q = 20 mC, and I = 3.0 mA, what is the potential difference Vb Va?
a. b. c. d. e.
+7.0 V +19 V +9.0 V 3.0 V 14 V
ANS: C
PTS: 2
DIF: Average
25. If R = 3.0 k, C = 5.0 mF, = 6.0 V, Q = 15 mC, and I = 4.0 mA, what is the potential difference Vb Va?
a. b. c. d. e.
3.0 V +9.0 V 15 V +21 V 6.0 V
ANS: A
PTS: 2
DIF: Average
26. If R = 4.0 k, C = 3.0 mF, = 15 V, Q = 12 mC, and I = 2.0 mA, what is the potential difference Vb Va?
a. b. c. d. e.
+3.0 V 19 V 3.0 V +27 V +21 V
ANS: C
PTS: 2
DIF: Average
27. If R = 3.0 k, C = 6.0 nF, 1 = 10.0 V, Q = 18 nC, 2 = 6.0 V, and I = 5.0 mA, what is the potential difference Vb Va?
a. b. c. d. e.
13 V +28 V +13 V 28 V +2.0 V
ANS: D
PTS: 2
DIF: Average
28. If 1 = 4.0 V, 2 = 12.0 V, R1 = 4 , R2 = 12 , C = 3 F, Q = 18 C, and I = 2.5 A, what is the potential difference Va Vb?
a. b. c. d. e.
30 V 30 V 5.0 V 5.0 V 1.0 V
ANS: A
PTS: 2
DIF: Average
29. If the current in the 4.0- resistor is 1.4 A, what is the magnitude of the potential difference, VA VB?
a. b. c. d. e.
69 V 55 V 62 V 48 V 31 V
ANS: D
PTS: 3
DIF: Challenging
30. If I = 0.40 A in the circuit segment shown below, what is the potential difference Va Vb?
a. 31 V b. 28 V c. 25 V
d. 34 V e. 10 V ANS: C
PTS: 2
DIF: Average
31. If I = 2.0 A in the circuit segment shown below, what is the potential difference VB VA?
a. b. c. d. e.
+10 V 20 V 10 V +20 V +30 V
ANS: C
PTS: 2
DIF: Average
32. Determine the potential difference, VA VB, in the circuit segment shown below when I = 2.0 mA and Q = 50 C.
a. b. c. d. e.
40 V +40 V +20 V 20 V 10 V
ANS: D
PTS: 2
DIF: Average
33. If Q = 400 C and the potential difference VA VB = 10 V in the circuit segment shown below, what is the current in the resistor?
a. b. c. d. e.
1.0 mA right to left 1.0 mA left to right 3.5 mA right to left 3.5 mA left to right None of the above
ANS: A
PTS: 2
DIF: Average
34. If Q = 350 C and I = 4.0 mA in the circuit segment shown below, determine the potential difference, VA VB.
a. b. c. d. e.
30 V +80 V +40 V 40 V +10 V
ANS: D
PTS: 2
DIF: Average
35. In an RC circuit, how many time constants must elapse if an initially uncharged capacitor is to reach 80% of its final potential difference? a. 2.2 b. 1.9 c. 1.6 d. 3.0 e. 5.0 ANS: C
PTS: 2
DIF: Average
36. How many time constants must elapse if an initially charged capacitor is to discharge 55% of its stored energy through a resistor? a. 0.60 b. 0.46 c. 0.52 d. 0.40 e. 1.1 ANS: D
PTS: 3
DIF: Challenging
37. In an RC circuit, what fraction of the final energy is stored in an initially uncharged capacitor after it has been charging for 3.0 time constants? a. 0.84 b. 0.90 c. 0.75 d. 0.60 e. 0.03 ANS: B
PTS: 2
DIF: Average
38. How long will it take a charged 80-F capacitor to lose 20% of its initial energy when it is allowed to discharge through a 45- resistor? a. 0.92 ms b. 0.64 ms c. 0.40 ms d. 0.19 ms e. 0.80 ms ANS: C
PTS: 3
DIF: Challenging
39. At t = 0 the switch S is closed with the capacitor uncharged. If C = 50 F, = 20 V, and R = 4.0 k, what is the charge on the capacitor when I = 2.0 mA?
a. b. c. d. e.
360 C 480 C 240 C 600 C 400 C
ANS: D
PTS: 3
DIF: Challenging
40. At t = 0 the switch S is closed with the capacitor uncharged. If C = 30 F, = 30 V, and R = 5.0 k, at what rate is energy being stored in the capacitor when I = 2.0 mA?
a. b. c. d. e.
32 mW 40 mW 44 mW 36 mW 80 mW
ANS: B
PTS: 2
DIF: Average
41. At t = 0 the switch S is closed with the capacitor uncharged. If C = 40 F, = 50 V, and R = 5.0 k, how much energy is stored by the capacitor when I = 2.0 mA?
a. b. c. d. e.
20 mJ 28 mJ 32 mJ 36 mJ 40 mJ
ANS: C
PTS: 2
DIF: Average
42. At t = 0 the switch S is closed with the capacitor uncharged. If C = 30 F, = 50 V, and R = 10 k, what is the potential difference across the capacitor when I = 2.0 mA?
a. b. c. d. e.
20 V 15 V 25 V 30 V 45 V
ANS: D
PTS: 2
DIF: Average
43. A capacitor in a single-loop RC circuit is charged to 85% of its final potential difference in 2.4 s. What is the time constant for this circuit? a. 1.5 s b. 1.3 s c. 1.7 s d. 1.9 s e. 2.9 s ANS: B
PTS: 2
DIF: Average
44. What is the equivalent resistance between points a and b when R = 13 ?
a. b. c. d. e.
29 23 26 20 4.6
ANS: D
PTS: 2
DIF: Average
45. What is the equivalent resistance between points a and b when R = 30 ?
a. b. c. d. e.
27 21 24 18 7.5
ANS: D
PTS: 2
DIF: Average
46. What is the equivalent resistance between points a and b when R = 12 ?
a. 20 b. 16
c. 24 d. 28 e. 6.0 ANS: B
PTS: 2
DIF: Average
47. What is the equivalent resistance between points a and b?
a. b. c. d. e.
14 8.0 6.0 25 40
ANS: D
PTS: 2
DIF: Average
48. If R1 = 10 , R2 = 15 , R3 = 20 , and I = 0.50 A, at what rate is heat being generated in these resistors?
a. b. c. d. e.
29 W 16 W 22 W 11 W 1.1 W
ANS: D
PTS: 2
DIF: Average
49. If R1 = 3.0 , R2 = 6.0 , R3 = 12 , and I = 0.50 A, at what rate is heat being generated in R1?
a. 20 W b. 17 W c. 12 W
d. 31 W e. 6.0 W ANS: C
PTS: 2
DIF: Average
50. A certain brand of hot dog cooker applies a potential difference (120 V) to opposite ends of the hot dog and cooks by means of the joule heat produced. If 60 kJ is needed to cook each hot dog, what current is needed to cook four hot dogs simultaneously in 3.0 min? a. 11 A b. 2.8 A c. 8.3 A d. 2.1 A e. 3.6 A ANS: A
PTS: 2
DIF: Average
51. If 480 C pass through a 4.0- resistor in 10 min, what is the potential difference across the resistor? a. 3.6 V b. 2.8 V c. 2.4 V d. 3.2 V e. 5.0 V ANS: D
PTS: 2
DIF: Average
52. A 10-V battery is connected to a 15- resistor and an unknown resistor R, as shown. The current in the circuit is 0.40 A. How much heat is produced in the 15- resistor in 2.0 min?
a. b. c. d. e.
0.40 kJ 0.19 kJ 0.29 kJ 0.72 kJ 0.80 kJ
ANS: C
PTS: 2
DIF: Average
53. What is the equivalent resistance between points A and B in the figure when R = 20 ?
a. b. c. d. e.
77 63 70 84 140
ANS: C
PTS: 2
DIF: Average
54. What is the equivalent resistance between points A and B in the figure when R = 18 ?
a. b. c. d. e.
48 64 80 96 110
ANS: D
PTS: 2
DIF: Average
55. What is the equivalent resistance between points A and B in the figure when R = 10 ?
a. b. c. d. e.
20 10 25 15 3.2
ANS: B
PTS: 2
DIF: Average
56. In a loop in a closed circuit, the sum of the currents entering a junction equals the sum of the currents leaving a junction because a. the potential of the nearest battery is the potential at the junction. b. there are no transformations of energy from one type to another in a circuit loop. c. capacitors tend to maintain current through them at a constant value. d. current is used up after it leaves a junction. e. charge is neither created nor destroyed at a junction. ANS: E
PTS: 1
DIF: Easy
57. When a capacitor is fully charged, the current through the capacitor in a direct-current circuit is a. zero. b. at its maximum value. c. equal to the current in a resistive circuit in parallel with the capacitor circuit. d. greater than the current in a resistor that is farther from the battery than the capacitor. e. zero if it is the only capacitor, but maximum if there is another capacitor in series with it. ANS: A
PTS: 1
DIF: Easy
58. The algebraic sum of the changes of potential around any closed circuit loop is a. zero. b. maximum. c. zero only if there are no sources of emf in the loop. d. maximum if there are no sources of emf in the loop. e. equal to the sum of the currents in the branches of the loop. ANS: A
PTS: 1
DIF: Easy
59. The circuit below contains three 100-W light bulbs. The emf = 110 V. Which light bulb(s) is(are) brightest?
a. b. c. d. e.
A B C B and C All three are equally bright.
ANS: A
PTS: 1
DIF: Easy
60. The circuit below contains three 100-watt light bulbs. The emf = 110 V. Which light bulb(s) is(are) the brightest?
a. b. c. d. e.
A B C B and C All three are equally bright.
ANS: A
PTS: 1
DIF: Easy
61. The circuit below contains three 100-watt light bulbs and a capacitor. The emf = 110V. The capacitor is fully charged. Which light bulb(s) is(are) dimmest?
a. b. c. d. e.
A B C A and B All three are equally bright (or dim).
ANS: C
PTS: 1
DIF: Easy
62. The circuit below contains three 100-W light bulbs and a capacitor. The emf = 110V. At the instant the switch S is closed, which light bulb is brightest?
a. A b. B
c. C d. A and B e. All three are equally bright. ANS: C
PTS: 1
DIF: Easy
63. The circuit below contains three resistors, A, B, and C, which all have equal resistances. The emf = 110V. Which resistor generates the most thermal energy after the switch is closed?
a. b. c. d. e.
A B C A and B All three generate equal amounts of thermal energy.
ANS: C
PTS: 1
DIF: Easy
64. The diagram shown represents a portion of a wire in a circuit. A current is flowing in the wire in the direction shown. Under the convention that it is positive charge that flows the electric field points in the direction of the current. How can the electric field change direction where the wire bends?
a. b. c. d.
There is an excess of negative charge in the center of the wire. There is an excess of positive charge at the bottom end of the wire. There is an excess of negative charge at the right end of the upper portion of the wire. There is an accumulation of positive charge on the surface, particularly at the bend, such that the sum of electric fields gives the new electric field. e. There is an accumulation of electrical potential as the current traverses the wire: The higher potential in the lower half is the source of the field. ANS: D
PTS: 1
DIF: Easy
65. The circuit below contains three 100-W light bulbs and a capacitor. The emf is 110 V and the capacitor is fully charged. Which light bulb(s) is(are) brightest?
a. b. c. d. e.
A B C A and B A and C
ANS: B
PTS: 1
DIF: Easy
66. The circuit below contains 4 100-W light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?
a. b. c. d. e.
A B C D C and D
ANS: B
PTS: 1
DIF: Easy
67. The circuit below contains 4 100-W light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?
a. b. c. d.
A B C D
e. C and D ANS: B
PTS: 1
DIF: Easy
68. The circuit below contains 3 100-W light bulbs and a capacitor. The emf is 110 V. Which light bulb(s) is(are) brightest? (Assume the capacitor is fully charged.)
a. b. c. d. e.
A B C A and B All three are equally bright.
ANS: D
PTS: 1
DIF: Easy
69. Which of the identical light bulb(s) is(are) brightest when the capacitor has half its maximum charge?
a. b. c. d. e.
A B C A and B All three are equally bright.
ANS: B
PTS: 1
DIF: Easy
70. The circuit below contains 5 identical light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?
a. b. c. d. e.
A: The one closest to the positive terminal of the battery. A and C: The bulbs closest to the positive terminal of the battery. A and B: Because they are closest to the terminals of the battery. C and D: Because they receive current from A and B and from E. E: Because the potential difference across E is that of the battery.
ANS: E
PTS: 1
DIF: Easy
71. The battery is disconnected from a series RC circuit after the capacitor is fully charged and is replaced by an open switch. When the switch is closed, a. the current through the resistor is always greater than the current through the capacitor. b. the current through the resistor is always less than the current through the capacitor. c. the current through the resistor is always equal to the current through the capacitor. d. the capacitor does not allow current to pass. e. the current stops in the resistor. ANS: C
PTS: 1
DIF: Easy
72. The capacitors are completely discharged in the circuit shown below.
The two resistors have the same resistance R and the two capacitors have the same capacitance C. After the switch is closed, the current a. is greatest in C1. b. is greatest in C2. c. is greatest in R1. d. is greatest in R2. e. is the same in C1, C2, R1 and R2. ANS: E
PTS: 1
73. Which two circuits are exactly equivalent?
DIF: Easy
a. b. c. d. e.
A and B B and C C and D D and E B and E
ANS: E
PTS: 1
DIF: Easy
74. A circuit consists of 2N resistors, all of resistance R, connected as shown below. A potential difference V is applied to one end, and the other end is at ground potential. The equivalent resistance of the circuit is
a. b. R. c.
.
.
d. NR. e. 2NR. ANS: C
PTS: 2
DIF: Average
75. A circuit consists of N resistors, all of resistance R, connected as shown below. A potential difference V is applied to the circuit. The equivalent resistance of the circuit is
a.
.
b. R. c.
.
d. NR. e. 4NR. ANS: C
PTS: 2
DIF: Average
76. A circuit consists of N resistors, all of resistance R, connected as shown below. A potential difference V is applied to the circuit. The equivalent resistance of the circuit is
a. b.
. .
c. R. d. NR. e. 2NR. ANS: B
PTS: 1
DIF: Easy
77. The circuit below shows three resistors in parallel. R3 > R2 > R1. The resistors are all made of the same wire with the same diameter but have different lengths. Rank the magnitudes of the electric fields in the resistors from least to greatest.
a. b. c. d. e.
E3 < E2 < E1. E2 < E1 = E3. E1 = E2 = E3. E1 = E3 < E2. E1 < E2 < E3.
ANS: A
PTS: 2
DIF: Average
78. The circuit below shows three resistors in series. R3 > R2 > R1. The resistors are all made of the same wire with the same diameter but have different lengths. Rank the magnitudes of the electric fields in the resistors from least to greatest.
a. b. c. d. e.
E3 < E2 < E1. E2 < E1 = E3. E1 = E2 = E3. E1 = E3 < E2. E1 < E2 < E3.
ANS: C
PTS: 2
DIF: Average
79. A series circuit consists of a 100 V DC power source, a 100 resistor, and a variable resistor of resistance R, which varies from 0 to 100 . The current in the circuit is
a. b. c. d. e.
directly proportional to R. inversely proportional to R. directly proportional to (100 + R). inversely proportional to (100 + R). neither directly nor inversely proportional to R or to (100 + R).
ANS: D
PTS: 1
DIF: Easy
80. A parallel circuit consists of a 100 V DC power source, a 100 resistor, and a variable resistor of resistance R, which varies from 0 to 100 . The current in the circuit is
a. b. c. d. e.
directly proportional to R. inversely proportional to R. directly proportional to (100 + R). inversely proportional to (100 + R). neither directly nor inversely proportional to R or to (100 + R).
