Chapter 21

53. Determine the magnitude of the total magnetic field at the center of the loop (due both to the loop and the solenoid) if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla.

B) 3.0 × 10-4 T

61. What is the magnitude and direction of the magnetic field at point B? [four ringed circle]

B) 3.3 × 10-5 T, counterclockwise

31. A circular coil consists of 5 loops each of diameter 1.0 m. The coil is placed in an external magnetic field of 0.5 T. When the coil carries a current of 4.0 A, a torque of magnitude 3.93 N-m acts on it. Determine the angle between the normal to the plane of the coil and the direction of the magnetic field.

B) 30°

[vertical road, P on sidewalk] 56. Determine the magnitude of the magnetic field at the point P.

B) 4.8 × 10-5 T

59. Each second, 1.25 × 1019 electrons in a narrow beam pass through a small hole in a wall. The beam is perpendicular to the wall. Using Ampere's law, determine the magnitude of the magnetic field in the wall at a radius of 0.750 m from the center of the beam.

B) 5.34 × 10-7 T

30. A current-carrying, rectangular coil of wire is placed in a magnetic field. The magnitude of the torque on the coil is not dependent upon which one of the following quantities?

B) the direction of the current in the loop

14. A proton is traveling south as it enters a region that contains a magnetic field. The proton is deflected downward toward the earth. What is the direction of the magnetic field?

B) west

21. Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.

B)M1 > m2 Sign of charge Q1- Sign of charge Q2+

25. A 0.0150-m wire oriented horizontally between the poles of an electromagnet carries a direct current of 9.5 A. The angle between the direction of the current and that of the magnetic field is 25.0° as shown. If the magnetic field strength is 0.845 T, what is the magnitude and direction of the magnetic force on the wire between the poles?

C) 0.0509 N, upward

[hockey rink w/S zamboni inside and N zamboni outside] 29. What is the magnitude of the magnetic force acting on the wire?

C) 0.48 N

65. Determine the magnetic moment of the loop. [same fig as 63]

C) 0.63 A × m2

19. A mass spectrometer is used to separate two isotopes of uranium with masses m1 and m2 where m2 > m1. The two types of uranium atom exit an ion source S with the same charge of +e and are accelerated through a potential difference V. The charged atoms then enter a constant, uniform magnetic field B as shown. If r1 = 0.5049 m and r2 = 0.5081 m, what is the value of the ratio m1/m2?

C) 0.9874

7. A charged particle is launched with a velocity of 5.2 × 104 m/s at an angle of 35° with respect to a 0.0045-T magnetic field. If the magnetic field exerts a force of 0.0026 N on the particle, determine the magnitude of the charge on the particle.

C) 19 µC

51. What is the magnitude of the magnetic field at the point P? [same figure as 50]

C) 2.5 × 10-5 T

39. The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin?

C) 3 × 10-6 T

35. A coil consists of 240 circular loops, each of radius 0.044 m, and carries a current of 2.2 A. Determine the magnetic moment of the coil.

C) 3.2 A × m2

[centipede pic; current carrying loop in center] 52. Determine the value of the current in the solenoid so that the magnetic field at the center of the loop is zero tesla.

C) 6.0 × 10-2 A

[horizontal road, C in center, O on sidewalk] 55. Determine the magnitude of the magnetic field at point C if d = 0.10 m.

C) 9.6 × 10-5 T

13. An proton travels through a region of space with no acceleration. Which one of the following statements is the best conclusion?

C) E and B might both be non-zero, but they must be mutually perpendicular.

43. A coil of wire carries current I as shown in the figure. If the observer could "see" the magnetic field inside this arrangement of loops, how would it appear?

C) c [has x's in center]

16. An electron traveling horizontally enters a region where a uniform magnetic field is directed into the plane of the paper as shown [square 5x4 e enters top left]. Which one of the following phrases most accurately describes the motion of the electron once it has entered the field?

C) downward and circular

[DOUBLE RAINBOW PIC] 23. What is the direction of the magnetic field?

C) into the page

6. A proton traveling due west in a region that contains only a magnetic field experiences a vertically upward force (away from the surface of the earth). What is the direction of the magnetic field?

C) south

[DOUBLE RAINBOW PIC] 24. Determine the magnitude of the magnetic field if ion A travels in a semicircular path of radius 0.50 m at a speed of 5.0 × 106 m/s.

D) 0.21 T

27. A loop of wire with a weight of 0.55 N is oriented vertically and carries a current I = 2.25 A. A segment of the wire passes through a magnetic field directed into the plane of the page as shown. The net force on the wire is measured using a balance and found to be zero. What is the magnitude of the magnetic field?

