Solved Problems- Chap29

Abu Dhabi University College of Arts & Sciences PHY201. Physics II.

Solved Problems Ch 29. Magnetic Fields

that is directed along the positive x axis. 1. A electron is projected into a magnetic field that Find the direction of the magnetic force exerted on the electron for each of the following directions of the electron’s velocity: (a) the positive y direction, (b) the negative y direction, (c) the positive x direction.

2. A positively charged particle has a velocity in the negative z direction  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? d ata? a. B x is positive. b. B z is positive. c. B y is negative. d. B y is positive.

Phy201

Dr.Hikmat A. Hamad

e. B x is negative

Page 1

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3. An electron has a velocity of 6 × 10  m/s in the positive  x direction at a point where the magnetic field has the components B x = 3 T, B y = 1.5 T and B z = 2 T. What is the magnitude of the acceleration of the electron at this point? Answer. 2.6 x 1018 m/s2

3 µg) moves in a region where the magnetic field has 4. A particle (q = 5 nC, m = 3 µ components B x = 2 mT, B y = 3 mT, and B z = – 4 mT. At an instant when the speed of the  particle is 5000 m/s and the direction direction of its velocity is 120° relative to the magnetic field, what is the magnitude of the acceleration of the particle? Answer. 39 m/s2

5. A 2 C charge moves with a velocity of (2 i + 4 j + 6k) m/s and experiences a magnetic force of (4i – 20 j + 12k) N. The x component of the magnetic field is equal to zero. Determine the y the y component of the magnetic field. Answer. + 3 T

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with a speed of 5.02 x 106 m/s in a direction that makes an angle of 60.0 o 6. A proton travels with with the direction of a magnetic field of magnitude 0.180 T in the positive x direction. What are the magnitudes of (a) the magnetic force on the proton and (b) the proton’s acceleration?

7. An electron is accelerated through 2.40 x 10 3 V from rest and then enters a uniform 1.70 T magnetic field. What are (a) the maximum and (b) the minimum values of the magnetic force this particle experiences?

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8. A proton moves with a velocity of magnetic field is experiences?

in a region in which the

What is the magnitude of the magnetic force this particle

9. A proton moves perpendicular to a uniform magnetic field B at a speed of 1.00 x 107 m/s 13 2 and experiences an acceleration of 2.00x 10  m/s  in the positive x- direction when its velocity is in the positive z- direction. Determine the magnitude and direction of the field.

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10. An electron moves in a circular path perpendicular to a uniform magnetic field with a magnitude of 2.00 mT. If the speed of the electron is 1.50 x 10 7 m/s, determine (a) the radius of the circular path and (b) the time interval required to complete one revolution.

11. A cyclotron designed to accelerate protons has a magnetic field of magnitude 0.450 T over a region of radius 1.20 m. What are (a) the cyclotron frequency and (b) the maximum speed acquired by the protons?

12. A wire carries a steady current of 2.40 A. A straight section section of the wire is 0.750 m long and lies along the x axis within a uniform magnetic field, If the current is in the positive x direction, what is the magnetic force on the section of o f wire?

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13. A straight wire carries a current of 40 A in a uniform magnetic field of 80 mT. If the force per unit length on this wire is 2 N/m, determine the angle between the wire and the magnetic field. Answer. either 39° or 141°

14. A straight wire is bent into the shape shown. Determine the net magnetic force on the wire when the current I  travels  travels in the direction shown in the magnetic field B. Justify your  choice by drawing drawing and calculations. calculations. a. 2 IBL in the –   z direction b. 2 IBL in the + z direction c. 4 IBL in the + z direction d. 4 IBL in the –   z direction e. zero F=I LxB= I(2L) B sin90=2ILB in the +z direction

15. A straight wire is bent into the shape shown. Determine the net magnetic force on the wire. Justify your choice. a. Zero a. Zero b. IBL in the + z direction c. IBL in the –   z direction d. 1.7 IBL in the + z direction e. 1.4 IBL in the –   z direction

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16. A proton moves around a circular path (radius = 2 mm) in a uniform 0.25T magnetic field. What total distance does this proton travel during dur ing a 1s time interval? -27 -19 (m p = 1.67 x 10  kg, q = 1.6 x 10  C). Answer. 48 km

17. What is the radius of curvature of the path of a 3 keV proton in a perpendicular -19 magnetic field of magnitude 0.8 T? (1 eV = 1.6 x10  J) Answer. 9.9 mm

metal rod carrying a current of I =10.0 A slides on two horizontal hor izontal rails 18. A 0.200-kg metal that are a distance distance d = 0.500 m apart. If the coefficient of kinetic friction between the rod and rails is 0.100, what vertical magnetic field B is required to keep the rod moving at a constant speed? Ans: 39.2 mT

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19. A charged particle (m = 2.0 g, q = −50 µ C) 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? Ans: 72 o

20. A 0.200-kg metal metal rod carrying a current of I =10.0 A slides on two horizontal rails that are a distance d = 0.500 m apart. If the coefficient of kinetic friction between the rod and rails is 0.100, what vertical magnetic field B is required to keep the rod moving at a constant speed? Ans: 39.2 mT