ANS: E
PTS: 2
DIF: Average
81. A battery has an internal resistance of 4.0 . Which of the following load resistors would have the most power delivered to it when connected across the battery? a. 1.4 b. 2.0 c. 4.0 d. 8.0 e. 16 ANS: C
PTS: 2
DIF: Average
PROBLEM 82. What is the maximum number of 100-W lightbulbs you can connect in parallel in a 120-V home circuit without tripping the 20-A circuit breaker? ANS: 23 PTS: 2
DIF: Average
83. A 5000- resistor and a 50-F capacitor are connected in series at t = 0 with a 6-V battery. The capacitor is initially uncharged. What is the current in the circuit at t = 0? At t = 0.5 s? What is the maximum charge stored on the capacitor? ANS: 1.2 mA, 0.162 mA, 300 C PTS: 3
DIF: Challenging
84. An initially uncharged 10-F capacitor is charged by a 10-V battery through a resistance R. The capacitor reaches a potential difference of 4 V in a period of 3 s after the charging began. Find the value of R. ANS: 587 k PTS: 3
DIF: Challenging
Chapter 29—Magnetic Fields MULTIPLE CHOICE 1. An electron has a velocity of 6.0 106 m/s in the positive x direction at a point where the magnetic field has the components Bx = 3.0 T, By = 1.5 T, and Bz = 2.0 T. What is the magnitude of the acceleration of the electron at this point? a. 2.1 1018 m/s2 b. 1.6 1018 m/s2 c. 2.6 1018 m/s2 d. 3.2 1018 m/s2 e. 3.7 1018 m/s2 ANS: C
PTS: 3
DIF: Challenging
2. A particle (q = 5.0 nC, m = 3.0 g) moves in a region where the magnetic field has components Bx = 2.0 mT, By = 3.0 mT, and Bz = 4.0 mT. At an instant when the speed of the particle is 5.0 km/s and the direction of its velocity is 120 relative to the magnetic field, what is the magnitude of the acceleration of the particle? a. 33 m/s2 b. 17 m/s2 c. 39 m/s2 d. 25 m/s2 e. 45 m/s2 ANS: C
PTS: 2
DIF: Average
3. A particle (q = 4.0 C, m = 5.0 mg) moves in a uniform magnetic field with a velocity having a magnitude of 2.0 km/s and a direction that is 50 away from that of the magnetic field. The particle is observed to have an acceleration with a magnitude of 5.8 m/s2. What is the magnitude of the magnetic field? a. 5.3 mT b. 4.9 mT c. 5.1 mT d. 4.7 mT e. 3.6 mT ANS: D
PTS: 2
DIF: Average
4. An electron moving in the positive x direction experiences a magnetic force in the positive z direction. If Bx = 0, what is the direction of the magnetic field? a. negative y direction b. positive y direction c. negative z direction d. positive z direction e. negative x direction ANS: A
PTS: 1
DIF: Easy
5. A 2.0-C charge moves with a velocity of ( ) m/s and experiences a magnetic force of ( ) N. The x component of the magnetic field is equal to zero. Determine the y component of the magnetic field. a. 3.0 T b. +3.0 T c. +5.0 T d. 5.0 T e. +6.0 T ANS: B
PTS: 3
DIF: Challenging
6. A 2.0-C charge moves with a velocity of ( ) m/s and experiences a magnetic force of ( ) N. The x component of the magnetic field is equal to zero. Determine the z component of the magnetic field. a. 3.0 T b. +3.0 T c. +5.0 T d. 5.0 T e. +6.0 T
ANS: C
PTS: 2
DIF: Average
7. A particle (mass = 2.0 mg, charge = 6.0 C) moves in the positive direction along the x axis with a velocity of 3.0 km/s. It enters a magnetic field of ( ) mT. What is the acceleration of the particle? a. (36 27 ) m/s2 b. (36 + 27 ) m/s2 c. (24 + 18 ) m/s2 d. (24 18 ) m/s2 e. (24 27 ) m/s2 ANS: A
PTS: 2
DIF: Average
8. A particle (mass = 6.0 mg) moves with a speed of 4.0 km/s in a direction that makes an angle of 37 above the positive x axis in the xy plane. At the instant it enters a magnetic field of (5.0 ) mT it experiences an acceleration of (8.0 ) m/s2. What is the charge of the particle? a. 4.8 C b. 4.0 C c. 4.0 C d. 4.8 C e. 5.0 C ANS: C
PTS: 2
DIF: Average
9. A positively charged particle has a velocity in the negative z direction at point P. The magnetic force on the particle at this point is in the negative y direction. Which one of the following statements about the magnetic field at point P can be determined from this data? a. Bx is positive. b. Bz is positive. c. By is negative. d. By is positive. e. Bx is negative. ANS: A
PTS: 1
DIF: Easy
10. A charged particle (mass = 4.0 g, charge = 5.0 C) moves in a region where the only force on it is magnetic. What is the magnitude of the acceleration of the particle at a point where the speed of the particle is 5.0 km/s, the magnitude of the magnetic field is 8.0 mT, and the angle between the direction of the magnetic field and the velocity of the particle is 60? a. 39 km/s2 b. 43 km/s2 c. 48 km/s2 d. 52 km/s2 e. 25 km/s2 ANS: B
PTS: 2
DIF: Average
11. A charged particle (mass = M, charge = Q > 0) moves in a region of space where the magnetic field has a constant magnitude of B and a downward direction. What is the magnetic force on the particle at an instant when it is moving horizontally toward the north with speed V? a. QVB toward the east b. Zero
c. QVB toward the west d. QVB upward e. QVB toward the south ANS: C
PTS: 1
DIF: Easy
12. A 2.0-m wire carries a current of 15 A directed along the positive x axis in a region where the magnetic field is uniform and given by B = (30 40 ) mT. What is the resulting magnetic force on the wire? a. (+1.2 ) N b. (1.2 ) N c. (1.5 ) N d. (+1.5 ) N e. (+0.90 ) N ANS: B
PTS: 2
DIF: Average
13. A straight wire carries a current of 40 A in a uniform magnetic field (magnitude = 80 mT). If the force per unit length on this wire is 2.0 N/m, determine the angle between the wire and the magnetic field. a. either 39 or 141 b. either 25 or 155 c. either 70 or 110 d. either 42 or 138 e. either 65 or 115 ANS: A
PTS: 2
DIF: Average
14. A segment of wire carries a current of 25 A along the x axis from x = 2.0 m to x = 0 and then along the y axis from y = 0 to y = 3.0 m. In this region of space, the magnetic field is equal to 40 mT in the positive z direction. What is the magnitude of the force on this segment of wire? a. 2.0 N b. 5.0 N c. 1.0 N d. 3.6 N e. 3.0 N ANS: D
PTS: 2
DIF: Average
15. A segment of wire carries a current of 25 A along the x axis from x = 2.0 m to x = 0 and then along the z axis from z = 0 to z = 3.0m. In this region of space, the magnetic field is equal to 40 mT in the positive z direction. What is the magnitude of the force on this segment of wire? a. 1.0 N b. 5.0 N c. 2.0 N d. 3.6 N e. 3.0 N ANS: C
PTS: 2
DIF: Average
16. A straight wire of length 70 cm carries a current of 50 A and makes an angle of 60 with a uniform magnetic field. If the force on the wire is 1.0 N what is the magnitude of B? a. 41 mT b. 33 mT c. 55 mT
d. 87 mT e. 57 mT ANS: B
PTS: 2
DIF: Average
17. What is the magnitude of the magnetic force on a charged particle (Q = 5.0 C) moving with a speed of 80 km/s in the positive x direction at a point where Bx = 5.0 T, By = 4.0 T, and Bz = 3.0 T? a. 2.8 N b. 1.6 N c. 1.2 N d. 2.0 N e. 0.4 N ANS: D
PTS: 2
DIF: Average
18. A straight wire of length L carries a current I in the positive z direction in a region where the magnetic field is uniform and specified by Bx = 3B, By = 2B, and Bz = B, where B is a constant. What is the magnitude of the magnetic force on the wire? a. 3.2 ILB b. 5.0 ILB c. 4.2 ILB d. 3.6 ILB e. 1.0 ILB ANS: D
PTS: 2
DIF: Average
19. A straight wire is bent into the shape shown. Determine the net magnetic force on the wire when the current I travels in the direction shown in the magnetic field .
a. b. c. d. e.
2IBL in the z direction 2IBL in the +z direction 4IBL in the +z direction 4IBL in the z direction zero
ANS: B
PTS: 2
DIF: Average
20. A straight wire is bent into the shape shown. Determine the net magnetic force on the wire.
a. b. c. d. e.
Zero IBL in the +z direction IBL in the z direction 1.7 IBL in the +z direction 1.4 IBL in the z direction
ANS: A
PTS: 2
DIF: Average
21. What is the magnetic force on a 2.0-m length of (straight) wire carrying a current of 30 A in a region where a uniform magnetic field has a magnitude of 55 mT and is directed at an angle of 20 away from the wire? a. 1.5 N b. 1.3 N c. 1.1 N d. 1.7 N e. 3.1 N ANS: C
PTS: 2
DIF: Average
22. The figure shows the orientation of a rectangular loop consisting of 80 closely wrapped turns each carrying a current I. The magnetic field in the region is ( ) mT. The loop can turn about the y axis. If = 30, a = 0.40 m, b = 0.30 m, and I = 8.0 A, what is the magnitude of the torque exerted on the loop?
a. b. c. d. e.
2.5 N m 1.5 N m 3.1 N m 2.7 N m 0.34 N m
ANS: D
PTS: 2
DIF: Average
23. A current of 4.0 A is maintained in a single circular loop having a circumference of 80 cm. An external magnetic field of 2.0 T is directed so that the angle between the field and the plane of the loop is 20. Determine the magnitude of the torque exerted on the loop by the magnetic forces acting upon it. a. 0.41 N m b. 0.14 N m c. 0.38 N m d. 0.27 N m
e. 0.77 N m ANS: C
PTS: 2
DIF: Average
24. The figure shows the orientation of a flat circular loop consisting of 50 closely wrapped turns each carrying a current I. The magnetic field in the region is directed in the positive z direction and has a magnitude of 50 mT. The loop can turn about the y axis. If = 20, R = 0.50 m, and I = 12A, what is the magnitude of the torque exerted on the loop?
a. b. c. d. e.
8.1 N m 24 N m 22 N m 13 N m 16 N m
ANS: A
PTS: 2
DIF: Average
25. What current must be maintained in a square loop (50 cm on a side) to create a torque of 1.0 N m about an axis through its center and parallel to one of its sides when a magnetic field of magnitude 70 mT is directed at 40 to the plane of the loop? a. 66 A b. 89 A c. 61 A d. 75 A e. 37 A ANS: D
PTS: 2
DIF: Average
26. A straight 10-cm wire bent at its midpoint so as to form an angle of 90 carries a current of 10 A. It lies in the xy plane in a region where the magnetic field is in the positive z direction and has a constant magnitude of 3.0 mT. What is the magnitude of the magnetic force on this wire? a. 3.2 mN b. 2.1 mN c. 5.3 mN d. 4.2 mN e. 6.0 mN ANS: B
PTS: 2
DIF: Average
27. A wire (mass = 50 g, length = 40 cm) is suspended horizontally by two vertical wires which conduct a current I = 8.0 A, as shown in the figure. The magnetic field in the region is into the paper and has a magnitude of 60 mT. What is the tension in either wire?
a. b. c. d. e.
0.15 N 0.68 N 0.30 N 0.34 N 0.10 N
ANS: D
PTS: 2
DIF: Average
28. A circular loop (radius = 0.50 m) carries a current of 3.0 A and has unit normal vector of ( )/3. What is the x component of the torque on this loop when it is placed in a uniform magnetic field of ( )T? a. 4.7 N m b. 3.1 N m c. 19 N m d. 9.4 N m e. 12 N m ANS: D
PTS: 2
DIF: Average
29. A square loop (L = 0.20 m) consists of 50 closely wrapped turns, each carrying a current of 0.50 A. The loop is oriented as shown in a uniform magnetic field of 0.40 T directed in the positive y direction. What is the magnitude of the torque on the loop?
a. b. c. d. e.
0.21 N m 0.20 N m 0.35 N m 0.12 N m 1.73 N m
ANS: C
PTS: 2
DIF: Average
30. A rectangular coil (0.20 m 0.80 m) has 200 turns and is in a uniform magnetic field of 0.30 T. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is 0.080 N m. What is the current in the coil? a. 5.0 mA b. 1.7 A
c. 8.3 mA d. 1.0 A e. 42 mA ANS: C
PTS: 2
DIF: Average
31. A circular coil (radius = 0.40 m) has 160 turns and is in a uniform magnetic field. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is 0.16 N m when the current in the coil is 4.0 mA. What is the magnitude of the magnetic field? a. 0.37 T b. 1.6 T c. 0.50 T d. 1.2 T e. 2.5 T ANS: C
PTS: 2
DIF: Average
32. A uniform magnetic field of 0.50 T is directed along the positive x axis. A proton moving with a speed of 60 km/s enters this field. The helical path followed by the proton shown has a pitch of 5.0 mm. Determine the angle between the magnetic field and the velocity of the proton.
a. b. c. d. e.
39 51 44 34 71
ANS: B
PTS: 3
DIF: Challenging
33. A deuteron is accelerated from rest through a 10-kV potential difference and then moves perpendicularly to a uniform magnetic field with B = 1.6 T. What is the radius of the resulting circular path? (deuteron: m = 3.3 1027 kg, q = 1.6 1019 C) a. 19 mm b. 13 mm c. 20 mm d. 10 mm e. 9.0 mm ANS: B
PTS: 2
DIF: Average
34. A particle (m = 3.0 g, q = 5.0 C) moves in a uniform magnetic field given by ( ) mT. At t = 0 the velocity of the particle is equal to ( ) m/s. The subsequent path of the particle is a. circular with a 50-cm radius. b. helical with a 6.3-cm pitch. c. circular with a period of 31 ms.
d. helical with a 40-cm radius. e. none of the above ANS: D
PTS: 2
DIF: Average
35. A 500-eV electron and a 300-eV electron trapped in a uniform magnetic field move in circular paths in a plane perpendicular to the magnetic field. What is the ratio of the radii of their orbits? a. 2.8 b. 1.7 c. 1.3 d. 4.0 e. 1.0 ANS: C
PTS: 2
DIF: Average
36. The boundary shown is that of a uniform magnetic field directed in the positive z direction. An electron enters the magnetic field with a velocity pointing along the x axis and exits 0.63 s later at point A. What is the magnitude of the magnetic field?
a. b. c. d. e.
18 T 14 T 28 T 34 T 227 T
ANS: B
PTS: 3
DIF: Challenging
37. A proton moves around a circular path (radius = 2.0 mm) in a uniform 0.25-T magnetic field. What total distance does this proton travel during a 1.0-s time interval? (m = 1.67 1027 kg, q = 1.6 1019 C) a. 82 km b. 59 km c. 71 km d. 48 km e. 7.5 km ANS: D
PTS: 2
DIF: Average
38. A charged particle (m = 2.0 g, q = 50 C) moves in a region of uniform field along a helical path (radius = 4.0 cm, pitch = 8.0 cm) as shown. What is the angle between the velocity of the particle and the magnetic field?
a. b. c. d. e.
27 72 63 18 58
ANS: B
PTS: 2
DIF: Average
39. A charged particle moves in a region of uniform magnetic field along a helical path (radius = 5.0 cm, pitch = 12 cm, period = 5.0 ms). What is the speed of this particle as it moves along this path? a. 67 m/s b. 26 m/s c. 63 m/s d. 24 m/s e. 87 m/s ANS: A
PTS: 2
DIF: Average
40. A charged particle (m = 5.0 g, q = 70 C) moves horizontally at a constant speed of 30 km/s in a region where the free fall gravitational acceleration is 9.8 m/s2 downward, the electric field is 700 N/C upward, and the magnetic field is perpendicular to the velocity of the particle. What is the magnitude of the magnetic field in this region? a. 47 mT b. zero c. 23 mT d. 35 mT e. 12 mT ANS: A
PTS: 3
DIF: Challenging
41. Two single charged ions moving perpendicularly to a uniform magnetic field (B = 0.40 T) with speeds of 5 000 km/s follow circular paths that differ in diameter by 5.0 cm. What is the difference in the mass of these two ions? a. 2.6 1028 kg b. 6.4 1028 kg c. 3.2 1028 kg d. 5.1 1028 kg e. 1.1 1028 kg ANS: C
PTS: 2
DIF: Average
42. A charged particle moves in a region of uniform magnetic field along a helical path (radius = 4.0 cm, pitch = 20 cm, period = 2.0 ms). What is the speed of the particle as it moves along this path? a. 0.13 km/s b. 0.10 km/s
c. 0.16 km/s d. 0.23 km/s e. 0.06 km/s ANS: C
PTS: 3
DIF: Challenging
43. What is the radius of curvature of the path of a 3.0-keV proton in a perpendicular magnetic field of magnitude 0.80 T? a. 9.9 mm b. 1.1 cm c. 1.3 cm d. 1.4 cm e. 7.6 mm ANS: A
PTS: 2
DIF: Average
44. An electron moves in a region where the magnetic field is uniform and has a magnitude of 80 T. The electron follows a helical path which has a pitch of 9.0 mm and a radius of 2.0 mm. What is the speed of this electron as it moves in this region? a. 48 km/s b. 28 km/s c. 20 km/s d. 35 km/s e. 8.0 km/s ANS: D
PTS: 3
DIF: Challenging
45. An electron moves in a region where the magnetic field is uniform, has a magnitude of 60 T, and points in the positive x direction. At t = 0 the electron has a velocity that has an x component of 30 km/s, a y component of 40 km/s, and a z component of zero. What is the radius of the resulting helical path? a. 4.7 mm b. 18 mm c. 3.8 mm d. 2.8 mm e. 5.7 mm ANS: C
PTS: 2
DIF: Average
46. An electron follows a circular path (radius = 15 cm) in a uniform magnetic field (magnitude = 3.0 G). What is the period of this motion? a. 0.12 s b. 1.2 ms c. 0.18 s d. 1.8 ms e. 1.8 s ANS: A
PTS: 2
DIF: Average
47. A proton with a kinetic energy of 0.20 keV follows a circular path in a region where the magnetic field is uniform and has a magnitude of 60 mT. What is the radius of this path? a. 4.1 cm b. 2.9 cm c. 3.4 cm d. 5.1 cm
e. 2.4 cm ANS: C
PTS: 2
DIF: Average
48. A proton is accelerated from rest through a potential difference of 150 V. It then enters a region of uniform magnetic field and moves in a circular path (radius = 12 cm). What is the magnitude of the magnetic field in this region? a. 18 mT b. 12 mT c. 15 mT d. 22 mT e. 10 mT ANS: C
PTS: 2
DIF: Average
49. A proton is accelerated from rest through a potential difference of 2.5 kV and then moves perpendicularly through a uniform 0.60-T magnetic field. What is the radius of the resulting path? a. 15 mm b. 12 mm c. 18 mm d. 24 mm e. 8.5 mm ANS: B
PTS: 2
DIF: Average
50. An electron moves in a region where the magnetic field is uniform, has a magnitude of 60 T, and points in the positive x direction. At t = 0 the electron has a velocity that has an x component of 30 km/s, a y component of 40 km/s, and a z component of zero. What is the pitch of the resulting helical path? a. 13 mm b. 32 mm c. 24 mm d. 18 mm e. 3.8 mm ANS: D
PTS: 2
DIF: Average
51. What is the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E = 4.0 kV/m and B = 8.0 mT? a. 0.65 eV b. 0.71 eV c. 0.84 eV d. 0.54 eV e. 1.4 eV ANS: B
PTS: 2
DIF: Average
52. What value of B should be used in a velocity selector to separate out 2.0-keV protons if E is fixed at 80 kV/m? a. 0.18 T b. 0.11 T c. 0.15 T d. 0.13 T e. 0.23 T ANS: D
PTS: 2
DIF: Average
53. A velocity selector uses a fixed electric field of magnitude E and the magnetic field is varied to select particles of various energies. If a magnetic field of magnitude B is used to select a particle of a certain energy and mass, what magnitude of magnetic field is needed to select a particle of equal mass but twice the energy? a. 0.50 B b. 1.4 B c. 2.0 B d. 0.71 B e. 1.7 B ANS: D
PTS: 2
DIF: Average
54. Equal charges, one at rest, the other having a velocity of 104 m/s, are released in a uniform magnetic field. Which charge has the largest force exerted on it by the magnetic field? a. The charge that is at rest. b. The charge that is moving, if its velocity is parallel to the magnetic field direction when it is released. c. The charge that is moving if its velocity makes an angle of 45o with the direction of the magnetic field when it is released. d. The charge that is moving if its velocity is perpendicular to the magnetic field direction when it is released. e. All the charges above experience equal forces when released in the same magnetic field. ANS: D
PTS: 1
DIF: Easy
55. Three particles of equal charge, X, Y, and Z, enter a uniform magnetic field B. X has velocity of magnitude v parallel to the field. Y has velocity of magnitude v perpendicular to the field. Z has equal velocity components v parallel and perpendicular to the field. Rank the radii of their orbits from least to greatest. a. Rx = Ry < Rz. b. Rx < Ry < Rz. c. Rx = Ry = Rz. d. Rx > Ry > Rz. e. Rx < Ry = . ANS: D
PTS: 1
DIF: Easy
56. One reason why we know that magnetic fields are not the same as electric fields is because the force exerted on a charge +q a. is in opposite directions in electric and magnetic fields. b. is in the same direction in electric and magnetic fields. c. is parallel to a magnetic field and perpendicular to an electric field. d. is parallel to an electric field and perpendicular to a magnetic field. e. is zero in both if the charge is not moving. ANS: D
PTS: 1
DIF: Easy
57. You stand near the earth's equator. A positively charged particle that starts moving parallel to the surface of the earth in a straight line directed east is initially deflected upwards. If you know there are no electric fields in the vicinity, a possible reason why the particle does not initially acquire a downward component of velocity is because near the equator the magnetic field lines of the earth are directed a. upward.