D) 1.2 T

64. What is the magnitude of the magnetic field at the center of the loop? [same fig as 63]

D) 1.3 × 10-4 T

A long, straight wire carries a 10.0-A current in the +y direction as shown in the figure. Next to the wire is a square copper loop that carries a 2.00-A current as shown. The length of each side of the square is 1.00 m. [figure is a box!] 66. What is the magnitude of the net magnetic force that acts on the loop?

D) 1.7 × 10-5 N

[horizontal road, C in center, O on sidewalk] 54. Determine the value of the current, I, in the top wire.

D) 18 A

46. Four long, straight wires are parallel to each other; and their cross-section forms a square. Each side of the square is 0.020 m as shown in the figure. If each wire carries a current of 8.0 A in the direction shown in the figure, determine the magnitude of the total magnetic field at P, the center of the square.

D) 2.3 × 10-4 T

33. A rectangular loop has sides of length 0.06 m and 0.08 m. The wire carries a current of 10 A in the direction shown. The loop is in a uniform magnetic field of magnitude 0.2 T and directed in the positive x direction. What is the magnitude of the torque on the loop?

D) 8 × 10-3 N × m

18. Two particles move through a uniform magnetic field that is directed out of the plane of the page. The figure shows the paths taken by the two particles as they move through the field. The particles are not subject to any other forces or fields. Which one of the following statements concerning these particles is true? [two semi circles, top left and bottom right corners]

D) Particle 1 is negatively charged; 2 is negative.

8. Which one of the following statements best explains why a constant magnetic field can do no work on a moving charged particle?

D) The magnetic force is always perpendicular to the velocity of the particle.

A long, straight, vertical segment of wire traverses a magnetic field of magnitude 2.0 T in the direction shown in the diagram. The length of the wire that lies in the magnetic field is 0.060 m. When the switch is closed, a current of 4.0 A flows through the wire from point P to point Q. [hockey rink w/S zamboni inside and N zamboni outside] 28. Which one of the following statements concerning the effect of the magnetic force on the wire is true?

D) The wire will be pushed downward, into the plane of the paper.

58. Which one of the following materials is not ferromagnetic?

D) aluminum

48. Two loops carry equal currents I in the same direction. They are held in the positions shown in the figure and project above and below the plane of the paper. The point P lies exactly halfway between them on the line that joins their centers. The centers of the loops and the point P lie in the plane of the paper. Which one of the figures below shows the position of a compass needle if the compass were placed in the plane of the paper at P?

D) d [horizontal n to the left]

9. An electron traveling due north enters a region that contains a uniform magnetic field that points due east. In which direction will the electron be deflected?

D) down

A wire is bent into the shape of a circle of radius r = 0.10 m and carries a 20.0-A current in the direction shown. [current flows clockwise] 63. What is the direction of the magnetic field at the center of the loop?

D) into the plane of the paper

2. Which combination of units can be used to express the magnetic field?

D) kg/(C × s)

49. Two long, straight wires are perpendicular to the plane of the paper as shown in the drawing. Each wire carries a current of magnitude I. The currents are directed out of the paper toward you. Which one of the following expressions correctly gives the magnitude of the total magnetic field at the origin of the x, y coordinate system?

E

60. What is the magnitude and direction of the magnetic field at point A? [four ringed circle]

E) 2.7 × 10-4 T, clockwise

11. An electron is moving with a speed of 3.5 × 105 m/s when it encounters a magnetic field of 0.60 T. The direction of the magnetic field makes an angle of 60.0° with respect to the velocity of the electron. What is the magnitude of the magnetic force on the electron?

E) 2.9 × 10-14 N

15. A particle with a mass of 6.64 × 10-27 kg and a charge of +3.20 × 10-19 C is accelerated from rest through a potential difference of 2.45 × 106 V. The particle then enters a uniform 1.60-T magnetic field. If the particle's velocity is perpendicular to the magnetic field at all times, what is the magnitude of the magnetic force exerted on the particle?

E) 7.87 × 10-12 N

45. Two loops carry equal currents I in the same direction. The loops are held in the positions shown in the figure and are then released. Which one of the following statements correctly describes the subsequent behavior of the loops?

E) The loops attract each other.

3. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true?

E) The magnetic force depends on the component of the particle's velocity that is perpendicular to the field.

1. Which one of the following statements concerning permanent magnets is false?

E) When a permanent magnet is cut in half, one piece will be a north pole and one piece will be a south pole.

[vertical road, P on sidewalk] 57. What is the direction of the magnetic field at the point P?

E) into the plane of the page

A long, straight wire is carrying a current of 5.0 A in the direction shown in the figure. The point P is 0.040 m from the wire. 50. What is the direction of the magnetic field at point P due to the current in the wire?

