Electrostatics

DC Pandey Electrostatics Level – I Q 1. The minimum electrostatic force between two charged particles placed at a distance of 1m is (a) 2.3 × 10-28N (b) 6.2 × 10-34N (c) 1.02 × 1026 N (d) 4.2 × 10-27N 



Q 2. Electric field on the axis of a small electric dipole at a distance r is E1 and E 2 at a distance of 2r on a line of perpendicular bisector. Then         (a) E 2 =  E1 /8 (b) E 2 =  E1 /16 (c) E 2 =  E1 /4 (d) E 2 = E1 /8 Q 3. Three point charges q,  2q and 2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to 2a will be (a) 1/40. 2q2/a (b) negative (c) zero (d) 1/40. 3q2/a Q 4. A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be 1/40 times (a) q/2R (b) 4q/3R (c) 5q/6R (d) 2q/2R Q 5. The potential field of an electric field E =  yˆi  xˆj is (a) V = xy + constant (b) V = (x + y) + constant (d) V = constant 

(c) V = - (x2 + y2) + constant

Q 6. Figure shows three spherical and equipotential surfaces 1, 2 and 3 round a point charge q. The potential difference V1  V2 = V2  V3. If t1 and t2 be the distance between them. Then

(a) t1 = t2

(b) t1 > t2

(c) t1 < t2

(d) t1  t2

Q 7. The distance between plates of a parallel plate capacitor is 5d. The positively charged plate is at x = 0 and negatively charged plate is at x = 5d. Two slabs one of conductor and the other of a dielectric of same thickness dare inserted between the plates as shown in figure. Potential (V) versus distance x graph will be

(a)

(b)

(c)

(d)

Q 8. A point charge q is placed at a distance of r from the centre of an uncharged conducting sphere of radius R (< r). The potential at any point on the sphere is (a) zero (b) 1/40. q/r (c) 1/40. qR/r2 (d) 1/40. qr2/R Q 9. An electric field is given by E   yˆi  xˆj N/C. The work done in moving a 1 C charge from   rA  2ˆi  2ˆj m or rB   4ˆi  ˆj m is (a) + 4 J (b) – 4 J (c) + 8 J (d) zero 

Q 10. Capacity of a spherical capacitor is C1 when inner sphere is charged and outer sphere is earthed and C2 when inner sphere is earthed and outer sphere is charged. Then C1/C2 is (a = radius of inner sphere, b = radius of outer sphere) (a) 1 (b) a/b (c) b/a (d) a + b/a – b Q 11. In the circuit shown in figure C = 6F. The charge stored in capacitor of capacity C is

(a)zero

(b) 90C

(c) 40 C

(d) 60C

Q 12. A capacitor of capacity C1 = 1F is charged to a potential of 100 V. The charging battery is then removed and it is connected to another capacitor of capacity C2 = 2F. One plate of C2 is earthed as shown in figure. The charges on C1 and C2 in steady state will be

(a) 50 C, 50 C

(b) 100 C, zero

(c) 100/3 C, 200/3 C (d) zero, zero

Q 13. Capacity of an isolated sphere is increased n times when it is enclosed by an earthed concentric sphere. The ratio of their radii is (a) n2/n – 1 (b) n/n – 1 (c) 2n/n + 1 (d) 2n + 1/n + 1 Q 14. Three conducting spheres A, B and C are as shown in figure. The radii of the spheres area, b and c respectively. A and B are connected by a conducting wire. The capacity of the system is

(a) 40(a + b + c) (b) 40(bc/c  b) (c) 40(1/a + 1/b + 1/c) (d) 40(abc/ab + bc + ca) Q 15. Capacitance of a capacitor becomes 4/3 times its original value if a dielectric slab of thickness t= d/2 is inserted between the plates (d = separation between the plates). The dielectric constant of the slab is (a)2 (b)4 (c)6 (d)8 Q 16. The plates of a parallel plate capacitor are charged upto 100 volt. A 2mm thick insulator sheet is inserted between the plates. Then to maintain the same potential difference, the distance between the capacitor plates is increased by 1.6 mm. The dielectric constant of the insulator is (a) 6 (b)8 (c)5 (d)4 Q 17. The metal plate on the left in figure carries a charge + q. The metal plate on the right has a charge of  2q. What charge will flow through S when it is closed, if central plate is initially neutral

(a) zero

(b) q

(c) + q

(d) + 2q

Q 18. A capacitor is connected to a battery. The force of attraction between the plates when the separation between them is halved (a) remains the same (b) becomes eight times (c) becomes four times (d) becomes two times