b. c. d. e.
downward. from south to north. from north to south. from east to west.
ANS: C
PTS: 1
DIF: Easy
58. A current loop is oriented in three different positions relative to a uniform magnetic field. In position 1 the plane of the loop is perpendicular to the field lines. In position 2 and 3 the plane of the loop is parallel to the field as shown. The torque on the loop is maximum in
a. b. c. d. e.
position 1. position 2. position 3 positions 2 and 3. all three positions.
ANS: D
PTS: 1
DIF: Easy
59. A magnetic field is directed out of the page. Two charged particles enter from the top and take the paths shown in the figure. Which statement is correct?
a. b. c. d. e.
Particle 1 has a positive charge and particle 2 has a negative charge. Both particles are positively charged. Both particles are negatively charged. Particle one has a negative charge and particle 2 has a positive charge. The direction of the paths depends on the magnitude of the velocity, not on the sign of the charge.
ANS: A
PTS: 1
DIF: Easy
60. A coaxial cable has an inner cylindrical conductor surrounded by cylindrical insulation and an outer cylindrical conducting shell. The outer shell carries the same current but in the opposite direction from that in the inner conductor as shown. If the coaxial cable sits in a uniform magnetic field directed upwards with respect to the cable, the effect of the field on the cable is
a. b. c. d.
a net force to the left. a net force to the right. a net force upwards. no net force but a slight shift of the inner conductor to the left and the outer conductor to the right. e. no net force but a slight shift of the inner conductor to the right and the outer conductor to the left. ANS: D
PTS: 1
DIF: Easy
61. The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.
When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is a. A. b. B. c. C. d. D. e. E. ANS: C
PTS: 1
DIF: Easy
62. The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is
a. D. b. E.
c. F. d. G. e. H. ANS: B
PTS: 1
DIF: Easy
63. The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is
a. b. c. d. e.
E. F. G. H. A.
ANS: C
PTS: 1
DIF: Easy
64. The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is
a. b. c. d. e.
E. F. G. H. A.
ANS: E
PTS: 1
DIF: Easy
65. The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T that are perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed up out of the page, the direction of the magnetic field at P is closest to the direction of
a. b. c. d. e.
E. F. G. H. A
ANS: E
PTS: 1
DIF: Easy
66. The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed up out of the page, the direction of the magnetic field at P is closest to the direction of
a. b. c. d. e.
E. F. G. H. A.
ANS: A
PTS: 1
DIF: Easy
67. The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed into the page, the direction of the magnetic field at P is closest to the direction of
a. b. c. d. e.
E. F. G. H. A.
ANS: E
PTS: 1
DIF: Easy
68. The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed into the page, the direction of the magnetic field at P is closest to the direction of
a. b. c. d. e.
A B. C. D. E.
ANS: E
PTS: 1
DIF: Easy
69. The magnetic field in a region of space is parallel to the surface of a long flat table. Imagine that this page is lying flat on the table. When current is present in the coil, which is lying on the table, the coil tends to rotate so that the left side moves up and the right side moves down. The magnetic field is
a. b. c. d. e.
directed parallel to the page and downwards. directed parallel to the page and upwards. directed parallel to the page and to the right. directed parallel to the page and to the left. in a direction that cannot be determined in this experiment
ANS: C
PTS: 1
DIF: Easy
70. A charged particle (mass = M, charge = Q > 0) moves in a region of space where the magnetic field has a constant magnitude of B and a downward direction. What is the magnetic force on the particle at an instant when it is moving horizontally toward the north with a speed V? a. QVB toward the east b. Zero c. QVB toward the west d. QVB upward e. QVB toward the south ANS: C
PTS: 1
DIF: Easy
71. An explorer walks into a lab in a science building. She has a compass in her hand and finds that the south pole of her compass points toward the room's East wall when she is nearer that wall and toward the west wall when she is nearer that wall. You could explain this if magnetized metal had been installed in the East and West walls with North poles pointing into the room. If no magnetic material was installed in the North or South walls of the room, she would expect that a. the south pole of the compass would tend to point toward those walls. b. the north pole of the compass would tend to point toward those walls. c. the compass needle would not point in any particular direction. d. the north pole of the compass needle would tend to point toward the centers of those walls, but the south pole would tend to point toward the sides of those walls. e. the south pole of the compass needle would tend to point toward the centers of those walls, but the north pole would tend to point toward the sides of those walls. ANS: B
PTS: 2
DIF: Average
72. A physicist claims that she has found a new particle with a mass 200 000 times the mass of the proton (1.67 1027 kg) and a charge of 3.20 1019 C. If she is correct, such a particle traveling in a circle in a uniform 5.00 T magnetic field at a velocity of 2 500 m/s will have a radius of a. 0.261 m. b. 0.522 m. c. 1.04 m. d. 3.27 m. e. 3.13 1026 m. ANS: B
PTS: 2
DIF: Average
73. An unusual lightning strike has a vertical portion with a positive current of +400 A upwards. The Earth's magnetic field at that location is parallel to the ground and has a magnitude of 30 T. In N, the force exerted by the Earth's magnetic field on the 25 m-long current is a. 0. b. 0.012 N, East. c. 0.012 N, West. d. 0.30 N, West. e. 300 N, East. ANS: D
PTS: 2
DIF: Average
74. An unusual lightning strike has a vertical portion with a current of 400 A downwards. The Earth's magnetic field at that location is parallel to the ground and has a magnitude of 30 T. In N, the force exerted by the Earth's magnetic field on the 25 m-long current is a. 0. b. 0.012 N, East. c. 0.012 N, West. d. 0.30 N, West. e. 300 N, East. ANS: D
PTS: 2
DIF: Average
75. Bert says that a charged particle in a vacuum can travel in a helix only if a uniform electric field and a uniform magnetic field are both present and both parallel to the axis of the helix. Stuart says that only a magnetic field with a component parallel to the axis of the helix is needed. Which one, if either, is correct, and why? a. Bert, because the charged particle's velocity can have a vertical component only if an electric field in the vertical direction is present. b. Stuart, because a component of velocity in the vertical direction is not changed by a
vertical component of a magnetic field. c. Bert, because a component of velocity in the vertical direction is changed by a vertical component of a magnetic field. d. Stuart, because an electric field in the vertical direction would cause the particle to come to a complete stop. e. Neither, because particles cannot move in helical paths in the presence of magnetic and electric fields. ANS: B
PTS: 1
DIF: Easy
76. The reason the north pole of a bar magnet free to rotate points north is because a. the south geographic pole of the earth is the earth's magnetic north pole. b. the south geographic pole of the earth is the earth's magnetic south pole. c. there is a net accumulation of negative magnetic charge at the earth's south geographic pole. d. there is a net accumulation of positive magnetic charge at the earth's north geographic pole. e. the north geographic pole of the earth is the earth's magnetic north pole. ANS: A
PTS: 1
DIF: Easy
PROBLEM 77. A magnetic field of 2.00 T is applied to a bubble chamber to make the tracks of protons and other charged particles identifiable by the radius of the circles they move in. If a high-energy proton moves along an arc of a 3.30-m circle, what is the momentum of the proton? [q = 1.60 1019 C, m = 1.67 1027 kg] ANS: 1.06 C 1018 kg m/s PTS: 2
DIF: Average
78. At what speed would a proton need to circle the Earth at a height of 1 000 km above the equator if the Earth's magnetic field is horizontal and directed north-south, with an intensity of 4.00 108 T? (The radius of the Earth is 6 400 km and the charge and mass of the proton are q = 1.60 1019 C and mp = 1.67 1027 kg. Ignore relativistic corrections.) ANS: 2.84 107 m/s PTS: 2
DIF: Average
79. A thin ribbon of a silver alloy 2.00-cm wide and 0.015 0-mm thick carries a current of 6.98 A perpendicular to a magnetic field. The Hall voltage is found to be 1.24 104 V when the magnetic field is 2.50 T. Calculate n, the number of charge carriers per cubic meter. ANS: 5.86 1028/m3 PTS: 2
DIF: Average
80. A stream of electrons passes through a velocity filter where the crossed magnetic and electric fields are 0.020 T and 5.00 104 V/m, respectively. Find the kinetic energy (in electron volts) of the electrons passing through the filter. [1 eV = 1.60 1019 J] ANS: 17.8 eV PTS: 2
DIF: Average
Chapter 30—Sources of the Magnetic Field MULTIPLE CHOICE 1. One long wire carries a current of 30 A along the entire x axis. A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0, 4, 0) m. What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis? a. 4.0 T b. 5.0 T c. 3.0 T d. 7.0 T e. 1.0 T ANS: B
PTS: 2
DIF: Average
2. Two long parallel wires each carry a current of 5.0 A directed to the east. The two wires are separated by 8.0 cm. What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires? a. 72 T b. 48 T c. 24 T d. 96 T e. 32 T ANS: C
PTS: 2
DIF: Average
3. A 2.0-cm length of wire centered on the origin carries a 20-A current directed in the positive y direction. Determine the magnetic field at the point x = 5.0 m on the x-axis. a. 1.6 nT in the negative z direction b. 1.6 nT in the positive z direction c. 2.4 nT in the negative z direction d. 2.4 nT in the negative z direction e. None of the above ANS: A
PTS: 3
DIF: Challenging
4. Three long wires parallel to the x axis carry currents as shown. If I = 20 A, what is the magnitude of the magnetic field at the origin?
a. b. c. d. e.
37 T 28 T 19 T 47 T 58 T
ANS: C
PTS: 2
DIF: Average
5. Each of two long straight parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction. What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire? a. 57 T b. 80 T c. 64 T d. 48 T e. 40 T ANS: D
PTS: 2
DIF: Average
6. Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions. What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire? a. 51 T b. 33 T c. 72 T d. 64 T e. 46 T ANS: B
PTS: 3
DIF: Challenging
7. Two long parallel wires carry unequal currents in the same direction. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 T. What is the larger of the two currents? a. 5.3 A b. 3.8 A c. 4.5 A d. 3.0 A e. 0.5 A ANS: D
PTS: 2
DIF: Average
8. Two long straight wires carry currents perpendicular to the xy plane. One carries a current of 50 A and passes through the point x = 5.0 cm on the x axis. The second wire has a current of 80 A and passes through the point y = 4.0 cm on the y axis. What is the magnitude of the resulting magnetic field at the origin? a. 200 T b. 600 T c. 450 T d. 300 T e. 400 T ANS: C
PTS: 2
DIF: Average
9. Two very long parallel wires carry currents in the positive x direction. One wire (current = 15 A) is coincident with the x axis. The other wire (current = 50 A) passes through the point (0, 4.0 mm, 0). What is the magnitude of the magnetic field at the point (0, 0, 3.0 mm)? a. 3.8 mT b. 2.7 mT c. 2.9 mT d. 3.0 mT e. 0.6 mT ANS: B
PTS: 3
DIF: Challenging
10. Each of two parallel wires separated by 8.0 mm carries a 20-A current. These two currents are oppositely directed. Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires. a. 2.0 mT b. 1.6 mT c. 1.3 mT d. 1.8 mT e. 1.0 mT ANS: C
PTS: 3
DIF: Challenging
11. Each of two parallel wires separated by 6.0 mm carries a 40-A current. These two currents are in the same direction. Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires. a. 2.6 mT b. zero c. 1.9 mT d. 1.6 mT e. 3.2 mT ANS: A
PTS: 2
DIF: Average
12. Two long parallel wires separated by 5.0 mm each carry a current of 60 A. These two currents are oppositely directed. What is the magnitude of the magnetic field at a point that is between the two wires and 2.0 mm from one of the two wires? a. 2.0 mT b. 10 mT c. 8.0 mT d. 1.6 mT e. 7.2 mT ANS: B
PTS: 2
DIF: Average
13. Two long parallel wires separated by 4.0 mm each carry a current of 24 A. These two currents are in the same direction. What is the magnitude of the magnetic field at a point that is between the two wires and 1.0 mm from one of the two wires? a. 4.8 mT b. 6.4 mT c. 3.2 mT d. 9.6 mT e. 5.3 mT ANS: C
PTS: 2
DIF: Average
14. A long straight wire carries a current of 40 A in a region where a uniform external magnetic field has a 30-T magnitude and is parallel to the current. What is the magnitude of the resultant magnetic field at a point that is 20 cm from the wire? a. 70 T b. 40 T c. 10 T d. 50 T e. 36 T ANS: D
PTS: 2
DIF: Average
15. Two long parallel wires carry unequal currents in opposite directions. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 T. What is the larger of the two currents? a. 0.5 A b. 1.0 A c. 1.5 A d. 2.0 A e. 3.0 A ANS: C
PTS: 2
DIF: Average
16. A segment of wire of total length 3.0 m carries a 15-A current and is formed into a semicircle. Determine the magnitude of the magnetic field at the center of the circle along which the wire is placed. a. 1.6 T b. 4.9 T c. 1.0 T d. 9.8 T e. 15 T ANS: B
PTS: 2
DIF: Average
17. A segment of wire of total length 2.0 m is formed into a circular loop having 5.0 turns. If the wire carries a 1.2-A current, determine the magnitude of the magnetic field at the center of the loop. a. 79 T b. 69 T c. 59 T d. 89 T e. 9.4 T ANS: C
PTS: 3
DIF: Challenging
18. If a = 2.0 cm, b = 5.0 cm, and I = 20 A, what is the magnitude of the magnetic field at the point P?
a. b. c. d. e.
4.5 T 7.5 T 9.0 T 6.0 T 3.6 T
ANS: D
PTS: 2
DIF: Average
19. If a = 1.0 cm, b = 3.0 cm, and I = 30 A, what is the magnitude of the magnetic field at point P?
a. b. c. d. e.
0.62 mT 0.59 mT 0.35 mT 0.31 mT 0.10 mT
ANS: D
PTS: 2
DIF: Average
20. A straight wire (length = 8.0 m) is bent to form a square. If the wire carries a current of 20 A, what is the magnitude of the magnetic field at the center of the square? a. 17 T b. 14 T c. 11 T d. 20 T e. 36 T ANS: C
PTS: 2
DIF: Average
21. In the figure, if a = 2.0 cm, b = 4.0 cm, and I = 2.0 A, what is the magnitude of the magnetic field at point P?
a. b. c. d. e.
