Solved Problems- Chap29

Phy201 Dr.Hikmat A. Hamad Page 1

Abu Dhabi University Solved Problems College of Arts & Sciences Ch 29. Magnetic Fields PHY201. Physics II. 1. A electron is projected into a magnetic field that is directed along the positive x axis. Find the direction of the magnetic force exerted on the electron for each of the following directions of the electrons 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 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


3. An electron has a velocity of 6 106 m/s in the positive x direction at a point where the magnetic field has the components Bx = 3 T, By = 1.5 T and Bz = 2 T. What is the magnitude of the acceleration of the electron at this point? Answer. 2.6 x 1018 m/s2

4. A particle (q = 5 nC, m = 3 g) moves in a region where the magnetic field has components Bx = 2 mT, By = 3 mT, and Bz = 4 mT. At an instant when the speed of the particle is 5000 m/s and the 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 (2i + 4j + 6k) m/s and experiences a magnetic force of (4i 20j + 12k) N. The x component of the magnetic field is equal to zero. Determine the y component of the magnetic field. Answer. + 3 T

By comparing each side with term by term we have


6. A proton travels with a speed of 5.02 x 106 m/s in a direction that makes an angle of 60.0o 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 protons acceleration?

7. An electron is accelerated through 2.40 x 103 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?


8. A proton moves with a velocity of in a region in which the magnetic field is What is the magnitude of the magnetic force this particle experiences?

9. A proton moves perpendicular to a uniform magnetic field B at a speed of 1.00 x 107 m/s and experiences an acceleration of 2.00x 1013 m/s2 in the positive x- direction when its velocity is in the positive z- direction. Determine the magnitude and direction of the field.


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 107 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 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 wire?


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 in the direction shown in the magnetic field B. Justify your choice by drawing and calculations. a. 2IBL in the z direction b. 2IBL in the +z direction c. 4IBL in the +z direction d. 4IBL 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 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


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 a 1s time interval? (mp = 1.67 x 10-27 kg, q = 1.6 x 10-19 C). Answer. 48 km

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

18. A 0.200-kg 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


19. 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? Ans: 72o

20. A 0.200-kg 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

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Solved Problems- Chap29