Q 19. A dielectric slab of area A and thickness d is inserted between the plates of capacitor of area 2A and distance between plates d with a constant speed v as shown in figure. The capacitor is connected to a battery of emf E. The current in the circuit varies with time as

(a)

(b)

(c)

(d)

Q 20. A number of spherical conductors of different radii have same potential. Then the surface charge density on them (a) is proportional to their radii (b) is inversely proportional to their radii (c) are equal (d) is proportional to square of their radii Q 21. Three charged particles are initially in position 1. They are free to move and they come in position 2 after some time. Let U1 and U2 be the electrostatic potential energies in position 1 and 2. Then (a) U1 > U2 (b) U2 > U1 (c) U1 = U2 (d) U2  U1 Q 22. A conducting sphere of radius R is charged to a potential of V volts. Then the electric field at a distance r (>R) from the centre of the sphere would be (a)

V r

(b)

R 2V r

3

(c)

RV r2

(d)

rV R2

Q 23. A spherical charged conductor has surface charged density . The electric field on its surface is E and electric potential of conductor is V. Now the radius of the sphere is halved keeping the charge to be constant. The new values of electric field and potential would be (a) 2E, 2V (b) 4E, 2V (c) 4E, 4V (d)2E, 4V Q 24. In the above problem, radius is halved keeping surface charge density to be constant. Then the new values will be (a) E, V/2 (b) E, 2V (c) 2E, V (d) E/2, V Q 25. Two concentric spherical conducting shells of radii R and 2R carry charges Q and 2Q respectively. Change in electric potential on the outer shell when both are connected by a conducting wire is (k = 1/40) (a) zero (b) 3kQ/2R (c) kQ/R (d) 2kQ/R Q 26. A conducting shell of radius R carries charge  Q. A point charge + Q is placed at the centre. The electric field E varies with distance r (from the centre of the shell) as

Q 27. An insulator plate is passed between the plates of a capacitor. Then current

(a) always flows from A to B (b) always flows from B to A (c) first flows from A to B and then from B to A (d) first flows from B to A and then from A to B

Q 28. The gap between the plates of a parallel plate capacitor is filled with glass of resistivity . The capacitance of the capacitor without glass equals C. The leakage current of the capacitor when a voltage V is applied to it is (a) V/c0 (b) CV/0 (c) V0/C (d) CV/ 0 Q 29. If the capacitance of each capacitor is C, then effective capacitance of the shown network across any two junctions is:

(a) 2C

(b) C

(c) C/2

(d) 5C

Q 30. Two identical positive charges are fixed on the y-axis, at equal distances from the origin O. A particle with a negative charge starts on the negative x-axis at a large distance from O, moves along the x-axis, passed through O and moves far away from O. Its acceleration a is taken as positive along its direction of motion. The particle’s acceleration a is plotted against its x-coordinate. Which of the following best represents the plot? (a)

(b)

(c)

(d)

Q 31. Two identical point charges are placed at a separation of l.p is a point on the line joining the charges, at a distance x from any one charge. The field at P is E. E is plotted against x for values of x from close to zero to slightly less than l. Which of the following best represents the resulting curve?

(a)

(b)

(c)

(d)

Q 32. An air capacitor consists of two parallel plates A and B as shown in the figure. Plate A is given a charge Q and plate B is given a charge 3Q. P is the median plane of the capacitor. If C0 is the capacitance of the capacitor, then:

(a) VP – VA = Q/4C0 - Q/4C0

(b) VP – VA = Q/2C0

(c) VP – VA = - Q/C0

(d) VP – VB =

Q 33. A hollow sphere of radius 2R is charged to V volts and another smaller sphere of radius R is charged to V/2 volts. Now the smaller sphere is placed inside the bigger sphere without changing the net charge on each sphere. The potential difference between the two spheres would be: (a) 3V/2 (b) V/4 (c) V/2 (d) V

Q 34. A point charge q is placed at a distance r from the centre O of a uncharged spherical shell of inner radius R and outer radius 2R. The distance r < R. The electric potential at the centre of the shell will be:

q

1

q

1

  (a) 4  r  2R   0 

(b) 4 r 0

q

1

1

  (c) 4  r  2R   0 

(d) none of these

Q 35. Find equivalent capacitance between A and B

(a) 5 F

(b) 4 F

(c) 3 F

(d) 2F

Level – II Q 1. The potential field depends on x and y coordinates as V = (x2  y2). Corresponding electric field lines in x-y plane are as

Q 2. A small electric dipole is placed at origin with its dipole moment directed along positive x-axis. The direction of electric field at point (2, 2 2 , 0) is (a) along z-axis (b) along y-axis (c) along negative y-axis (d) along negative z-axis Q 3. Four equal charges of magnitude q each are placed at four corners of a square with its centre at origin and lying in y - z plane. A fifth charge +Q is moved along x-axis. The electrostatic potential energy (U) varies on x-axis as

Q 4.