49 T 39 T 50 T 69 T 13 T
ANS: B
PTS: 2
DIF: Average
22. The segment of wire (total length = 6R, including the incoming and outgoing portions of the wire) is formed into the shape shown and carries a current I. What is the magnitude of the resulting magnetic field at the point P?
a. b. c. d. e.
ANS: A
PTS: 2
DIF: Average
23. The segment of wire (total length including portions of incoming and outgoing wire = 6R) is formed into the shape shown and carries a current I. What is the magnitude of the resulting magnetic field at the point P?
a. b. c. d. e.
ANS: A
PTS: 2
DIF: Average
24. What is the magnitude of the magnetic field at point P if a = R and b = 2R?
a. b. c. d. e.
ANS: B
PTS: 2
DIF: Average
25. What is the magnitude of the magnetic field at point P if a = R and b = 2R?
a. b. c. d. e.
ANS: A
PTS: 2
DIF: Average
26. What is the magnitude of the magnetic field at point P if a = R and b = 2R?
a. b. c. d. e.
ANS: D
PTS: 2
DIF: Average
27. What is the magnitude of the magnetic field at point P in the figure if a = 2.0 cm, b = 4.5 cm, and I = 5.0 A?
a. b. c. d. e.
87 T, into the paper 87 T, out of the paper 0.23 mT, out of the paper 0.23 mT, into the paper 23 T, into the paper
ANS: A
PTS: 2
DIF: Average
28. Three long, straight, parallel wires each carry a current of 10 A in the positive x direction. If the distance between each wire and the other two is 10 cm, what is the magnitude of the magnetic force on a 20-cm length of either of the wires? a. 57 N b. 40 N c. 69 N d. 50 N e. 20 N ANS: C
PTS: 3
DIF: Challenging
29. Two long parallel wires are separated by 6.0 mm. The current in one of the wires is twice the other current. If the magnitude of the force on a 3.0-m length of one of the wires is equal to 8.0 N, what is the greater of the two currents? a. 0.20 A b. 0.40 A c. 40 mA d. 20 mA e. 0.63 A ANS: B
PTS: 2
DIF: Average
30. Two long parallel wires are separated by 2.0 cm. The current in one of the wires is three times the other current. If the magnitude of the force on a 2.0-m length of one of the wires is equal to 60 N, what is the greater of the two currents? a. 2.0 A b. 1.0 A c. 3.0 A d. 9.0 A e. 1.5 A ANS: C
PTS: 2
DIF: Average
31. Three long, straight, parallel wires all lie in the yz plane and each carries a current of 20 A in the positive z direction. The two outer wires are each 4.0 cm from the center wire. What is the magnitude of the magnetic force on a 50-cm length of either of the outer wires?
a. b. c. d. e.
1.0 mN 0.50 mN 1.1 mN 1.5 mN 2.0 mN
ANS: D
PTS: 2
DIF: Average
32. Two long parallel wires are separated by 4.0 cm. One of the wires carries a current of 20 A and the other carries a 30-A current. Determine the magnitude of the magnetic force on a 2.0-m length of the wire carrying the greater current. a. 7.0 mN b. 6.0 mN c. 8.0 mN d. 9.0 mN e. 4.0 mN ANS: B
PTS: 2
DIF: Average
33. The figure shows a cross section of three parallel wires each carrying a current of 5.0 A out of the paper. If the distance R = 6.0 mm, what is the magnitude of the magnetic force on a 2.0-m length of any one of the wires?
a. b. c. d. e.
2.5 mN 3.3 mN 2.2 mN 2.9 mN 1.7 mN
ANS: D
PTS: 2
DIF: Average
34. The figure shows a cross section of three parallel wires each carrying a current of 20 A. The currents in wires A and B are out of the paper, while that in wire C is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 2.0-m length of wire A?
a. b. c. d. e.
23 mN 64 mN 32 mN 46 mN 55 mN
ANS: C
PTS: 2
DIF: Average
35. The figure shows a cross section of three parallel wires each carrying a current of 15 A. The currents in wires A and C are out of the paper, while that in wire B is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 4.0-m length of wire C?
a. b. c. d. e.
90 mN 54 mN 30 mN 18 mN 36 mN
ANS: D
PTS: 2
DIF: Average
36. The figure shows a cross section of three parallel wires each carrying a current of 24 A. The currents in wires B and C are out of the paper, while that in wire A is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 4.0-m length of wire A?
a. b. c. d. e.
15 mN 77 mN 59 mN 12 mN 32 mN
ANS: B
PTS: 2
DIF: Average
37. A long cylindrical wire (radius = 2.0 cm) carries a current of 40 A that is uniformly distributed over a cross section of the wire. What is the magnitude of the magnetic field at a point which is 1.5 cm from the axis of the wire? a. 0.53 mT b. 28 mT c. 0.30 mT d. 40 mT e. 1.9 mT ANS: C
PTS: 2
DIF: Average
38. A long straight wire (diameter = 2.0 mm) carries a current of 25 A. What is the magnitude of the magnetic field 0.50 mm from the axis of the wire? a. 5.0 mT b. 10 mT c. 0.63 mT d. 2.5 mT e. 0.01 mT ANS: D
PTS: 2
DIF: Average
39. A long straight wire (diameter = 2.0 mm) carries a current of 40 A. What is the magnitude of the magnetic field 1.5 mm from the axis of the wire? a. 3.0 mT b. 12 mT c. 5.3 mT d. 7.4 mT e. 8.0 mT ANS: C
PTS: 2
DIF: Average
40. A hollow cylindrical (inner radius = 1.0 mm, outer radius = 3.0 mm) conductor carries a current of 80 A parallel to its axis. This current is uniformly distributed over a cross section of the conductor. Determine the magnitude of the magnetic field at a point that is 2.0 mm from the axis of the conductor. a. 8.0 mT b. 3.0 mT c. 5.3 mT d. 16 mT e. 1.2 mT ANS: B
PTS: 2
DIF: Average
41. A hollow cylindrical (inner radius = 2.0 mm, outer radius = 4.0 mm) conductor carries a current of 24 A parallel to its axis. This current is uniformly distributed over a cross section of the conductor. Determine the magnitude of the magnetic field at a point that is 5.0 mm from the axis of the conductor. a. 0.96 mT b. 1.7 mT c. 0.55 mT d. 1.2 mT e. 0.40 mT ANS: A
PTS: 2
DIF: Average
42. A long straight wire (diameter = 2.0 mm) carries a current of 30 A. What is the magnitude of the magnetic field 2.5 mm from the axis of the wire?
a. b. c. d. e.
3.2 mT 2.8 mT 2.4 mT 3.6 mT 3.0 mT
ANS: C
PTS: 2
DIF: Average
43. A long hollow cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 24 A distributed uniformly across its cross section. A long wire which is coaxial with the cylinder carries an equal current in the opposite direction. What is the magnitude of the magnetic field 3.0 mm from the axis? a. 0.82 mT b. 0.93 mT c. 0.70 mT d. 0.58 mT e. 0.40 mT ANS: B
PTS: 2
DIF: Average
44. A long hollow cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 12 A distributed uniformly across its cross section. A long wire which is coaxial with the cylinder carries an equal current in the same direction. What is the magnitude of the magnetic field 3.0 mm from the axis? a. 1.1 mT b. 1.4 mT c. 1.7 mT d. 2.0 mT e. 0.2 mT ANS: A
PTS: 2
DIF: Average
45. A long, straight wire (radius = 2.0 mm) carries a current of 2.0 A distributed uniformly over a cross section perpendicular to the axis of the wire. What is the magnitude of the magnetic field at a distance of 1.0 mm from the axis of the wire? a. 0.40 mT b. 0.80 mT c. 0.10 mT d. 0.20 mT e. 0.75 mT ANS: C
PTS: 2
DIF: Average
46. A long wire is known to have a radius greater than 4.0 mm and to carry a current uniformly distributed over its cross section. If the magnitude of the magnetic field is 0.285 mT at a point 4.0 mm from the axis of the wire and 0.200 mT at a point 10 mm from the axis, what is the radius of the wire? a. 4.6 mm b. 7.1 mm c. 5.3 mm d. 12 mm e. 10 mm ANS: C
PTS: 3
DIF: Challenging
47. A long wire carries a current of 3.0 A along the axis of a long solenoid (radius = 3.0 cm, n = 900 turns/m, current = 30 mA). What is the magnitude of the magnetic field at a point 2.0 cm from the axis of the solenoid? Neglect any end effects. a. 34 T b. 64 T c. 30 T d. 45 T e. 4.0 T ANS: D
PTS: 3
DIF: Challenging
48. A solenoid 4.0 cm in radius and 4.0 m in length has 8 000 uniformly spaced turns and carries a current of 5.0 A. Consider a plane circular surface (radius = 2.0 cm) located at the center of the solenoid with its axis coincident with the axis of the solenoid. What is the magnetic flux through this surface? (1 Wb = 1 T m2) a. 63 Wb b. 16 Wb c. 0.25 mWb d. 10 Wb e. 5.0 Wb ANS: B
PTS: 2
DIF: Average
49. A long solenoid (diameter = 5.0 cm) is wound with 960 turns per meter of thin wire through which a current of 300 mA is maintained. A wire carrying 12 A is inserted along the axis of the solenoid. What is the magnitude of the magnetic field at a point 2.0 cm from the axis? a. 0.41 mT b. 0.48 mT c. 0.38 mT d. 0.56 mT e. 0.24 mT ANS: C
PTS: 2
DIF: Average
50. A current-carrying 2.0-cm long segment of wire is inside a long solenoid (radius = 4.0 cm, n = 800 turns/m, current = 50 mA). The wire segment is oriented perpendicularly to the axis of the solenoid. If the current in the wire segment is 12 A, what is the magnitude of the magnetic force on this segment? a. 22 N b. 16 N c. 18 N d. 12 N e. 0 N ANS: D
PTS: 2
DIF: Average
51. A long solenoid (n = 1 200 turns/m, radius = 2.0 cm) has a current of a 0.30 A in its winding. A long wire carrying a current of 20 A is parallel to and 1.0 cm from the axis of the solenoid. What is the magnitude of the resulting magnetic field at a point on the axis of the solenoid? a. 0.60 mT b. 0.85 mT c. 52 T d. 0.40 mT e. 0.75 mT
ANS: A
PTS: 2
DIF: Average
52. A long solenoid (1 500 turns/m) carries a current of 20 mA and has an inside diameter of 4.0 cm. A long wire carries a current of 2.0 A along the axis of the solenoid. What is the magnitude of the magnetic field at a point that is inside the solenoid and 1.0 cm from the wire? a. 78 T b. 55 T c. 48 T d. 68 T e. 2.0 T ANS: B
PTS: 2
DIF: Average
53. A long solenoid (1 000 turns/m) carries a current of 25 mA and has an inside radius of 2.0 cm. A long wire which is parallel to and 4.0 cm from the axis of the solenoid carries a current of 6.0 A. What is the magnitude of the magnetic field at a point on the axis of the solenoid? a. 51 T b. 61 T c. 43 T d. 81 T e. 1.4 T ANS: C
PTS: 2
DIF: Average
54. Two long parallel wires lie in the xz plane. One wire passes through the point (2 m, 0, 0) and the other through the point (+2 m, 0, 0). The wires carry equal currents in the positive z direction. 1. 2. 3. 4. a. b. c. d. e.
The magnetic field at (3 m, 0, 0) is in the negative y direction. The magnetic field at (1 m, 0, 0) is in the positive y direction. The magnetic field at (+1 m, 0, 0) is in the positive y direction. The magnetic field at (+3 m, 0, 0) is in the negative y direction. 1 and 2 are correct. 1 and 4 are correct. 2 and 3 are correct. 3 and 4 are correct. None of the above are correct.
ANS: A
PTS: 1
DIF: Easy
55. A single circular (radius = R) loop of wire is located in the yz plane with its center at the origin. The loop has a clockwise current as seen from the point (+R, 0, 0). The direction of the magnetic field at the point a. (0, 0, 0) is i and at the point (+R, 0, 0) is i. b. (0, 0, 0) is i and at the point (0, +2R, 0) is i. c. (0, 0, 0) is +i and at the point (+R, 0, 0) is +i. d. (0, 0, 0) is +i and at the point (0, +2R, 0) is +i. e. None of the above ANS: A
PTS: 1
DIF: Easy
56. A conducting hollow cylinder (inner radius = a, outer radius = b) carries a current of 40 A that is uniformly distributed over the cross section of the conductor. If a = 3.0 mm and b = 6.0 mm, what is the magnitude of the (line) integral
around a circular path (radius = 5.0 mm) centered on the
axis of the cylinder and in a plane perpendicular to that axis? a. 50 T m b. 30 T m c. 22 T m d. 37 T m e. 47 T m ANS: B
PTS: 2
DIF: Average
57. A conducting rod with a square cross section (3.0 cm 3.0 cm) carries a current of 60 A that is uniformly distributed across the cross section. What is the magnitude of the (line) integral around a square path (1.5 cm 1.5 cm) if the path is centered on the center of the rod and lies in a plane perpendicular to the axis of the rod? a. 14 T m b. 75 T m c. 19 T m d. 57 T m e. 38 T m ANS: C
PTS: 2
DIF: Average
58. A current element (length = 1.0 cm) lies along the x axis with its center at x = 0 and carries a 20-A current in the positive x direction. Consider only the field of this current element and decide which combination of the following statements is correct. 1. 2. 3. 4. a. b. c. d. e.
The field at (0, 0, 1.0 m) is in the positive z direction. The field at (0, 1.0 m, 0) is in the negative y direction. The field at (1.0 m, 0, 0) is zero. The field at (0, 0, 1.0 m) is in the negative y direction. 3 and 4 1 and 3 2 and 4 1 and 2 None of these
ANS: A
PTS: 2
DIF: Average
59. Which diagram correctly shows the magnetic field lines created by a circular current loop in which current flows in the direction shown? a.
b.
c.
d.
e.
ANS: C
PTS: 1
DIF: Easy
60. Gauss's Law states that the net electric flux, charge enclosed: a.
, through any closed surface is proportional to the
. The analogous formula for magnetic fields is: .
b. . c. d. e. ANS: A
. . . PTS: 1
DIF: Easy
61. When the number of turns in a solenoid and its length are both doubled, the ratio of the magnitude of the new magnetic field inside to the magnitude of the original magnetic field inside is: a. 0.25 b. 0.50 c. 1 d. 2 e. 4 ANS: C
PTS: 1
DIF: Easy
62. By using a compass to measure the magnetic field direction at various points adjacent to a long straight wire, you can show that the wire's magnetic field lines are a. straight lines in space that go from one magnetic charge to another. b. straight lines in space that are parallel to the wire. c. straight lines in space that are perpendicular to the wire. d. circles that have their centers on the wire and lie in planes perpendicular to the wire. e. circles that have the wire lying along a diameter of the circle. ANS: D
PTS: 1
DIF: Easy
63. The following statements all refer to the human brain when mental activity is occurring. Which statement is correct? a. In order to detect electric currents in the brain, you must open the skull and make direct electrical contact with the brain. b. The electric currents in the brain can be detected outside the brain by detecting the magnetic fields they produce. c. The electric currents in the brain can be mapped by shaving a person's head and dropping iron filings on the head. d. The electric currents in the brain produce an aura that can be detected visually. e. The electric currents in the brain cannot be detected by any means. ANS: B
PTS: 1
DIF: Easy
64. At a point in space where the magnetic field is measured, the magnetic field produced by a current element a. points radially away in the direction from the current element to the point in space. b. points radially in the direction from the point in space towards the current element. c. points in a direction parallel to the current element. d. points in a direction parallel to but opposite in direction to the current element. e. points in a direction that is perpendicular to the current element and perpendicular to the radial direction. ANS: E
PTS: 1
DIF: Easy
65. A long wire lies in a tangle on the surface of a table, as shown below. When a current is run through the wire as shown, the largest component of the magnetic field at X points
a. b. c. d. e.
into the table. out of the table. parallel to the nearest segment of wire. antiparallel to the nearest segment of wire. along a circle which has its center at the center of the overall loop.
