Chapter (30)

Chapter 30

Sources of the Magnetic Field

Multiple Choice

1. One long wire carries a current of 30 A along the entire x axis. A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0, 4, 0) m. What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis?

a. 4.0 μT b. 5.0 μT c. 3.0 μT d. 7.0 μT e. 1.0 μT

2. Two long parallel wires each carry a current of 5.0 A directed to the east. The two wires are separated by 8.0 cm. What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires?

a. 72 μT b. 48 μT c. 24 μT d. 96 μT e. 32 μT

3. A 2.0-cm length of wire centered on the origin carries a 20-A current directed in the positive y direction. Determine the magnetic field at the point x = 5.0 m on the x-axis.

a. 1.6 nT in the negative z direction b. 1.6 nT in the positive z direction c. 2.4 nT in the negative z direction d. 2.4 nT in the negative z direction e. None of the above

159

160 CHAPTER 30

4. Three long wires parallel to the x axis carry currents as shown. If I = 20 A, what is the magnitude of the magnetic field at the origin?

y = 2 m

y = –1 m�

y = –3 m

x

y

4 I

3 I

I a. 37 μT b. 28 μT c. 19 μT d. 47 μT e. 58 μT

5. Each of two long straight parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction. What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire?


6. Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions. What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire?


7. Two long parallel wires carry unequal currents in the same direction. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μT. What is the larger of the two currents?

a. 5.3 A b. 3.8 A c. 4.5 A d. 3.0 A e. 0.5 A

Sources of the Magnetic Field 161

8. Two long straight wires carry currents perpendicular to the xy plane. One carries a current of 50 A and passes through the point x = 5.0 cm on the x axis. The second wire has a current of 80 A and passes through the point y = 4.0 cm on the y axis. What is the magnitude of the resulting magnetic field at the origin?


9. Two very long parallel wires carry currents in the positive x direction. One wire (current = 15 A) is coincident with the x axis. The other wire (current = 50 A) passes through the point (0,4.0 mm,0). What is the magnitude of the magnetic field at the point (0,0,3.0 mm)?

a. 3.8 mT b. 2.7 mT c. 2.9 mT d. 3.0 mT e. 0.6 mT

10. Each of two parallel wires separated by 8.0 mm carries a 20-A current. These two currents are oppositely directed. Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.


11. Each of two parallel wires separated by 6.0 mm carries a 40-A current. These two currents are in the same direction. Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

a. 2.6 mT b. zero c. 1.9 mT d. 1.6 mT e. 3.2 mT

12. Two long parallel wires separated by 5.0 mm each carry a current of 60 A. These two currents are oppositely directed. What is the magnitude of the magnetic field at a point that is between the two wires and 2.0 mm from one of the two wires?

a. 2.0 mT b. 10 mT c. 8.0 mT d. 1.6 mT e. 7.2 mT

162 CHAPTER 30

13. Two long parallel wires separated by 4.0 mm each carry a current of 24 A. These two currents are in the same direction. What is the magnitude of the magnetic field at a point that is between the two wires and 1.0 mm from one of the two wires?


14. A long straight wire carries a current of 40 A in a region where a uniform external magnetic field has a 30-μT magnitude and is parallel to the current. What is the magnitude of the resultant magnetic field at a point that is 20 cm from the wire?


15. Two long parallel wires carry unequal currents in opposite directions. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μT. What is the larger of the two currents?

a. 0.5 A b. 1.0 A c. 1.5 A d. 2.0 A e. 3.0 A

16. A segment of wire of total length 3.0 m carries a 15-A current and is formed into a semicircle. Determine the magnitude of the magnetic field at the center of the circle along which the wire is placed.

a. 1.6 μT b. 4.9 μT c. 1.0 μT d. 9.8 μT e. 15 μT

17. A segment of wire of total length 2.0 m is formed into a circular loop having 5.0 turns. If the wire carries a 1.2-A current, determine the magnitude of the magnetic field at the center of the loop.

a. 79 μT b. 69 μT c. 59 μT d. 89 μT e. 9.4 μT


18. If a = 2.0 cm, b = 5.0 cm, and I = 20 A, what is the magnitude of the magnetic field at the point P?

b aP

I

30˚�

a. 4.5 μT b. 7.5 μT c. 9.0 μT d. 6.0 μT e. 3.6 μT

19. If a = 1.0 cm, b = 3.0 cm, and I = 30 A, what is the magnitude of the magnetic field at point P?

b

a

90˚�

P

I


20. A straight wire (length = 8.0 m) is bent to form a square. If the wire carries a current of 20 A, what is the magnitude of the magnetic field at the center of the square?