A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20cm. A charge q =20 C is given to the inner sphere. Find the heat generated in the process, the inner sphere is connected to the shell by a conducting wire (a) 12J (b)9J (c)24J (d)zero

Q 5. Two identical particles of charge q each are connected by a massless spring of force constant k. They are placed over a smooth horizontal surface. They are released when the separation between them is r and spring is unstretched. If maximum extension of the spring is r, the value of k is (neglect gravitational effect)

q

1

(a) 4r  r 0

q

1

(b) 2r  r 0

2q

(c) r

1  0 r

q

1

(d) r  r 0

Q 6. Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge q be placed between them so that the electrical potential energy of the system is a minimum

(a) at a distance of r/ 3 from 2q (c) at a distance of r/16 from 2q

(b) at a distance of 2r/3 from 2q (d) none of these

Q 7. Electric lines of force are as shown in figure. Then potential at point P

(a) is zero

(b) is not zero (c) may be zero also

(d) is not defined

Q 8. A capacitor of capacitance 10 F is charged to a potential 50 V with a battery. The battery is now disconnected and an additional charge 200 C is given to the positive plate of the capacitor. The potential difference across the capacitor will be (a)50V (b)80V (c) 100V (d)60V Q 9. A capacitor is filled with an insulator and a certain potential difference is applied to its plates. The energy stored in the capacitor is U. Now the capacitor is disconnected from the source and the insulator is pulled out of the capacitor. The work performed against the forces of electric field in pulling out the insulator is 4 U. Then dielectric constant of the insulator is (a) 4 (b) 8 (c) 5 (d) 3 Q 10. In the circuit shown in figure potential difference between A and B is

(a) 30 V

(b) 60 V

(c) 10 V

(d) 90 V

Q 11. A parallel plate capacitor has two layers of dielectrics as shown in figure. This capacitor is connected across a battery, then the ratio of potential difference across the dielectric layers is

(a) 4/3

(b) 1/2

(c) 1/3

(d) 3/2

Q 12. In the circuit shown in figure charge stored in 4F capacitor is

(a) 20 C

(b) 40 C

(c) 10 C

(d) 120 C

Q 13. In the circuit shown in figure charge stored in the capacitor of capacity 5F is

(a) 60 C

(b) 20 C

(c) 30 C

(d) zero

Q 14. One plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state separation between the plates is 0.8 d (spring was unstretched and the distance between the plates was d when the capacitor was uncharged). The force constant of the spring is approximately

(a)

4 0 AE 2 d3

(b)

2 0 AE 2 d2

(c)

6 0 E 2

(d)

Ad 3

 0 AE 3 2d 2

Q 15. In the circuit shown in figure C1 = 1F and C2 = 2 F. Capacitor C1 is charged to 100 V and C2 is charged to 20 V. After charging they are connected as shown. When the switches S1, S2 and S3 all are closed

(a) no charge will flow through S2 (b) 80 C charge will flow through S1 (c) 40C charge will flow through S2 (d) 60 C charge will flow through S3 Q 16. Current versus time and voltage versus time graph of a circuit element is shown below the type of the circuit element is

(a) capacitance of 2 F voltage source of emf 1 V

(b) resistance of 2

(c) capacitance of 1 F

(d) a

Q 17. Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure. Capacitor 2 contains a dielectric slab of dielectric constant K as shown. Q 1 and Q2 are the charges stored in the capacitors. Now the dielectric slab is removed and the corresponding charges are Q'1 and Q'2. Then

(a) Q'1/Q1 = K + 1/K K/2

(b) Q'2/Q2 = K + 1/2

(c) Q'2/Q2 = K + 1/2K

(d) Q'1/Q1 =

Q 18. Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure at a distance of x (>>a) from O is

Qa

(a)  x 3 0

2Qa

(b)  x 3 0

(c)

3Qa  0 x 3

(d) zero

Q 19. If an electron enters into a space between the plates of a parallel plate capacitor at an angle  with the plates and leaves at an angle  to the plates. The ratio of its kinetic energy while entering the capacitor to that while leaving will be (a) (cos /cos )2 (b) (cos /cos )2 (c) (sin /sin )2 (d) (sin /sin )2 Q 20. A part of the circuit is shown in the figure. All the capacitors have capacitance of 2F:

(a) Charge on capacitor C1 is zero (c) Charge on capacitor C3 is zero

(b) Charge on capacitor C2 is zero (d) Charge on capacitor cannot be determined

Q 21. A capacitor of capacitance C is charged to a potential difference V from a cell and then disconnected from it. A charge +Q is now given to its positive plate. The potential difference across the capacitor is now: (a) V (b) V + Q/C (c) V + Q/2C (d) V – Q/C, if V < CV Q 22. Three identical, parallel conducting plates A, B and C are placed as shown. Switches S1 and S2 are open, and can connect A and C to earth when closed. +Q charge is given to B, then:

(a) if S1 is closed with S2 open, a charge of amount Q will pass through S1 (b) if S2 is closed with S1 open, a charge of amount Q will pass through S2 (c) if S1 and S2 are closed together, a charge of amount Q/ 3 will pass through S1 and a charge of amount 2Q/3 will pass through S2. (d) all of the above Q 23. The ratio between the energy stored in 5F capacitor to the 4F capacitor in the given circuit is :

(a) 1.2

(b) 1

(c) 1.8

(d) 3.6

Q 24. What will be the charge on earthed side of plate A:

(a) Q1 + Q2/2

(b) Q1 – Q2/2

(c) 0

(d) None of these

Q 25. In an insulated parallel-plate capacitor of capacitance C, the four surfaces have charge Q1, Q2, Q3 and Q4, as shown. The potential difference between the plates is:

(a) Q1 + Q2 + Q3 + Q4/2C

(b) Q2 + Q3/2C

(c) Q2 – Q3/2C

(d) Q1 + Q4/2C

Q 26. Five conducting plates are placed parallel to each other. Separation between them is and area of each plate is A. Plate number 1, 2 and 3 are connected with each other and at the same time through a cell of emf E. The charge on plate number 1 is

(a)

E 0 A d

(b)

E 0 A 2d

(c)

2E 0 A d

(d) zero

Q 27. The charge flowing through the cell on closing the key k is equal to

(a) CV/4

(b) 4CV

(c) 4/3CV

(d) 3/4CV

Q 28. In the given arrangement of the capacitors, one 3 F capacitor has got 600J of energy. Then the potential difference across 2F capacitor is

(a) 40V

(b) 15 V

(c) 60 V

(d) 45 V

Q 29. For given circuit, charge on capacitor C1 ,C2 in steady state will be equal to

(a) C1(VA – VC), C2(VC – VB) respectively (c) (C1 + C2) (VA – VB) on each capacitor capacitor

(b) C1(VA – VB), C2(VA – VB) respectively (d) (C1C2/C1 + C2)(VA - VB) on each

Q 30. Two concentric shells have radii R and 2R charges qA and qB and potentials 2 V and (3/2) V respectively. Now shell B is earthed and let charges on them become q'A and q'B. Then

(a) qA/qB = 1/2 (b) q'A /q'B = 1 (c) potential of A after earthing becomes (3/2) V (d) potential difference between A and B after earthing becomes V/2 Q 31. Three capacitors each having capacitance C = 2F are connected with a battery of emf 30V as shown in figure. When the switch S is closed

(a) the amount of charge flown through the battery is 20 C (b) the heat generated in the circuit is 0.6 mJ (c) the energy supplied by the battery is 0.6 mJ (d) the amount of charge flown through the switch S is 60 C 





Q 32. A point charge q is placed at origin. Let E A , E B and E C be the electric field at three points A(1, 2, 3), B(1, 1, -1) and C(2, 2, 2) due to charge q. then         (a) E A  E B (b) E A || E C (c) | E B| = 4| E C| (d) | E B| = 8| E C|

Q 33. Figure shows some of the electric field lines corresponding to an electric field. The figure suggests that (E = electric field, V = potential)

(a) EA > EB (b) EA < EB (c) VA > VB

(d) VA < VB

Q 34. A circular ring carries a uniformly distributed positive charge. The electric field (E) and potential (V) varies with distance (r) from the centre of the ring along its axis as (a)

(b)

(c)

(d)

Q 35. In the circuit shown in figure C1 = C2 = 2F. Then charge stored in

(a) capacitor C1 is zero capacitor C1 is 40 C

(b) capacitor C2 is zero

(c) both capacitors is zero

(d)

Q 36. Three concentric conducting spherical shells have radii r, 2r and 3r and charges q1, q2 and q3 respectively. Innermost and outermost shells are earthed as shown in figure. Select the correct alternative(s)