ANS: B
PTS: 1
DIF: Easy
66. A solenoid consists of 100 circular turns of copper wire. Parts of three turns, A, B and C, are shown below.
When a current flows through the coil, a. both A and C are repelled by B. b. A is attracted to B; C is repelled by B. c. neither A nor C is attracted to or repelled by B. d. A is repelled by B; C is attracted to B. e. both A and C are attracted to B. ANS: E
PTS: 1
DIF: Easy
67. When a microwave filter consisting of vertical parallel metal rods is in the absorbing position, oscillating currents are set up in the rods. At any one instant, the current in each rod has the same magnitude and direction. At that instant a. the rods will try to move apart horizontally. b. the rods will try to move together horizontally. c. the rods will try to shift vertically upwards. d. the rods will try to shift vertically downwards. e. the rods will not be affected because the source of current is not a battery. ANS: B
PTS: 1
DIF: Easy
68. A toroid is made of 2 000 turns of wire of radius 2.00 cm formed into a donut shape of inner radius 10.0 cm and outer radius 14.0 cm. When a 30.0-A current is present in the toroid, the magnetic field at a distance of 11.0 cm from the center of the toroid is a. 0.0857 T. b. 0.109 T. c. 0.120 T. d. 0.600 T. e. 0.685 T. ANS: B
PTS: 2
DIF: Average
69. Two solenoids are each made of 2 000 turns of copper wire per meter. Solenoid I is 2 m long, while solenoid II is 1 m long. When equal currents are present in the two solenoids, the ratio of the magnetic field BI along the axis of solenoid I to the magnetic field BII along the axis of solenoid II, BI/BII, is a. 1/4. b. 1/2. c. 1. d. 2 e. 4. ANS: C
PTS: 1
DIF: Easy
70. A 0.50-m long solenoid consists of 1 000 turns of copper wire wound with a 4.0 cm radius. When the current in the solenoid is 18 A, the magnetic field at a point 1.0 cm from the central axis of the solenoid is a. 0.090 mT. b. 0.36 mT. c. 23 mT. d. 36 mT. e. 45 mT. ANS: E
PTS: 1
DIF: Average
71. Two solenoids of equal length are each made of 2 000 turns of copper wire per meter. Solenoid I has a 5.00 cm radius; solenoid II a 10.0 cm radius. When equal currents are present in the two solenoids, the ratio of the magnitude of the magnetic field BI along the axis of solenoid I to the magnitude of the magnetic field BII along the axis of solenoid II, BI/BII, is a. 1/4. b. 1/2. c. 1. d. 2. e. 4. ANS: C
PTS: 1
DIF: Easy
72. A thin infinitely large current sheet lies in the y-z plane. Current of magnitude Js per unit length along the z axis travels in the y-axis direction, which is up out of the page. Which diagram below correctly represents the direction of the magnetic field on either side of the sheet? a.
b.
c.
d.
e.
ANS: D
PTS: 1
DIF: Easy
73. The magnetic moment of an electron (charge = e; mass = me) moving in a circular orbit of radius r with speed v about a nucleus of mass mN is proportional to a. r. b. v. c. vr.
d. evr. e. mNvr. ANS: D
PTS: 1
DIF: Easy
74. On the average, in a ferromagnetic domain permanent atomic magnetic moments are aligned ____ to one another. a. antiparallel b. parallel c. perpendicular d. alternately parallel and antiparallel e. randomly relative ANS: B
PTS: 1
DIF: Easy
75. Equal currents of magnitude I travel out of the page in wires M and N. Eight directions are indicated by letters A through H.
The direction of the magnetic field at point P is a. E. b. F. c. G. d. H. e. A. ANS: E
PTS: 1
DIF: Easy
76. Equal currents of magnitude I travel out of the page in wire M and into the page in wire N. Eight directions are indicated by letters A through H.
The direction of the magnetic field at point P is a. A. b. B. c. C. d. D. e. E. ANS: C
PTS: 1
DIF: Easy
77. Equal currents of magnitude I travel into the page in wire M and out of the page in wire N. Eight directions are indicated by letters A through H.
The direction of the magnetic field at point P is a. C. b. E. c. F. d. G. e. H. ANS: D
PTS: 1
DIF: Easy
78. Equal currents of magnitude I travel into the page in wires M and N. Eight directions are indicated by letters A through H.
The direction of the magnetic field at point P is a. B. b. C. c. D. d. E. e. F. ANS: D
PTS: 1
DIF: Easy
79. If you were to travel parallel to an infinitely long straight wire with current I at the same velocity as the electrons in the wire at a distance a from the wire, the magnitude of the magnetic field (according to your measuring instruments) would be a. 0. b. . c. . d. . e. . ANS: A
PTS: 1
DIF: Easy
80. Two parallel and coaxial current loops of radius a are placed a distance 2L apart. The current in each ring circulates in the same direction. At a point on the axis half way between the loops the magnetic field in T has magnitude a. 0. b. . c. . d. . e. . ANS: D
PTS: 2
DIF: Average
81. Two parallel and coaxial current loops of radius a are placed a distance 2L apart. When you look along the axis at the loops, the current in one is clockwise, and counterclockwise in the other. At a point on the axis half way between the loops the magnetic field in T has magnitude a. 0. b. . c. . d. . e. . ANS: A
PTS: 1
DIF: Easy
82. Two current loops are coaxial and coplanar. One has radius a and the other has radius 2a. Current 2I in the outer loop is parallel to current I in the inner loop. The magnitude of the magnetic field at the center of the two loops is a. 0. b. . c. . d. . e. . ANS: D
PTS: 2
DIF: Average
83. Two current loops are coaxial and coplanar. One has radius a and the other has radius 2a. Current 2I in the outer loop is antiparallel to current I in the inner loop. The magnitude of the magnetic field at the center of the two loops is a. 0. b. . c. . d. . e. . ANS: A
PTS: 2
DIF: Average
84. We find that N current loops are coplanar and coaxial. The first has radius a and current I. The second has radius 2a and current 2I, and the pattern is repeated up to the Nth, which has radius Na and current NI. The current in each loop is counterclockwise as seen from above. The magnitude of the magnetic field at the center of the loops is a. . b. c. . d. . e. . ANS: D
PTS: 3
DIF: Challenging
85. We find that 2N current loops are coplanar and coaxial. The first has radius a and current I. The second has radius 2a and current 2I, and the pattern is repeated up to the Nth, which has radius Na and current NI. The current in the loops alternates in direction from loop to loop as seen from above. Thus the current in the first loop is counterclockwise, in the next clockwise, up to the last loop where it is again clockwise. The magnitude of the magnetic field at the center of the loops is a. 0. b. . c. . d. . e. . ANS: A
PTS: 2
DIF: Average
86. Three coplanar parallel straight wires carry equal currents I to the right as shown below. Each pair of wires is a distance a apart. The direction of the magnetic force on the middle wire
a. b. c. d. e.
is up out of the plane of the wires. is down into the plane of the wires. is in the plane of the wires, directed upwards. is in the plane of the wires, directed downwards cannot be defined, because there is no magnetic force on the middle wire.
ANS: E
PTS: 1
DIF: Easy
87. Three coplanar parallel straight wires carry equal currents I as shown below. The current in the outer wires is directed to the right, and that in the middle wire is directed to the left. Each pair of wires is a distance a apart. The direction of the magnetic force on the middle wire
a. b. c. d. e.
is up out of the plane of the wires. is down into the plane of the wires. is in the plane of the wires, directed upwards. is in the plane of the wires, directed downwards cannot be defined, because there is no magnetic force on the middle wire.
ANS: E
PTS: 1
DIF: Easy
88. Three coplanar parallel straight wires carry equal currents I to the right as shown below. The current in the upper two wires is directed to the right, but the current in the bottom wire is directed to the left. Each pair of wires is a distance a apart. The direction of the magnetic force on the middle wire
a. b. c. d. e.
is up out of the plane of the wires. is down into the plane of the wires. is in the plane of the wires, directed upwards. is in the plane of the wires, directed downwards cannot be defined, because there is no magnetic force on the middle wire.
ANS: C
PTS: 1
DIF: Easy
89. An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux B through any circular area of radius a inside the solenoid, centered on and perpendicular to the solenoid axis is a. . b. . c. 0a nI. d. 20a2nI. e. 0. 2
ANS: C
PTS: 2
DIF: Average
90. An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux B through any area completely inside the solenoid, centered on the solenoid axis but at a 45 angle to the axis, so that it touches the inside of the solenoid, as shown below, is
a. . b. . c. 0a2nI. d. 20a2nI. e. 0. ANS: C
PTS: 2
DIF: Average
91. Which of the following type(s) of materials is(are) repelled when a magnet is brought near by? a. paramagnetic b. diamagnetic c. ferromagnetic d. paramagnetic and ferromagnetic e. paramagnetic, ferromagnetic, and diamagnetic ANS: B
PTS: 1
DIF: Easy
92. When a ferromagnetic material that has been magnetized is brought to a temperature greater than the Curie temperature, what happens to its residual magnetism. a. Nothing happens to the residual magnetism. b. The residual magnetism disappears. c. The residual magnetism reaches it’s highest value. d. All the magnetic domains causing magnetism become a single domain. e. The material of the magnet melts causing currents that are magnetic. ANS: B PROBLEM
PTS: 1
DIF: Easy
93. A long solenoid (n = 80 turns/cm) carries a current of 70 mA. Determine the magnitude of the magnetic field inside the solenoid. ANS: 7.0 gauss PTS: 2
DIF: Average
94. Two wires, each having a weight per unit length of 1.0 104 N/m, are strung parallel, one 0.10 m above the other. If the wires carry the same current, though in opposite directions, how great must the current in each wire be for the magnetic field of the lower conductor to balance the weight of the upper conductor? ANS: 7.1 A PTS: 2
DIF: Average
95. What current in a solenoid 15.0-cm long wound with 100 turns would produce a magnetic field equal to that of the Earth, 5.00 105 T? ANS: 59.7 mA PTS: 2
DIF: Average
96. A superconducting wire carries a current of 1.0 104 A. Find the magnetic field at a distance of 1.0 m from the wire. ANS: 2.0 103 T PTS: 2
DIF: Average
97. The planetary model of the hydrogen atom consists of an electron in a circular orbit about a proton. The motion of the electron of charge 1.60 1019 C creates an electric current. The radius of the electron orbit is 5.30 1011 m and the electron's velocity is 2.20 106 m/s. What is the magnetic field strength at the location of the proton? ANS: 12.5 T PTS: 3
DIF: Challenging
Chapter 31—Faraday's Law MULTIPLE CHOICE
1. A coil is wrapped with 300 turns of wire on the perimeter of a circular frame (radius = 8.0 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is turned on perpendicular to the plane of the coil. This field changes at a constant rate from 20 to 80 mT in a time of 20 ms. What is the magnitude of the induced emf in the coil at the instant the magnetic field has a magnitude of 50 mT? a. 24 V b. 18 V c. 15 V d. 10 V e. 30 V ANS: B
PTS: 2
DIF: Average
2. A flat coil of wire consisting of 20 turns, each with an area of 50 cm2, is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 2.0 T to 6.0 T in 2.0 s. If the coil has a total resistance of 0.40 , what is the magnitude of the induced current? a. 0.70 A b. 0.60 A c. 0.50 A d. 0.80 A e. 0.20 A ANS: C
PTS: 2
DIF: Average
3. A 40-turn circular coil (radius = 4.0 cm, total resistance = 0.20 ) is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies with time as given by B = 50 sin(10 t) mT where t is measured in s. What is the magnitude of the induced current in the coil at 0.10 s? a. 50 mA b. 1.6 A c. 0.32 A d. zero e. 0.80 A ANS: B
PTS: 3
DIF: Challenging
4. A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magnitude that varies sinusoidally with a frequency of 90 Hz. If the maximum value of the induced emf in the coil is observed to be 4.2 V, what is the maximum value of the magnitude of the varying magnetic field? a. 59 mT b. 62 mT c. 65 mT d. 68 mT e. 31 mT ANS: A
PTS: 3
DIF: Challenging
5. A square loop (length along one side = 20 cm) rotates in a constant magnetic field which has a magnitude of 2.0 T. At an instant when the angle between the field and the normal to the plane of the loop is equal to 20 and increasing at the rate of 10/s, what is the magnitude of the induced emf in the loop? a. 13 mV b. 0.27 V c. 4.8 mV
d. 14 mV e. 2.2 mV ANS: C
PTS: 2
DIF: Average
6. A loop of wire (resistance = 2.0 m) is positioned as shown with respect to a long wire which carries a current. If d = 1.0 cm, D = 6.0 cm, and L = 1.5 m, what current is induced in the loop at an instant when the current in the wire is increasing at a rate of 100 A/s?
a. b. c. d. e.
34 mA 30 mA 27 mA 38 mA 0.50 mA
ANS: C
PTS: 3
DIF: Challenging
7. A rectangular wire loop (length = 60 cm, width = 40 cm) lies completely within a perpendicular and uniform magnetic field of magnitude of 0.5 T. If the length of the loop starts increasing at a rate of 20 mm/s at time t = 0, while the width is decreasing at the same rate, what is the magnitude of the induced emf at time t = 4.0 s? a. 6.8 mV b. 5.2 mV c. 3.6 mV d. 8.4 mV e. 10 mV ANS: C
PTS: 3
DIF: Challenging
8. A coil is wrapped with 300 turns of wire on the perimeter of a square frame (side length = 20 cm). Each turn has the same area as the frame, and the total resistance of the coil is 1.5 . A uniform magnetic field perpendicular to the plane of the coil changes in magnitude at a constant rate from 0.50 T to 0.90 T in 2.0 s. What is the magnitude of the induced emf in the coil while the field is changing? a. 2.4 V b. 1.6 V c. 3.2 V d. 4.0 V e. 8.4 V ANS: A
PTS: 2
DIF: Average
9. A planar loop consisting of four turns of wire, each of which encloses 200 cm2, is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms. What is the resulting induced current in the coil if the resistance of the coil is 5.0 ? a. 60 mA b. 12 mA c. 0.24 mA
d. 48 mA e. 6.0 mA ANS: D
PTS: 2
DIF: Average
10. A 5-turn square loop (10 cm along a side, resistance = 4.0 ) is placed in a magnetic field that makes an angle of 30 with the plane of the loop. The magnitude of this field varies with time according to B = 0.50t2, where t is measured in s and B in T. What is the induced current in the coil at t = 4.0 s? a. 25 mA b. 5.0 mA c. 13 mA d. 43 mA e. 50 mA ANS: A
PTS: 2
DIF: Average
11. A square coil (length of side = 24 cm) of wire consisting of two turns is placed in a uniform magnetic field that makes an angle of 60 with the plane of the coil. If the magnitude of this field increases by 6.0 mT every 10 ms, what is the magnitude of the emf induced in the coil? a. 55 mV b. 46 mV c. 50 mV d. 60 mV e. 35 mV ANS: D
PTS: 2
DIF: Average
12. A 50-turn circular coil (radius = 15 cm) with a total resistance of 4.0 is placed in a uniform magnetic field directed perpendicularly to the plane of the coil. The magnitude of this field varies with time according to B = A sin (t), where A = 80 T and = 50 rad/s. What is the magnitude of the current induced in the coil at t = 20 ms? a. 11 mA b. 18 mA c. 14 mA d. 22 mA e. zero ANS: A
PTS: 2
DIF: Average
13. A long straight wire is parallel to one edge and is in the plane of a single-turn rectangular loop as shown. If the loop is changing width so that the distance x changes at a constant rate of 4.0 cm/s, what is the magnitude of the emf induced in the loop at an instant when x = 6.0 cm? Let a = 2.0 cm, b = 1.2 m, and I = 30 A.
a. 5.3 V b. 2.4 V
c. 4.8 V d. 2.6 V e. 1.3 V ANS: C
PTS: 3
DIF: Challenging
14. A long solenoid (n = 1 500 turns/m) has a cross-sectional area of 0.40 m2 and a current given by I = (4.0 + 3.0t2) A, where t is in seconds. A flat circular coil (N = 300 turns) with a cross-sectional area of 0.15 m2 is inside and coaxial with the solenoid. What is the magnitude of the emf induced in the coil at t = 2.0 s? a. 2.7 V b. 1.0 V c. 6.8 V d. 0.68 V e. 1.4 V ANS: B
PTS: 2
DIF: Challenging
15. The coil shown in the figure has 2 turns, a cross-sectional area of 0.20 m2, and a field (parallel to the axis of the coil) with a magnitude given by B = (4.0 + 3.0t2) T, where t is in s. What is the potential difference, VA VC, at t = 3.0 s?
a. b. c. d. e.
7.2 V +7.2 V 4.8 V +4.8 V 12 V
ANS: A
PTS: 2
DIF: Average
16. A rectangular loop (area = 0.15 m2) turns in a uniform magnetic field with B = 0.20 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is (/2) rad and increasing at the rate of 0.60 rad/s, what is the magnitude of the emf induced in the loop? a. 24 mV b. zero c. 18 mV d. 20 mV e. 6.0 mV ANS: C
PTS: 2
DIF: Average
17. A circular loop (area = 0.20 m2) turns in a uniform magnetic field with B = 0.13 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is () rads and is decreasing at the rate of 0.50 rad/s, what is the magnitude of the emf induced in the loop? a. zero b. 13 mV c. 26 mV
d. 20 mV e. 18 mV ANS: A
PTS: 1
DIF: Easy
18. A conducting rectangular loop of mass M, resistance R, and dimensions a b is allowed to fall from rest through a uniform magnetic field which is perpendicular to the plane of the loop. The loop accelerates until it reaches a terminal speed (before the upper end enters the magnetic field). If a = 2.0 m, B = 6.0 T, R = 40 , and M = 0.60 kg, what is the terminal speed?
a. b. c. d. e.
1.6 m/s 20 m/s 2.2 m/s 26 m/s 5.3 m/s
ANS: A
PTS: 3
DIF: Challenging
19. A conducting rod (length = 80 cm) rotates at a constant angular rate of 15 revolutions per second about a pivot at one end. A uniform field (B = 60 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the emf induced between the ends of the rod? a. 2.7 V b. 2.1 V c. 2.4 V d. 1.8 V e. 3.3 V ANS: D
PTS: 2
DIF: Average
20. A metal blade spins at a constant rate of 5.0 revolutions per second about a pivot through one end of the blade. This rotation occurs in a region where the component of the earth's magnetic field perpendicular to the blade is 30 T. If the blade is 60 cm in length, what is the magnitude of the potential difference between its ends? a. 0.24 mV b. 0.20 mV c. 0.17 mV d. 0.27 mV e. 0.34 mV ANS: C
PTS: 2
DIF: Average
21. A 20-cm length of wire is held along an east-west direction and moved horizontally to the north with a speed of 3.0 m/s in a region where the magnetic field of the earth is 60 T directed 30 below the horizontal. What is the magnitude of the potential difference between the ends of the wire?
a. b. c. d. e.
