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
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. 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
ANS: B PTS: 2 DIF: Average
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
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. 2.5 N m b. 1.5 N m c. 3.1 N m d. 2.7 N m e. 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. 8.1 N m b. 24 N m c. 22 N m d. 13 N m e. 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. 0.15 N b. 0.68 N c. 0.30 N d. 0.34 N e. 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. 0.21 N m b. 0.20 N m c. 0.35 N m d. 0.12 N m e. 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. 39 b. 51 c. 44 d. 34 e. 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. 18 T b. 14 T c. 28 T d. 34 T e. 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. 27 b. 72 c. 63 d. 18 e. 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
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
b. downward.
c. from south to north. d. from north to south. e. 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. position 1. b. position 2. c. position 3
d. positions 2 and 3. e. 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. Particle 1 has a positive charge and particle 2 has a negative charge. b. Both particles are positively charged.
c. Both particles are negatively charged.
d. Particle one has a negative charge and particle 2 has a positive charge.
e. 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. a net force to the left. b. a net force to the right. c. a net force upwards.
d. 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