(a) q1 + q3 = - q2

(b) q1 = - q2/4

(c) q3/q1 = 3 (d) q3/q2 = 1/3

Q 37. A particle of charge q and mass m moves rectilinearly under the action of an electric field E =   x. Here  and  are positive constants and x is the distance from the point where the particle was initially at rest. Then (a) the motion of the particle is oscillatory (b) the amplitude of the particle is / (c) the mean position of the particle is at x = / (d) the maximum acceleration of the particle is q/m IIT JEE OBJECTIVES 

Q 38. The magnitude of electric field E in the annular region of a charged cylindrical capacitor: (1996) (a) is same throughout (b) is higher near the outer cylinder than near the inner cylinder (c) varies as 1/r where r is the distance from the axis (d) varies as 1/r2 where r is the distance from the axis Q 39. A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in figure as: (1996)

(a)1

(b) 2

(c) 3

(d) 4

Q 40. A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x = 0 and positive plate is at x = 3d. The slab is equidistant from the plates. The capacitor is given some charge. As x goes from 0 to 3d: (1998) (a) the magnitude of the electric field remains the same (b) the direction of the electric field remains the same (c) the electric potential increases continuously (d) the electric potential increases at first, then decreases and again increases. Q 41. A charge +q is fixed at each of the points x = x0, x = 3, x = 5, x0………  on the x-axis and a charge q is fixed at each of the points x = 2x0, x = 4x0, x = 6x0…………. . Here x0 is a positive constant. Take the electric potential at a point due to a charge Q at a distance r from it to be Q/40r . Then the potential at the origin due to the above system of charges is: (1998) (a)0 (b) q/80x0In2 (c)  (d) qln(2)/40x0 Q 42. A positively charged thin metal ring of radius R is fixed in the xy plane with its centre at the origin O. A negatively charged particle P is released from rest at the point (0, 0, z0) where z0 > 0. Then the motion of P is: (1998) (a) periodic for all values of z0 satisfying 0 < z0 <  (b) simple harmonic for all values of z0 satisfying 0 < z0  R (c) approximately simple harmonic provided z0 VB (c) VA < VC

(d) VA > VC

Q 53. Two equal point charges are fixed at x = a and x = + a on the x-axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x-axis, is approximately proportional to (2002) (a) x (b) x2 (c) x3 (d) 1/x Q 54. Two identical capacitors, have the same capacitance C. One of them is charged to potential V1 and the other to V2. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is (2002) (a) 1/4C(v12 – V22) (b) 1/4C(V12 + V22) (c) 1/4 C(V1 – V2)2 (d) 1/4 C(V1 + V2)2 Q 55. A metallic shell has a point charge ‘q’ kept diagrams correctly. Which one of the following diagrams correctly represents the electric lines of forces? (2003) (a)

(b)

(c)

(d)

Q 56. Consider the charge configuration and a spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface, the electric field will be due to(2004)

(a) q2 (b) only the positive charges (c) all the charges

(d) + q1 and q1

Q 57. Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at O is double the electric field when only one positive charge of same magnitude is placed at R. Which of the following arrangements of charges is possible for P, Q, R, S, T and U respectively? (2004)

(a) +, , +, , , + (b) +, , +, , +,  (c) +, +, , +, ,  (d) , +, +, , +,  Q 58. In an RC circuit while charging the graph of In l versus time is as shown by the dotted line in the adjoining diagram where l is the current. When the value of the resistance is doubled, which of the solid curves best represents the variation of In l versus time ? (2004)

(a)P

(b)Q

(c) R

(d)S

14. Electrostatics LEVEL-I 1. 8. 15. 22. 29.

a b a c a

2. 9. 16. 23. 30.

b d c b b

3. 10. 17. 24. 31.

c b c a d

4. 11. 18. 25. 32.

c c c a b

5. 12. 19. 26. 33.

a b b a b

6. 13. 20. 27. 34.

c b b d a

7. 14. 21. 28. 35.

b b a b a

d d c a b,c d b c

7. 14. 21. 28. 35. 42. 49. 56.

c a c d b,d a,c c c

LEVEL-II 1. 8. 15. 22. 29. 36. 43. 50. 57.

a d b d a a,b,c a,c c d

2. 9. 16. 23. 30. 37. 44. 51. 58.

b c c c a, d all d a b

3. 10. 17. 24. 31. 38. 45. 52.

b c c c a,c,d c d b

4. 11. 18. 25. 32. 39. 46. 53.

b d a c a,c d c,d b

5. 12. 19. 26. 33. 40. 47. 54.

b a b d a,d b,c b c

6. 13. 20. 27. 34. 41. 48. 55.