36 V 18 V 31 V 24 V 21 V
ANS: B
PTS: 2
DIF: Average
22. In the arrangement shown, a conducting bar of negligible resistance slides along horizontal, parallel, frictionless conducting rails connected as shown to a 2.0- resistor. A uniform 1.5-T magnetic field is perpendicular to the plane of the paper. If L = 60 cm, at what rate is thermal energy being generated in the resistor at the instant the speed of the bar is equal to 4.2 m/s?
a. b. c. d. e.
8.6 W 7.8 W 7.1 W 9.3 W 1.8 W
ANS: C
PTS: 2
DIF: Average
23. A rod (length = 10 cm) moves on two horizontal frictionless conducting rails, as shown. The magnetic field in the region is directed perpendicularly to the plane of the rails and is uniform and constant. If a constant force of 0.60 N moves the bar at a constant velocity of 2.0 m/s, what is the current through the 12- load resistor?
a. b. c. d. e.
0.32 A 0.34 A 0.37 A 0.39 A 0.43 A
ANS: A
PTS: 2
DIF: Average
24. A metal blade (length = 80 cm) spins at a constant rate of 10 radians/s about a pivot at one end. A uniform magnetic field of 2.0 mT is directed at an angle of 30 with the plane of the rotation. What is the magnitude of the potential difference between the two ends of the blade? a. 5.5 mV b. 6.4 mV c. 3.2 mV d. 11 mV e. 13 mV ANS: C
PTS: 2
DIF: Average
25. A conducting rod (length = 2.0 m) spins at a constant rate of 2.0 revolutions per second about an axis that is perpendicular to the rod and through its center. A uniform magnetic field (magnitude = 8.0 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the potential difference between the center of the rod and either of its ends? a. 16 mV b. 50 mV c. 8.0 mV d. 0.10 mV e. 100 mV ANS: B
PTS: 2
DIF: Average
26. A long straight wire is parallel to one edge and is in the plane of a single-turn rectangular loop as shown. If the loop is moving in the plane shown so that the distance x changes at a constant rate of 20 cm/s, what is the magnitude of the emf induced in the loop at the instant x = 5.0 cm? Let I = 50 A, a = 50 cm, b = 6.0 cm.
a. b. c. d. e.
11 V 22 V 27 V 16 V 34 V
ANS: A
PTS: 3
DIF: Challenging
27. In a region of space where the magnetic field of the earth has a magnitude of 80 T and is directed 30 below the horizontal, a 50-cm length of wire oriented horizontally along an east-west direction is moved horizontally to the south with a speed of 20 m/s. What is the magnitude of the induced potential difference between the ends of this wire? a. 0.45 mV b. 0.35 mV c. 0.30 mV d. 0.40 mV e. 0.69 mV ANS: D
PTS: 2
DIF: Average
28. A small airplane with a wing span of 12 m flies horizontally and due north at a speed of 60 m/s in a region where the magnetic field of the earth is 60 T directed 60 below the horizontal. What is the magnitude of the induced emf between the ends of the wing? a. 50 mV b. 31 mV c. 37 mV d. 44 mV e. 22 mV
ANS: C
PTS: 2
DIF: Average
29. A conducting bar moves as shown near a long wire carrying a constant 80-A current. If a = 1.0 mm, b = 20 mm, and v = 5.0 m/s, what is the potential difference, Va Vb?
a. b. c. d. e.
0.24 mV +0.24 mV 0.19 mV +0.19 mV 0.76 mV
ANS: A
PTS: 3
DIF: Challenging
30. A conducting bar moves as shown near a long wire carrying a constant 50-A current. If a = 4.0 mm, L = 50 cm, and v = 12 m/s, what is the potential difference, VA VB?
a. b. c. d. e.
+15 mV 15 mV +20 mV 20 mV +10 mV
ANS: A
PTS: 2
DIF: Average
31. A bar (L = 80 cm) moves on two frictionless rails, as shown, in a region where the magnetic field is uniform (B = 0.30 T) and into the paper. If v = 50 cm/s and R = 60 m, what is the magnetic force on the moving bar?
a. b. c. d. e.
0.48 N to the right 0.48 N to the left 0.32 N to the left 0.32 N to the right None of the above
ANS: B
PTS: 2
DIF: Average
32. A conducting bar of length L rotates in a counterclockwise direction with a constant angular speed of +2.0 rad/s about a pivot P at one end, as shown. A uniform magnetic field (magnitude = 0.20 T) is directed into the paper. If L = 0.40 m, what is the potential difference, VA VB?
a. b. c. d. e.
+24 mV 24 mV +16 mV 16 mV +32 mV
ANS: A
PTS: 2
DIF: Average
33. A conducting bar of length L rotates with a constant angular speed of +2.0 rad/s about a pivot P at one end, as shown. A uniform magnetic field (magnitude = 0.20 T) is directed into the paper. If L = 0.40 m, what is the potential difference, VA VP?
a. b. c. d. e.
12 mV +8.0 mV 8.0 mV +12 mV 16 mV
ANS: C
PTS: 2
DIF: Average
34. A long solenoid (radius = 3.0 cm, 2 500 turns per meter) carries a current given by I = 0.30 sin(200t) A, where t is measured in s. When t = 5.0 ms, what is the magnitude of the induced electric field at a point which is 2.0 cm from the axis of the solenoid? a. 7.3 103 V/m b. 6.4 103 V/m c. 6.9 103 V/m d. 5.9 103 V/m e. 8.9 103 V/m ANS: D
PTS: 3
DIF: Challenging
35. A long solenoid (radius = 3.0 cm, 2 500 turns per meter) carries a current given by I = 0.30 sin(200 t) A, where t is measured in s. When t = 2.5 ms, what is the magnitude of the induced electric field at a point which is 4.0 cm from the axis of the solenoid? a. 9.3 103 V/m b. 8.0 103 V/m c. 6.7 103 V/m d. 5.3 103 V/m e. 1.9 103 V/m
ANS: E
PTS: 3
DIF: Challenging
36. A long solenoid has a radius of 4.0 cm and has 800 turns/m. If the current in the solenoid is increasing at the rate of 3.0 A/s, what is the magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid? a. 3.3 105 V/m b. 3.6 105 V/m c. 3.9 105 V/m d. 4.2 105 V/m e. 6.0 105 V/m ANS: A
PTS: 2
DIF: Average
37. An electric field of 4.0 V/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm, 800 turns/m). At what rate is the current in the solenoid changing at this instant? a. 0.50 A/s b. 0.40 A/s c. 0.60 A/s d. 0.70 A/s e. 0.27 A/s ANS: B
PTS: 2
DIF: Average
38. A long solenoid has a radius of 2.0 cm and has 700 turns/m. If the current in the solenoid is decreasing at the rate of 8.0 A/s, what is the magnitude of the induced electric field at a point 2.5 cm from the axis of the solenoid? a. 56 V/m b. 8.8 V/m c. 88 V/m d. 69 V/m e. 44 V/m ANS: A
PTS: 2
DIF: Average
39. An AC generator consists of 6 turns of wire. Each turn has an area of 0.040 m2. The loop rotates in a uniform field (B = 0.20 T) at a constant frequency of 50 Hz. What is the maximum induced emf? a. 13 V b. 2.4 V c. 3.0 V d. 15 V e. 4.8 V ANS: D
PTS: 2
DIF: Average
40. At what frequency should a 200-turn, flat coil of cross sectional area of 300 cm2 be rotated in a uniform 30-mT magnetic field to have a maximum value of the induced emf equal to 8.0 V? a. 7.5 Hz b. 7.1 Hz c. 8.0 Hz d. 8.4 Hz e. 16 Hz ANS: B
PTS: 2
DIF: Average
41. The magnetic flux through a loop perpendicular to a uniform magnetic field will change
a. if the loop is replaced by two loops, each of which has half of the area of the original loop. b. if the loop moves at constant velocity while remaining perpendicular to and within the uniform magnetic field. c. if the loop moves at constant velocity in a direction parallel to the axis of the loop while remaining in the uniform magnetic field. d. if the loop is rotated through 180 degrees about an axis through its center and in the plane of the loop. e. in none of the above cases. ANS: D
PTS: 1
DIF: Easy
42. A current may be induced in a coil by a. moving one end of a bar magnet through the coil. b. moving the coil toward one end of the bar magnet. c. holding the coil near a second coil while the electric current in the second coil is increasing. d. all of the above. e. none of the above. ANS: D
PTS: 1
DIF: Easy
43. Coil 1, connected to a 100 resistor, sits inside coil 2. Coil 1 is connected to a source of 60 cycle per second AC current. Which statement about coil 2 is correct? a. No current will be induced in coil 2. b. DC current (current flow in only one direction) will be induced in coil 2. c. AC current (current flow in alternating directions) will be induced in coil 2. d. DC current will be induced in coil 2, but its direction will depend on the initial direction of flow of current in coil 1. e. Both AC and DC current will be induced in coil 2. ANS: C
PTS: 1
DIF: Easy
44. An induced emf is produced in a. a closed loop of wire when it remains at rest in a nonuniform static magnetic field. b. a closed loop of wire when it remains at rest in a uniform static magnetic field. c. a closed loop of wire moving at constant velocity in a nonuniform static magnetic field. d. all of the above. e. only (b) and (c) above. ANS: C
PTS: 1
DIF: Easy
45. A bar magnet is dropped from above and falls through the loop of wire shown below. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct?
a. b. c. d. e.
The current in the loop always flows in a clockwise direction. The current in the loop always flows in a counterclockwise direction. The current in the loop flows first in a clockwise, then in a counterclockwise direction. The current in the loop flows first in a counterclockwise, then in a clockwise direction. No current flows in the loop because both ends of the magnet move through the loop.
ANS: D
PTS: 1
DIF: Easy
46. The difference between a DC and an AC generator is that a. the DC generator has one unbroken slip ring. b. the AC generator has one unbroken slip ring. c. the DC generator has one slip ring split in two halves. d. the AC generator has one slip ring split in two halves. e. the DC generator has two unbroken slip rings. ANS: C
PTS: 1
DIF: Easy
47. A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity . While it rotates, the point(s) at highest potential is(are)
a. b. c. d. e.
A. B. C. D. A and E.
ANS: E
PTS: 1
DIF: Easy
48. A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity . While it rotates, the point(s) at lowest potential is(are)
a. b. c. d. e.
A. B. C. D. A and E.
ANS: C
PTS: 1
DIF: Easy
49. A metal rod of length L in a region of space where a constant magnetic field points into the page rotates about an axis through its center at constant angular velocity . The ends, A and E, make contact with a split ring that connects to an external circuit. The current in the external circuit of resistance R has magnitude
a. 0. b. . c. . d. . e. . ANS: A
PTS: 1
DIF: Easy
50. Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is closed,
a. b. c. d. e.
bulb 1 glows more brightly. bulb 2 glows more brightly. both bulbs continue to glow with the same brightness. bulb 1 goes out. bulb 2 goes out.
ANS: D
PTS: 1
DIF: Easy
51. Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is closed,
a. b. c. d. e.
bulb 1 glows more brightly. bulb 2 glows more brightly. both bulbs glow equally brightly. bulb 1 goes out. bulb 2 goes out.
ANS: C
PTS: 1
DIF: Easy
52. Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is open,
a. b. c. d. e.
bulb 1 is glowing; bulb 2 is dark. bulb 2 is glowing; bulb 1 is dark. both bulbs glow equally brightly. both bulbs glow one half as brightly as they do with the switch closed. both bulbs are dark.
ANS: E
PTS: 1
DIF: Easy
53. As shown below, a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity directed to the right. Judd says that the emf induced in the loop is zero. Roger claims that it has magnitude B . Which one, if either, is correct, and why?
a. b. c. d. e.
Judd, because the magnetic flux through the loop is constant. Roger, because the magnetic flux through the loop is constant. Judd, because the magnetic flux through the loop is not constant if Roger, because the magnetic flux through the loop is not constant if Roger, because the magnetic flux through the loop is B = 0.
ANS: A
PTS: 1
. .
DIF: Easy
54. As shown below, a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity directed to the right. Which statement regarding the electric field induced in the wires is correct for the wires at the left and right sides of the loop?
a. The electric field is directed upwards in both the right and left sides of the loop. b. The electric field is directed upwards in the right side and downwards in the left side of the loop. c. The electric field is directed upwards in the left side and downwards in the right side of the loop. d. The electric field is directed downwards in both the right and left sides of the loop. e. There is no electric field present in any side of the loop. ANS: D
PTS: 1
DIF: Easy
55. Starting outside the region with the magnetic field, a single square coil of wire moves across the region with a uniform magnetic field perpendicular to the page. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. Roger claims that the graph shown below represents the induced emf. Martin says he's wrong. In which direction did the loop move over the plane of the page, or is Martin correct?
a. b. c. d. e.
Roger is correct: the loop moved from bottom to top. Roger is correct: the loop moved from top to bottom. Roger is correct: the loop moved from left to right. Roger is correct: the loop moved from right to left. Martin is correct: none of these directions of motion will produce the graph of emf vs t.
ANS: E
PTS: 1
DIF: Easy
56. Starting outside the region with the magnetic field, a single square coil of wire enters, moves across, and then leaves the region with a uniform magnetic field perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. In which direction did the loop move over the plane of the page?
a. b. c. d.
The loop moved from bottom to top. The loop moved from top to bottom. The loop moved from left to right. The loop moved from right to left.
e. All of these directions of motion will produce the graph of emf vs t. ANS: E
PTS: 1
DIF: Easy
57. Starting outside the region with the magnetic field, a single square coil of wire enters, moves across, and then leaves the region with a uniform magnetic field perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. In which direction did the loop move over the plane of the page?
a. b. c. d. e.
The loop moved from bottom to top. The loop moved from top to bottom. The loop moved from left to right. The loop moved from right to left. All of these directions of motion will produce the graph of emf vs t.
ANS: E
PTS: 1
DIF: Easy
58. In a demonstration, a 4.00 cm2 square coil with 10 000 turns enters a larger square region with a uniform 1.50 T magnetic field at a speed of 100 m/s. The plane of the coil is perpendicular to the field lines. If the breakdown voltage of air is 4 000 V/cm on that day, the largest gap you can have between the two wires connected to the ends of the coil and still get a spark is a. 7.5 103 cm. b. 0.015 cm. c. 7.5 cm. d. 13 cm. e. 15 cm. ANS: C
PTS: 3
DIF: Challenging
PROBLEM 59. A rectangular coil of 100 turns measures 40.0 cm by 20.0 cm. This coil is placed next to an electromagnet which is switched on, increasing the magnetic field through the coil from zero to 0.800 T in 50.0 ms. If the resistance of the coil is 2.0 ohms, what are the induced voltage and current in the coil? ANS: 128 V, 64 A PTS: 2
DIF: Average
60. A 500-turn circular loop 15.0 cm in diameter is initially aligned so that its axis is parallel to the Earth's magnetic field. In 2.77 ms the coil is flipped so that its axis is perpendicular to the Earth's field. If a voltage of 0.166 V is induced in the coil, what is the value of the Earth's magnetic field? ANS: 5.20 105 T PTS: 2
DIF: Average
61. A car with a radio antenna 1.0 m long travels at 80 km/h in a locality where the Earth's magnetic field is 5.0 105 T. What is the maximum possible emf induced in the antenna as a result of moving through the Earth's magnetic field? ANS: 1.1 mV PTS: 2
DIF: Average
62. A bolt of lightning strikes the ground 200 m from a 100-turn coil oriented vertically and with the plane of the coil pointing toward the lightning strike. The radius of the coil is 0.800 m and the current in the lightning bolt falls from 6.02 106 A to zero in 10.5 s. What is the voltage induced in the coil over this time period? [A question for future electrical engineers: is there any way to get lightning to strike repeatedly at the same point?]
ANS: 115 000 V PTS: 2
DIF: Average
Chapter 32—Inductance MULTIPLE CHOICE 1. What is the inductance of a series RL circuit in which R = 1.0 K if the current increases to one-third of its final value in 30 s? a. 74 mH b. 99 mH c. 49 mH d. 62 mH e. none of the above
ANS: A
PTS: 2
DIF: Average
2. For the circuit shown, what is the rate of change of the current in the inductor when the current in the battery is 0.50 A?
a. b. c. d. e.
600 A/s 400 A/s 200 A/s 800 A/s 500 A/s
ANS: C
PTS: 2
DIF: Average
3. Before the switch is closed in the figure, the potential across the capacitor is 200 V. At some instant after the switch is closed, the instantaneous current is 0.70 A. What is the energy in the capacitor at this instant?
a. b. c. d. e.
49 mJ 31 mJ 80 mJ 0.13 J 62 mJ
ANS: B
PTS: 2
DIF: Average
4. The switch in the figure is closed at t = 0 when the current I is zero. When I = 15 mA, what is the potential difference across the inductor?
a. b. c. d. e.
240 V 60 V 0 180 V 190 V
ANS: D
PTS: 2
DIF: Average
5. There is no current in the circuit shown in the figure below until the switch is closed. The current through the 20- resistor the instant after the switch is closed is either [1] 15 A or [2] 5.0 A, and the current through the 20- resistor after the switch has been closed a long time is either [3] 5.0 A or [4] 15 A. Which combination of the above choices is correct?
a. b. c. d. e.