164 CHAPTER 30

21. In the figure, if a = 2.0 cm, b = 4.0 cm, and I = 2.0 A, what is the magnitude of the magnetic field at point P?

b

a

P

90˚�

I


22. The segment of wire (total length = 6R) is formed into the shape shown and carries a current I. What is the magnitude of the resulting magnetic field at the point P?

I

P

R

RIμ

80 a.

RIμ

20b.

RIμ

40c.

RIμ

π20d.

e. R

Iμ80π


23. The segment of wire (total length = 6R) is formed into the shape shown and carries a current I. What is the magnitude of the resulting magnetic field at the point P?

R

PI

a. Iμ3 0

R8

b. Iμ3 0

R2

c. Iμ3 0

R4

d. Iμ3 0

R2

e. R8

Iμ3 0π

24. What is the magnitude of the magnetic field at point P if a = R and b = 2R?

b

aP

I

RIμ

169 0a.

RIμ

163 0b.

RIμ

40c.

RIμ

43 0d.

e. R

Iμ8

3 0

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b

a

PI

I

a. Iμ3 0

R4

b. Iμ0

R4

c. Iμ2 0

R3

d. Iμ0

R3

e. R4

Iμ3 0π


b

a

P

I

RIμ

60a.

RIμ

163 0b.

RIμ

120c.

RIμ

160d.

e. RIμ

320


27. What is the magnitude of the magnetic field at point P in the figure if a = 2.0 cm, b = 4.5 cm, and I = 5.0 A?

b

a

PI

I

a. 87 μT, into the paper b. 87 μT, out of the paper c. 0.23 mT, out of the paper d. 0.23 mT, into the paper e. 23 μT, into the paper

28. Three long, straight, parallel wires each carry a current of 10 A in the positive x direction. If the distance between each wire and the other two is 10 cm, what is the magnitude of the magnetic force on a 20-cm length of either of the wires?

a. 57 μN b. 40 μN c. 69 μN d. 50 μN e. 20 μN

29. Two long parallel wires are separated by 6.0 mm. The current in one of the wires is twice the other current. If the magnitude of the force on a 3.0-m length of one of the wires is equal to 8.0 μN, what is the greater of the two currents?

a. 0.20 A b. 0.40 A c. 40 mA d. 20 mA e. 0.63 A

30. Two long parallel wires are separated by 2.0 cm. The current in one of the wires is three times the other current. If the magnitude of the force on a 2.0-m length of one of the wires is equal to 60 μN, what is the greater of the two currents?

a. 2.0 A b. 1.0 A c. 3.0 A d. 9.0 A e. 1.5 A

168 CHAPTER 30

31. Three long, straight, parallel wires all lie in the yz plane and each carries a current of 20 A in the positive z direction. The two outer wires are each 4.0 cm from the center wire. What is the magnitude of the magnetic force on a 50-cm length of either of the outer wires?

a. 1.0 mN b. 0.50 mN c. 1.1 mN d. 1.5 mN e. 2.0 mN

32. Two long parallel wires are separated by 4.0 cm. One of the wires carries a current of 20 A and the other carries a 30-A current. Determine the magnitude of the magnetic force on a 2.0-m length of the wire carrying the greater current.

a. 7.0 mN b. 6.0 mN c. 8.0 mN d. 9.0 mN e. 4.0 mN

33. The figure shows a cross section of three parallel wires each carrying a current of 5.0 A out of the paper. If the distance R = 6.0 mm, what is the magnitude of the magnetic force on a 2.0-m length of any one of the wires?