E) out of the plane of the page

10. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero magnetic field directed eastward is then applied to the region. In what direction, if any, will each electron be moving after the field is applied?

electron A at rest, electron B westward

26. A long, straight wire carries a 6.0-A current that is directed in the positive x direction. When a uniform magnetic field is applied perpendicular to a 3.0-m segment of the wire, the magnetic force on the segment is 0.36 N, directed in the negative y direction, as shown. What are the magnitude and direction of the magnetic field?

A) 0.020 T, out of the paper

62. A long straight wire carries a 40.0 A current in the +x direction. At a particular instant, an electron moving at 1.0 × 107 m/s in the +y direction is 0.10 m from the wire. The charge on the electron is -1.6 × 10-19 C. What is the force on the electron at this instant?

A) 1.3 × 10-16 N in the +x direction

32. A single circular loop of radius 1.00 m carries a current of 10.0 mA. It is placed in a uniform magnetic field of magnitude 0.500 T that is directed parallel to the plane of the loop as suggested in the figure. What is the magnitude of the torque exerted on the loop by the magnetic field? [circle on 5 right pointing arrows]

A) 1.57 × 10-2 N × m

38. A solenoid of length 0.250 m and radius 0.0250 m is comprised of 440 turns of wire. Determine the magnitude of the magnetic field at the center of the solenoid when it carries a current of 12.0 A.

A) 2.21 × 10-3 T

47. The figure shows two concentric metal loops, each carrying a current. The larger loop carries a current of 8.0 A and has a radius of 0.060 m. The smaller loop has a radius of 0.040 m. What is the value of a current in the smaller loop that will result in zero total magnetic field at the center of the system?

A) 5.3 A

42. An overhead electric power line carries a maximum current of 125 A. What is the magnitude of the maximum magnetic field at a point 4.50 m directly below the power line?

A) 5.56 × 10-6 T

40. The radius of a coil of wire with N turns is r = 0.28 m. A clockwise current of Icoil = 1.0 A flows in the coil, as shown. A long, straight wire carrying a current Iwire = 29 A toward the left is located 0.04 m from the edge of the coil. The magnetic field at the center of the coil is zero tesla. Determine N, the number of turns.

A) 8

41. A long, straight wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what is the magnitude of the magnetic field at a distance 2d from the wire?

A) B/2

44. A wire, connected to a battery and switch, passes through the center of a long current-carrying solenoid as shown in the drawing. When the switch is closed and there is a current in the wire, what happens to the portion of the wire that runs inside of the solenoid?

A) There is no effect on the wire.

4. Complete the following statement: The magnitude of the magnetic force that acts on a charged particle in a magnetic field is independent of

A) the sign of the charge.

20. Two charged particles of equal mass are traveling in circular orbits in a region of uniform, constant magnetic field as shown. The particles are observed to move in circular paths of radii R1 and R2 with speeds v1 and v2, respectively.

A) |v1/Q1| < |v2/Q2|

67. What is the direction of the net magnetic force that acts on the loop? [same fig as 66]

B) -x direction

34. A single circular loop of wire of radius 0.45 m carries a constant current of 2.4 A. The loop may be rotated about an axis that passes through the center and lies in the plane of the loop. When the orientation of the normal to the loop with respect to the direction of the magnetic field is 36°, the torque on the coil is 1.5 N × m. What is the magnitude of the uniform magnetic field exerting this torque on the loop?

B) 1.7 T

A beam consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Note: 1 mass unit = 1.67 × 10-27 kg and e = 1.6 × 10-19 C [DOUBLE RAINBOW PIC] 22. Which ion falls at position 2?

B) B

36. Which one of the following statements concerning the magnetic field inside (far from the surface) a long, current-carrying solenoid is true?

B) The magnetic field is non-zero and nearly uniform.

5. A charged particle is moving in a uniform, constant magnetic field. Which one of the following statements concerning the magnetic force exerted on the particle is false?

B) The magnetic force increases the speed of the particle.

37. Complete the following statement: The magnetic field around a current-carrying, circular loop is most like that of

B) a short bar magnet.

17. An electron enters a region that contains a magnetic field directed into the page as shown [square 5x5 e enters bottom left at 30]. The velocity vector of the electron makes an angle of 30° with the +y axis. What is the direction of the magnetic force on the electron when it enters the field?

B) at an angle of 30° below the positive x axis

12. An electron traveling due south enters a region that contains both a magnetic field and an electric field. The electric field lines point due west. It is observed that the electron continues to travel in a straight line due south. In which direction must the magnetic field lines point?

B) down