[1] and [3] [1] and [4] [2] and [3] [2] and [4] None of these
ANS: D
PTS: 2
DIF: Average
6. Which of the following are the units of a henry and a farad respectively? a. J s2/C2 and C2/J b. V s/A and V/C c. V/(A s) and C/V d. N m/A2 and 1/J e. None of the above ANS: A
PTS: 1
DIF: Easy
7. The figure shows an LR circuit with a switch and a 240-volt battery. At the instant the switch is closed the current in the circuit and the potential difference between points a and b, Vab, are
a. b. c. d. e.
0 A, 0 V 0 A, 240 V 0 A, +240 V 0.024 A, 0 V 0.024 A, +240 V
ANS: C
PTS: 2
DIF: Average
8. A series LC circuit contains a 100 mH inductor, a 36.0 mF capacitor and a 12 V battery. The angular frequency of the electromagnetic oscillations in the circuit is a. 36.0 104 rad/s. b. 6.00 102 rad/s. c. 2.78 rad/s. d. 16.7 rad/s. e. 277 rad/s. ANS: D
PTS: 2
DIF: Average
9. A series LC circuit contains a 100 mH inductor, a 36.0 mF capacitor and a 12 V battery. The frequency of the electromagnetic oscillations in the circuit is a. 5.73 104 Hz. b. 9.55 103 Hz. c. 0.442 Hz. d. 2.65 Hz. e. 44.0 Hz. ANS: D
PTS: 2
DIF: Average
10. A series LC circuit contains a 100 mH inductor, a 36.0 mF capacitor and a 12 V battery. The period of the electromagnetic oscillations in the circuit is a. 0.0227 s. b. 0.377 s. c. 2.26 s. d. 105 s. e. 1750 s. ANS: B
PTS: 2
DIF: Average
11. When a switch is closed, completing an LR series circuit, the time needed for the current to reach one half its maximum value is ____ time constants. a. 0.250 b. 0.500 c. 0.693 d. 1.00 e. 1.44
ANS: C
PTS: 2
DIF: Average
12. When a switch is closed, completing an LR series circuit, the time needed for the current to reach three-quarters its maximum value is ____ time constants. a. 0.500 b. 0.693 c. 0.725 d. 1.33 e. 1.39 ANS: E
PTS: 2
DIF: Average
13. A circuit contains two inductors of 6.0 mH inductance in parallel placed in series with an inductor of 8.0 mH inductance. After one of the 6.0 mH inductors burns out, the repairman wants to replace all three inductors with one inductor of equivalent inductance. Assuming inductors combine in series and parallel the same way resistors do, what inductance should he use? a. 3.0 mH b. 3.4 mH c. 4.8 mH d. 11 mH e. 20 mH ANS: D
PTS: 2
DIF: Average
14. A circuit contains two inductors of 6.0 mH inductance in series placed in parallel with an inductor of 8.0 mH inductance. After one of the 6.0 mH inductors burns out, the repair person wants to replace all three inductors with one inductor of equivalent inductance. Assuming inductors combine in series and parallel the same way resistors do, what inductance should she use? a. 3.0 mH b. 3.4 mH c. 4.8 mH d. 11 mH e. 20 mH ANS: C
PTS: 2
DIF: Average
15. An inductor produces a back emf in a DC series RL circuit when a switch connecting the battery to the circuit is closed. We can explain this by a. Lenz's law. b. increasing magnetic flux within the coils of the inductor. c. increasing current in the coils of the inductor. d. all of the above. e. only (a) and (c) above. ANS: D
PTS: 1
DIF: Easy
16. When a switch is closed to complete a DC series RL circuit, a. the electric field in the wires increases to a maximum value. b. the magnetic field outside the wires increases to a maximum value. c. the rate of change of the electric and magnetic fields is greatest at the instant when the switch is closed. d. all of the above are true. e. only (a) and (c) above are true. ANS: D
PTS: 1
DIF: Easy
17. After a switch is thrown to remove the battery from a DC LR circuit, but the circuit is still left complete, the time constant represents a. the time rate of change of the current in the circuit. b. the time rate of change of the induced emf in the circuit. c. the magnitude of the ratio of the current to the time rate of change of the current. d. all of the above. e. only (a) and (b) above. ANS: C
PTS: 1
DIF: Easy
18. Coaxial Cable A has twice the length, twice the radius of the inner solid conductor, and twice the radius of the outer cylindrical conducting shell of coaxial Cable B. What is the ratio of the inductance of Cable A to that of Cable B? a. b. c. 2 d. e. ANS: C
PTS: 2
DIF: Average
PROBLEM 19. The magnetic field in a superconducting solenoid is 3.0 T. How much energy per unit volume is stored in the solenoid, in J/m3? 0 = 4 107 T A/m ANS: 3.6 106 J/m3 PTS: 2
DIF: Average
20. Find the magnetic energy stored in the air gap between two very large magnetic pole pieces, one North, one South, each with an area of 100 cm2. Assume the 0.05 T magnetic field is uniform within the 2-cm gap. ANS: 0.2 J PTS: 2
DIF: Average
21. A 10-mH inductor is connected in series with a 10-ohm resistor, a switch and a 6-volt battery. What is the time constant of the circuit? How long after the switch is closed will the current reach 99 percent of its final value? ANS: 1.0 ms, 4.6 ms PTS: 2
DIF: Average
22. If we wished to construct a "tank circuit" where electric charge originally stored on a capacitor flows through an inductor, then back again, what value of inductance should we place in series with a fullycharged 100 F capacitor to get the circuit to resonate at 60.0 Hz?
ANS: 70.4 mH PTS: 2
DIF: Average
23. An RLC circuit has L = 250 mH, C = 0.200 F, and R = 2.00 kWhat is the angular frequency of its damped oscillations? ANS:
PTS: 2
DIF: Average
Chapter 33—Alternating-Current Circuits MULTIPLE CHOICE 1. An ac generator with peak voltage 100 volts is placed across a 10- resistor. What is the average power dissipated? a. 100 W b. 150 W c. 500 W d. 1 000 W e. 2 000 W ANS: C
PTS: 2
DIF: Average
2. An electric heater draws an average power of 1 100 Watts when plugged into a 110 V-rms outlet. Calculate the resistance of the heater and the rms current. a. 11, 10 A (rms) b. 110, 10 A (rms) c. 10, 11 A (rms) d. 10, 110 A (rms) e. 0.09, 11 A (rms) ANS: A
PTS: 2
DIF: Average
3. An incandescent lightbulb is rated at 100 Watts when plugged into a 110 V-rms household outlet. Calculate the resistance of the filament and the rms current. a. 12.2, 0.91 A (rms) b. 10, 1.0 A (rms) c. 110, 1.0 A (rms) d. 121, 0.91 A (rms) e. 11, 1.1 A (rms) ANS: D
PTS: 2
DIF: Average
4. A high-voltage powerline operates at 500 000 V-rms and carries an rms current of 500 A. If the resistance of the cable is 0.050/km, what is the resistive power loss in 200 km of the powerline? a. 250 kW b. 500 kW c. 1 Megawatt
d. 2.5 Megawatts e. 250 Megawatts ANS: D
PTS: 2
DIF: Average
5. A 230 000 V-rms powerline carries an average power Pavg = 250 MW a distance of 200 km. If the total resistance of the cables is 10 ohms, what is the resistive power loss? a. 1.0 MW b. 2.5 MW c. 5.4 MW d. 12 MW e. 10 kW ANS: D
PTS: 2
DIF: Average
6. Inductive reactance XL is given by a. L b. L/ c. 1/L d. /L e. 2L ANS: A
PTS: 1
DIF: Easy
7. Capacitive reactance XC is given by a. 1/C b. C c. /C d. C/ e. 1/2C ANS: A
PTS: 1
DIF: Easy
8. The total impedance Z of an RLC circuit driven by an ac voltage source at angular frequency is, a. b. c.
d. e. ANS: B
PTS: 1
DIF: Easy
9. At what frequency will a 12-F capacitor have a reactance XC = 300? a. 44 Hz b. 88 Hz c. 180 Hz d. 350 Hz e. 280 Hz ANS: A
PTS: 2
DIF: Average
10. At what frequency will a 50.0-mH inductor have a reactance XL = 700? a. 352 Hz b. 777 Hz c. 1.25 kHz d. 2.23 kHz e. 14 kHz ANS: D
PTS: 2
DIF: Average
11. A 2.0-F capacitor in series with a 2.0-k resistor is connected to a 60-Hz ac source. Calculate the impedance of the circuit. a. 1 500 ohms b. 1 800 ohms c. 2 100 ohms d. 2 400 ohms e. 8 600 ohms ANS: D
PTS: 2
DIF: Average
12. A 10.0-F capacitor is plugged into a 110 V-rms 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the capacitor? a. 0.202 A (rms) b. 0.415 A (rms) c. 0.626 A (rms) d. 0.838 A (rms) e. 0.066 A (rms) ANS: B
PTS: 2
DIF: Average
13. A 0.500-H inductor is connected into a 110 V-rms 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the inductor? a. 0.189 A (rms) b. 0.292 A (rms) c. 0.584 A (rms) d. 1.19 A (rms) e. 0.093 A (rms) ANS: C
PTS: 2
DIF: Average
14. An LC circuit is to have resonant oscillations at 5.0 MHz. Find the value of a capacitor which will work with a 1.0-mH inductor. a. 2.0 mF b. 1.0 F c. 0.020 F d. 1.0 pF e. 40 pF ANS: D
PTS: 2
DIF: Average
15. The inductance of a tuning circuit of an AM radio is 4.00 mH. Find the capacitance of the circuit required for reception at 1 200 kHz. a. 2.10 pF b. 4.40 pF c. 21.2 pF
d. 43.4 pF e. 27.6 pF ANS: B
PTS: 2
DIF: Average
16. Find the resonant frequency for a series RLC circuit where R = 10, C = 5.00 F, and L = 2.00 mH. a. 998 Hz b. 1.59 kHz c. 2.45 kHz d. 11.3 kHz e. 2.53 kHz ANS: B
PTS: 2
DIF: Average
17. The voltage 8.00 sin (400t) is applied to a series RLC circuit, with R = 200 , L = 0.100 H, and C = 1.00 F. What are the impedance Z and the phase angle ? a. 200 , 37.0 b. 566 , +87.0 c. 2 470 , 85.4 d. 2 540 , 88.8 e. 393 , 63.0 ANS: C
PTS: 3
DIF: Challenging
18. If an R = 1.0-k resistor, a C = 1.0-F capacitor, and an L = 0.20-H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source? a. 0.007 0 A b. 27 mA c. 54 mA d. 0.31 A e. 0.34 A ANS: C
PTS: 2
DIF: Average
19. If the input to an RLC series circuit is V = Vm cos t, then the current in the circuit is a. cos t b. c.
d.
e. ANS: D
PTS: 1
DIF: Easy
20. An RLC series circuit has R = 100 ohms, C = 25 F, and L = 0.16 H. For what angular frequency of an ac voltage is the current flow maximum? a. 251 rad/s
b. c. d. e.
500 rad/s 757 rad/s 884 rad/s 79.6 rad/s
ANS: B
PTS: 2
DIF: Average
21. Determine the rms voltage for the circuit.
a. b. c. d. e.
99 V (rms) 140 V (rms) 196 V (rms) 70 V (rms) 110 V (rms)
ANS: A
PTS: 1
DIF: Easy
22. Determine the impedance for the circuit.
a. b. c. d. e.
600 1 200 1 800 2 300 1 100
ANS: C
PTS: 2
23. Determine the rms current for the circuit.
DIF: Average
a. b. c. d. e.
55 mA 77 mA 99 mA 0.19 A 61 mA
ANS: A
PTS: 2
DIF: Average
24. Determine the resonant frequency of the circuit.
a. b. c. d. e.
159 Hz 32 Hz 5 Hz 500 Hz 79.5 Hz
ANS: A
PTS: 2
DIF: Average
25. Determine the rms voltage drop across the resistor in the circuit.
a. b. c. d.
55 V 77 V 9.9 V 5.5 V
e. 61 V ANS: A
PTS: 2
DIF: Average
26. Determine the rms voltage drop across the inductor in the circuit.
a. b. c. d. e.
11 V 27.5 V 33 V 38.5 V 30.5 V
ANS: B
PTS: 2
DIF: Average
27. Determine the rms voltage drop across the capacitor in the circuit.
a. b. c. d. e.
55 V 77 V 110 V 154 V 198 V
ANS: C
PTS: 2
DIF: Average
28. A current I = 3 sin (400 t) amperes flows in a series RL circuit in which L = 1 mH and R = 100. What is the average power loss? a. 225 W b. 450 W c. 980 W d. 1.12 kW e. 900 W ANS: B
PTS: 2
DIF: Average
29. What is the average power dissipation in a series RC circuit if R = 5.00 k, C = 2.00 F, and V = 170 cos (300t)? a. 0.930 W b. 2.60 W c. 28.2 W d. 157 W e. 5.20 W ANS: B
PTS: 2
DIF: Average
30. What is the average power dissipation in an RLC series circuit with R = 10, L = 0.1 H, C = 10 F when driven at resonance by a 100 V-rms source? a. 100 W b. 500 W c. 1000 W d. 2 kW e. 700 W ANS: C
PTS: 2
DIF: Average
31. A series RLC circuit has an impedance of 120 and a resistance of 64. What average power is delivered to this circuit when Vrms = 90 volts? a. 36 W b. 100 W c. 192 W d. 360 W e. 12 W ANS: A
PTS: 2
DIF: Average
32. A transformer is to be designed to increase the 30 kV-rms output of a generator to the transmissionline voltage of 345 kV-rms. If the primary winding has 80 turns, how many turns must the secondary have? a. 6 b. 70 c. 920 d. 9 200 e. 12 ANS: C
PTS: 2
DIF: Average
33. The primary winding of an electric train transformer has 400 turns and the secondary has 50. If the input voltage is 120V(rms) what is the output voltage? a. 15 V (rms) b. 30 V (rms) c. 60 V (rms) d. 2.4 V (rms) e. 960 V (rms) ANS: A
PTS: 2
DIF: Average
34. A step-up transformer has an input voltage of 110 V (rms). There are 100 turns on the primary and 1 500 on the secondary. What is the output voltage? a. 1 600 V (max) b. 1 650 V (rms)
c. 3 260 V (max) d. 165 kV (rms) e. 7.3 V (rms) ANS: B
PTS: 2
DIF: Average
35. A primary current of 6.0 A exists in an ideal iron-core transformer at a primary voltage of 100 volts. If the current in the secondary is 0.75 A, calculate the output voltage. a. 12.5 V b. 40 V c. 400 V d. 800 V e. 200 V ANS: D
PTS: 2
DIF: Average
36. An ideal step-down transformer has 200 primary turns and 50 secondary turns. If 440 volts (rms) is placed across the primary, what is the current in the secondary when the load resistance is 7.00 ohms? a. 3.6 A (rms) b. 7.3 A (rms) c. 11.4 A (rms) d. 15.7 A (rms) e. 12.4 A (rms) ANS: D
PTS: 2
DIF: Average
37. Calculate Vout/Vin for the circuit if R = 2.0 k, C = 0.020 F and V = 140V sin(50 000t).
a. b. c. d. e.
0.02 0.45 0.80 0.98 2.2
ANS: B
PTS: 2
DIF: Average
38. The impedance of the parallel RLC circuit shown is given by
a. b.
c. d.
e.
ANS: B
PTS: 3
DIF: Challenging
39. The phase angle between V and I is
a. b. c.
d.
e. ANS: A
PTS: 3
DIF: Challenging
40. For driving voltage V = Vm sin t, the current through the resistor is
a. Vm sin (t + ) b. Vm cos (t + ) c. sin (t + ) d. e.
sin (t + ) sin t
ANS: E
PTS: 2
DIF: Average
41. An alternating current circuit has resistance R, inductance L and capacitance C in series with a voltage source. Which statement is correct? a. The voltage across the capacitor leads the voltage across the inductor by 90. b. The voltage across the inductor leads the voltage across the capacitor by 90. c. The voltage across the inductor leads the voltage across the resistor by 180. d. The voltage across the inductor is out of phase with the voltage across the capacitor by 180. e. Both voltages lead the voltage across the resistor by 90. ANS: D
PTS: 1
DIF: Easy
42. The power output, Pout, of an ideal step-up transformer that receives power input, Pin, and which has N1 turns in the primary and N2 turns in the secondary coil is given by a. Pout = Pin. b. Pout = Pin. c. Pout =
Pin.
d. Pout =
Pin.
Pout =
Pin.
e.
ANS: A
PTS: 1
DIF: Easy
43. In a typical transmission line, the current I is very small and the voltage V is very large. A unit length of line has resistance R. For a power line that supplies power to 10 000 households, we can conclude that a. IV = I2R. b. I = V/R. c. IV < I2R. d. IV > I2R. e. I2R = 0. ANS: D
PTS: 2
DIF: Average
44. Whenever the alternating current frequency in a series RLC circuit is halved, a. the inductive reactance is doubled and the capacitive reactance is halved. b. the inductive reactance is doubled and the capacitive reactance is doubled. c. the inductive reactance is halved and the capacitive reactance is halved. d. the inductive reactance is halved and the capacitive reactance is doubled. e. the reactance of the circuit remains the same. ANS: D
PTS: 1
DIF: Easy
45. The average power input to a series alternating current circuit is minimum when a. there are only a resistor and capacitor in the circuit. b. there are only a resistor and inductor in the circuit. c. there is only a resistor in the circuit. d. XL = XC and the circuit contains a resistor, an inductor and a capacitor. e. there is only a capacitor in the circuit.