R R

R a. 2.5 mN b. 3.3 mN c. 2.2 mN d. 2.9 mN e. 1.7 mN


34. The figure shows a cross section of three parallel wires each carrying a current of 20 A. The currents in wires A and B are out of the paper, while that in wire C is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 2.0-m length of wire A?

A

R R

R

B Cx

a. 23 mN b. 64 mN c. 32 mN d. 46 mN e. 55 mN

35. The figure shows a cross section of three parallel wires each carrying a current of 15 A. The currents in wires A and C are out of the paper, while that in wire B is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 4.0-m length of wire C?

x

A B C

R R


36. The figure shows a cross section of three parallel wires each carrying a current of 24 A. The currents in wires B and C are out of the paper, while that in wire A is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 4.0-m length of wire A?

A B C

2R Rx


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37. A long cylindrical wire (radius = 2.0 cm) carries a current of 40 A that is uniformly distributed over a cross section of the wire. What is the magnitude of the magnetic field at a point which is 1.5 cm from the axis of the wire?

a. 0.53 mT b. 28 mT c. 0.30 mT d. 40 mT e. 1.9 mT

38. A long straight wire (diameter = 2.0 mm) carries a current of 25 A. What is the magnitude of the magnetic field 0.50 mm from the axis of the wire?




40. A hollow cylindrical (inner radius = 1.0 mm, outer radius = 3.0 mm) conductor carries a current of 80 A parallel to its axis. This current is uniformly distributed over a cross section of the conductor. Determine the magnitude of the magnetic field at a point that is 2.0 mm from the axis of the conductor.

a. 8.0 mT b. 3.0 mT c. 5.3 mT d. 16 mT e. 1.2 mT

41. A hollow cylindrical (inner radius = 2.0 mm, outer radius = 4.0 mm) conductor carries a current of 24 A parallel to its axis. This current is uniformly distributed over a cross section of the conductor. Determine the magnitude of the magnetic field at a point that is 5.0 mm from the axis of the conductor.





43. A long hollow cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 24 A distributed uniformly across its cross section. A long wire which is coaxial with the cylinder carries an equal current in the opposite direction. What is the magnitude of the magnetic field 3.0 mm from the axis?


44. A long hollow cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 12 A distributed uniformly across its cross section. A long wire which is coaxial with the cylinder carries an equal current in the same direction. What is the magnitude of the magnetic field 3.0 mm from the axis?


45. A long, straight wire (radius = 2.0 mm) carries a current of 2.0 A distributed uniformly over a cross section perpendicular to the axis of the wire. What is the magnitude of the magnetic field at a distance of 1.0 mm from the axis of the wire?


46. A long wire is known to have a radius greater than 4.0 mm and to carry a current uniformly distributed over its cross section. If the magnitude of the magnetic field is 0.285 mT at a point 4.0 mm from the axis of the wire and 0.200 mT at a point 10 mm from the axis, what is the radius of the wire?

a. 4.6 mm b. 7.1 mm c. 5.3 mm d. 12 mm e. 10 mm

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47. A long wire carries a current of 3.0 A along the axis of a long solenoid (radius = 3.0 cm, n = 900 turns/m, current = 30 mA). What is the magnitude of the magnetic field at a point 2.0 cm from the axis of the solenoid? Neglect any end effects.


48. A solenoid 4.0 cm in radius and 4.0 m in length has 8000 uniformly spaced turns and carries a current of 5.0 A. Consider a plane circular surface (radius = 2.0 cm) located at the center of the solenoid with its axis coincident with the axis of the solenoid. What is the magnetic flux through this surface? (1 Wb = 1 T ⋅ m2)

a. 63 μWb b. 16 μWb c. 0.25 mWb d. 10 μWb e. 5.0 μWb

49. A long solenoid (diameter = 5.0 cm) is wound with 960 turns per meter of thin wire through which a current of 300 mA is maintained. A wire carrying 12 A is inserted along the axis of the solenoid. What is the magnitude of the magnetic field at a point 2.0 cm from the axis?