ANS: E
PTS: 1
DIF: Easy
46. All three circuits shown below have R = 100 , L = 0.1 H and emf = (5.0 V) sin (377 t). Which statement regarding the angular resonance frequencies A, B and C is correct?
a. b. c. d. e.
C > A = B C < A = B A = B = C B < A = C B > A = C
ANS: C
PTS: 1
DIF: Easy
47. All three circuits below have R = 100 , C = 1.0 mF and emf = (5.0 V) sin (377 t). The inductors in (B) and (C) are placed sufficiently far apart so that they do not alter one another's inductance. Such inductors add combine like resistors. Which statement regarding the angular resonance frequencies A, B and C is correct?
a. b. c. d. e.
C > A = B C < A = B A = B = C B < A = C B > A = C
ANS: C
PTS: 2
DIF: Average
48. A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 and C = 300 F. The peak current in the circuit is a. 8.24 A. b. 8.84 A. c. 11.0 A. d. 12.4 A. e. 23.5 A.
ANS: A
PTS: 2
DIF: Average
49. A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 and C = 300 F. The impedance is a. 4.68 . b. 8.84 . c. 10.0 . d. 13.4 . e. 18.8 . ANS: D
PTS: 2
DIF: Average
50. A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 and C = 300 F. The power factor, cos , is a. 1.00. b. 0.749. c. +0.749. d. +0.834. e. +1.00. ANS: C
PTS: 2
DIF: Average
51. A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 and L = 10.0 mH. The peak current in the circuit is a. 0.963 A. b. 10.3 A. c. 11.0 A. d. 11.9 A. e. 29.2 A. ANS: B
PTS: 2
DIF: Average
52. A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 and L = 10.0 mH. The impedance is a. 3.77 . b. 9.26 . c. 10.0 . d. 10.7 . e. 13.8 . ANS: D
PTS: 2
DIF: Average
53. A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 and L = 10.0 mH. The power factor, cos , is a. 1.00. b. 0.936. c. +0.943. d. +0.936. e. +1.00. ANS: D
PTS: 2
DIF: Average
54. A 10-F capacitor in an LC circuit made entirely of superconducting materials (R = 0 ) is charged to 100 C. Then a superconducting switch is closed. At t = 0 s, plate 1 is positively charged and plate 2 is negatively charged. At a later time, Vab = +10 V. At that time, Vdc is
a. b. c. d. e.
0 V. 3.54 V. 5.0 V. 7.07 V. 10 V.
ANS: E
PTS: 2
DIF: Average
55. The graphs below show a voltage phasor at different instances of time. The voltage phasor which shows the instantaneous value of the voltage with the largest magnitude is a.
b.
c.
d.
e.
ANS: A
PTS: 1
DIF: Easy
56. The graphs below represent current and voltage phasors at one instant of time. The solid arrows represent the voltage phasors, V, and the dashed arrows represent the current phasors, Imax.The graph which shows the correct relationship between current and voltage phasors for an inductor in an RL circuit is
a.
b.
c.
d.
e.
ANS: A
PTS: 1
DIF: Easy
57. The graphs below represent current and voltage phasors at one instant of time. The solid arrows represent the voltage phasors, Vmax, and the dashed arrows represent the current phasors, Imax. The graph which shows the correct relationship between current and voltage phasors for a capacitor in an RC circuit is a.
b.
c.
d.
e.
ANS: C
PTS: 1
DIF: Easy
58. The graphs below show the phasors Vmax and Imax for five RLC series circuits. The solid arrows represent the voltage phasors, V, and the dashed arrows represent the current phasors, Imax. The graph which represents a circuit where the inductive reactance is greater than the capacitive reactance is a.
b.
c.
d.
e.
ANS: B
PTS: 1
DIF: Easy
59. The graphs below show the phasors Vmax and Imax for five RLC series circuits. The solid arrows represent the voltage phasors, V, and the dashed arrows represent the current phasors, Imax. The graph which represents a circuit where the capacitive reactance is greater than the inductive reactance is a.
b.
c.
d.
e.
ANS: A
PTS: 1
DIF: Easy
60. In a parallel RLC circuit, where IR = IR, max sin(t), the current through the capacitor, IC, is a. IC = IC, max sin(t). b. IC = IC, max sin(t). c. IC = IC, max cos(t). d. IC = IC, max cos(t). e. IC = IC, max tan(t). ANS: D
PTS: 1
DIF: Easy
61. In a parallel RLC circuit, where IR = IR, max sin(t), the current through the inductor, IL, is a. IL = IL, max sin(t). b. IL = IL, max sin(t). c. IL = IL, max cos(t). d. IL = IL, max cos(t). e. IL = IL, max tan(t). ANS: C
PTS: 1
DIF: Easy
62. Which of the following is true about a diode? a. A diode causes the voltage to shift in phase by 90, i.e., a right angle. b. A diode has high resistance in one current direction and low resistance in the opposite current direction. c. A diode can only be used with a transformer. d. All filter circuits contain a diode. e. All of the above. ANS: B
PTS: 1
DIF: Easy
PROBLEM 63. Suppose the circuit parameters in a series RLC circuit are: L = 1.00 H, C = 10.0 nF, R = 100, and the source voltage is 220 V. Determine the resonant frequency of the circuit and the amplitude of the current at resonance. ANS: 1.59 MHz, 2.20 A PTS: 2
DIF: Average
64. A 10.0- resistor, 10.0-mH inductor, and 10.0-F capacitor are connected in series with a 10.0-kHz voltage source. The rms current through the circuit is 0.200 A. Find the rms voltage drop across each of the 3 elements. ANS: 2.00 V, 126 V, 0.318 V
PTS: 3
DIF: Challenging
65. An ac power generator produces 50 A (rms) at 3600 V. The voltage is stepped up to 100 000 V by an ideal transformer and the energy is transmitted through a long distance power line which has a resistance of 100 ohms. What percentage of the power delivered by the generator is dissipated as heat in the long-distance power line? ANS: 0.18% PTS: 2
DIF: Average
Chapter 34—Electromagnetic Waves MULTIPLE CHOICE 1. The Earth is 1.49 1011 meters from the sun. If the solar radiation at the top of the Earth's atmosphere is 1 340 W/m2, what is the total power output of the sun? a. 7.10 1027 W b. 2.20 1030 W c. 6.62 1026 W d. 3.74 1026 W e. 2.98 1025 W ANS: D
PTS: 2
DIF: Average
2. If the radiant energy from the sun comes in as a plane EM wave of intensity 1 340 W/m2, calculate the peak values of E and B. a. 300 V/m, 104 T b. 1 000 V/m, 3.35 106 T c. 225 V/m, 1.60 103 T d. 111 V/m, 3.00 105 T e. 711 V/m, 2.37 106 T ANS: B
PTS: 2
DIF: Average
3. If the maximum E-component of an electromagnetic wave is 600 V/m, what is the maximum Bcomponent? a. 1.4 T b. 1.8 105 T c. 2.0 106 T d. 1.0 103 T e. 1.6 1010 T ANS: C
PTS: 2
DIF: Average
4. Find the force exerted by reflecting sunlight off a reflecting aluminum sheet in space if the area normal to the sunlight is 10 000 m2 and the solar intensity is 1 350 W/m2. a. 0.72 N b. 0.09 N c. 9 N d. 45 N e. 0.18 N
ANS: B
PTS: 2
DIF: Average
5. What is the average value of the magnitude of the Poynting vector lightbulb radiating in all directions? a. 1 W/m2 b. 4 W/m2 c. 2 W/m2 d. 8 W/m2 e. 12 W/m2 ANS: D
PTS: 2
at 1 meter from a 100-watt
DIF: Average
6. A 100-kW radio station emits EM waves in all directions from an antenna on top of a mountain. What is the intensity of the signal at a distance of 10 km? a. 8 105 W/m2 b. 8 106 W/m2 c. 3 103 W/m2 d. 0.8 W/m2 e. 2.5 105 W/m2 ANS: A
PTS: 2
DIF: Average
7. How much electromagnetic energy is contained in each cubic meter near the Earth's surface if the intensity of sunlight under clear skies is 1 000 W/m2? a. 3.3 106 J b. 3.3 J c. 0.003 J d. 104 J e. 3.0 105 J ANS: A
PTS: 2
DIF: Average
8. At a distance of 10 km from a radio transmitter, the amplitude of the E-field is 0.20 volts/meter. What is the total power emitted by the radio transmitter? a. 10 kW b. 67 kW c. 140 kW d. 245 kW e. 21 kW ANS: B
PTS: 2
DIF: Average
9. What is the maximum radiation pressure exerted by sunlight in space (S = 1 350 W/m2) on a flat black surface? a. 2.25 105 Pa b. 0.06 Pa c. 7 104 Pa d. 4.5 106 Pa e. 9.0 106 Pa ANS: D
PTS: 2
DIF: Average
10. What is the maximum radiation pressure exerted by sunlight in space (S = 1 350 W/m2) on a highly polished silver surface?
a. b. c. d. e.
1.4 102 Pa 0.12 Pa 9.0 106 Pa 4.5 105 Pa 2.3 106 Pa
ANS: C
PTS: 2
DIF: Average
11. Find the frequency of X-rays of wavelength 1 Å = 1010 m. a. 3 1018 Hz b. 3 1010 MHz c. 6 109 Hz d. 3 108 Hz e. 3 1020 Hz ANS: A
PTS: 2
DIF: Average
12. Green light has a wavelength of 5.4 107 m. What is the frequency of this EM-wave in air? a. 5.55 1014 Hz b. 6.00 1011 Hz c. 9.00 108 Hz d. 3.00 1010 MHz e. 1.80 1015 Hz ANS: A
PTS: 2
DIF: Average
13. An FM radio station broadcasts at 98.6 MHz. What is the wavelength of the radiowaves? a. 60.8 m b. 6.08 m c. 3.04 m d. 0.314 m e. 0.33 cm ANS: C
PTS: 2
DIF: Average
14. What should be the height of a dipole antenna (of dimensions 1/4 wavelength) if it is to transmit 1 200 kHz radiowaves? a. 11.4 m b. 60 cm c. 1.12 m d. 62.5 m e. 250 m ANS: D
PTS: 2
DIF: Average
15. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the maximum E-field? a. b. c. d. e.
1000 V/m 180 V/m 81 V/m 360 V/m 0.40 V/m
ANS: D
PTS: 2
DIF: Average
16. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the frequency of the wave? a. b. c. d. e.
500 MHz 250 kHz 1.25 MHz 10 mHz 300 MHz
ANS: C
PTS: 2
DIF: Average
17. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the wavelength of the EM wave? a. b. c. d. e.
120 m 240 m 60 m 100 m 360 m
ANS: B
PTS: 2
DIF: Average
18. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the speed of the EM wave? a. b. c. d. e.
3 108 m/s 100 m/s 106 m/s 2 107 m/s 2 108 m/s
ANS: A
PTS: 2
DIF: Average
19. The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. Find the average power per square meter carried by the EM wave. a. 720 W b. 172 W c. 500 W d. 2 107 W e. 86 W ANS: B
PTS: 2
DIF: Average
20. A solar cell has a light-gathering area of 10 cm2 and produces 0.2 A at 0.8 V (DC) when illuminated with S = 1 000 W/m2 sunlight. What is the efficiency of the solar cell?
a. b. c. d. e.
16% 7% 23% 4% 32%
ANS: A
PTS: 2
DIF: Average
21. High frequency alternating current is passed through a solenoid that contains a solid copper core insulated from the coils of the solenoid. Which statement is correct? a. A copper core remains cool no matter what the frequency of the current in the solenoid is. b. The copper core remains cool because the induced emf is parallel to the solenoid axis and fluctuates rapidly. c. The copper core heats up because an emf parallel to the solenoid axis is induced in the core. d. The copper core heats up because circular currents around its axis are induced in the core. e. The copper core heats up because the electric field induced in the copper is parallel to the magnetic field produced by the solenoid. ANS: D
PTS: 1
DIF: Easy
22. In an electromagnetic wave, 1) how are the electric and magnetic field directions related and 2) how is the direction of travel determined from their directions? ( is the velocity of the light wave.) a. . b. . c. . d. . e. . ANS: C
PTS: 1
DIF: Easy
23. The intensity of radiation reaching the earth from the sun is 1 350 W/m2. The earth's radius is 6.4 106 m. How big a force does this radiation exert on the earth? (Assume it is all absorbed.) a. 5.8 108 N b. 1.2 109 N c. 2.3 109 N d. 4.6 109 N e. 1.7 1017 N ANS: A
PTS: 2
24. The speed of light is given by the value of a. 00. b. .
DIF: Average
c.
.
d.
.
e. . ANS: C
PTS: 1
DIF: Easy
25. The magnetic field amplitude in an electromagnetic wave in vacuum is related to the electric field amplitude by B = a. . b.
.
c. E. d.
.
e. cE. ANS: A
PTS: 1
DIF: Easy
26. Since 0 = 8.85 1012 C2 / N m2, the units of 0E2 can be reduced to a. . b. c. d. e.
. . . .
ANS: C
PTS: 2
DIF: Average
27. When E and B are the amplitudes of the electric and magnetic fields in an electromagnetic wave in vacuum, the total average energy density in the wave is a. . b.
.
c. 0E2. d. . e.
.
ANS: B
PTS: 1
DIF: Easy
28. In the atmosphere, the shortest wavelength electromagnetic waves are called a. microwaves. b. infrared waves. c. ultraviolet waves. d. X-rays. e. gamma rays. ANS: E
PTS: 1
DIF: Easy
29. Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1) and 2R (sphere 2) from the sun respectively. The ratio of the pressure of solar radiation on sphere 2 to that on sphere 1 is a. 0.25. b. 0.50. c. 1.0. d. 2.0. e. 4.0. ANS: A
PTS: 2
DIF: Average
30. Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1) and 2R (sphere 2) from the sun respectively. The ratio of the gravitational force exerted by the sun on sphere 1 to the pressure of solar radiation on sphere 1 is T1; the ratio for sphere 2 is T2. The ratio of T2 to T1 is a. 0.25. b. 0.50. c. 1.0. d. 2.0. e. 4.0. ANS: C
PTS: 2
DIF: Average
31. Magnetic fields are produced by a. constant electric currents. b. electric currents that vary sinusoidally with time. c. time-varying electric fields. d. all of the above. e. only (a) and (b) above. ANS: D
PTS: 2
DIF: Average
32. At every instant the ratio of the magnitude of the electric to the magnetic field in an electromagnetic wave in vacuum is equal to a. the speed of radio waves. b. the speed of light. c. the speed of gamma rays. d. all of the above. e. only (a) and (b) above. ANS: D
PTS: 1
DIF: Easy
33. A spherical particle of density
and 2.00 mm radius is located at the same distance from
the Sun as the Earth. RSE = 1.5 1011 m.
. If
the particle absorbs 100 percent of the sunlight reaching it, the ratio of the force exerted by the solar radiation to the force of gravity exerted on the particle by the Sun is a. 5.8 105. b. 0.58. c. 1.0. d. 1.7. e. 1.7 104. ANS: E
PTS: 3
DIF: Challenging
34. You can raise the temperature of an object with a. microwaves. b. infrared waves. c. ultraviolet rays. d. all of the above. e. only (a) and (b) above. ANS: D
PTS: 1
DIF: Easy
35. An open circuit consists of a 12 F parallel plate capacitor charged to 200 V and a 10 resistor. At the instant when a switch closes the circuit (with no battery in it) the displacement current between the plates of the capacitor is a. 1.2 A. b. 2.4 104 A. c. 2.4 mA. d. 10 A. e. 20 A. ANS: E
PTS: 2
DIF: Average
36. The correct form of Ampere's law for circuits with gaps in them is a. . b. c.
. .
d. . e. . ANS: D
PTS: 1
DIF: Easy
37. A plane parallel plate capacitor has plates of 10 cm2 area that are 1.0 mm apart. At an instant when charge is being accumulated on the plates at a rate of 12 nC/s, the displacement current between the plates is a. 1.06 1016 A. b. 1.2 108 A.
c. 8.85 109 A. d. 1.00 A. e. 1.36 A. ANS: B
PTS: 1
DIF: Easy
PROBLEM 38. Near the surface of the planet, the Earth's magnetic field is about 0.50 104 T. How much energy is stored in 1.0 m3 of the atmosphere because of this field? ANS: 9.9 104 J PTS: 2
DIF: Average
39. The sun radiates energy at a rate of 3.86 1026 W. Its radius is 7.0 108 m. If the distance from the Earth to the sun is 1.5 1011 m, what is the intensity of solar radiation at the top of the Earth's atmosphere? ANS: W/m2 PTS: 2
DIF: Average
40. A possible means of spaceflight is to place a perfectly reflecting aluminized sheet into Earth orbit and use the light from the sun to push this solar sail. If a huge sail of area 6.00 105 m2 and mass 6 000 kg were placed into orbit and turned toward the sun, what would be the force exerted on the sail? (Assume a solar intensity of 1 380 W/m2.) ANS: 5.52 N PTS: 2
DIF: Average
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