50. A current-carrying 2.0-cm long segment of wire is inside a long solenoid (radius = 4.0 cm, n = 800 turns/m, current = 50 mA). The wire segment is oriented perpendicularly to the axis of the solenoid. If the current in the wire segment is 12 A, what is the magnitude of the magnetic force on this segment?

a. 22 μN b. 16 μN c. 18 μN d. 12 μN e. 0 μN

51. A long solenoid (n = 1200 turns/m, radius = 2.0 cm) has a current of a 0.30 A in its winding. A long wire carrying a current of 20 A is parallel to and 1.0 cm from the axis of the solenoid. What is the magnitude of the resulting magnetic field at a point on the axis of the solenoid?

a. 0.60 mT b. 0.85 mT c. 52 μT d. 0.40 mT e. 0.75 mT


52. A long solenoid (1500 turns/m) carries a current of 20 mA and has an inside diameter of 4.0 cm. A long wire carries a current of 2.0 A along the axis of the solenoid. What is the magnitude of the magnetic field at a point that is inside the solenoid and 1.0 cm from the wire?


53. A long solenoid (1000 turns/m) carries a current of 25 mA and has an inside radius of 2.0 cm. A long wire which is parallel to and 4.0 cm from the axis of the solenoid carries a current of 6.0 A. What is the magnitude of the magnetic field at a point on the axis of the solenoid?


54. Two long parallel wires lie in the xz plane. One wire passes through the point (–2 m, 0, 0) and the other through the point (+2 m, 0, 0). The wires carry equal currents in the positive z direction.

1. The magnetic field at (–3 m,0,0) is in the negative y direction. 2. The magnetic field at (–1 m,0,0) is in the positive y direction. 3. The magnetic field at (+1 m,0,0) is in the positive y direction. 4. The magnetic field at (+3 m,0,0) is in the negative y direction.

a. 1 and 2 are correct. b. 1 and 4 are correct. c. 2 and 3 are correct. d. 3 and 4 are correct. e. None of the above are correct.

55. A single circular (radius = R) loop of wire is located in the yz plane with its center at the origin. The loop has a clockwise current as seen from the point (+R, 0, 0). The direction of the magnetic field at the point

a. (0, 0, 0) is –i and at the point (+R, 0, 0) is –i. b. (0, 0, 0) is –i and at the point (0, +2R, 0) is –i. c. (0, 0, 0) is +i and at the point (+R, 0, 0) is +i. d. (0, 0, 0) is +i and at the point (0, +2R, 0) is +i. e. None of the above

174 CHAPTER 30

56. A conducting hollow cylinder (inner radius = a, outer radius = b) carries a current of 40 A that is uniformly distributed over the cross section of the conductor. If a = 3.0 mm and b = 6.0 mm, what is the magnitude of the (line)

integral ∫B ⋅ ds around a circular path (radius = 5.0 mm) centered on the axis of

the cylinder and in a plane perpendicular to that axis?

a. 50 μT ⋅ m b. 30 μT ⋅ m c. 22 μT ⋅ m d. 37 μT ⋅ m e. 47 μT ⋅ m

57. A conducting rod with a square cross section (3.0 cm × 3.0 cm) carries a current of 60 A that is uniformly distributed across the cross section. What is the

magnitude of the (line) integral ∫B ⋅ ds around a square path (1.5 cm × 1.5 cm) if

the path is centered on the center of the rod and lies in a plane perpendicular to the axis of the rod?

a. 14 μT ⋅ m b. 75 μT ⋅ m c. 19 μT ⋅ m d. 57 μT ⋅ m e. 38 μT ⋅ m

58. A current element (length = 1.0 cm) lies along the x axis with its center at x = 0 and carries a 20-A current in the positive x direction. Consider only the field of this current element and decide which combination of the following statements is correct.

1. The field at (0,0,1.0 m) is in the positive z direction. 2. The field at (0,1.0 m,0) is in the negative y direction. 3. The field at (1.0 m,0,0) is zero. 4. The field at (0,0,1.0 m) is in the negative y direction.

a. 3 and 4 b. 1 and 3 c. 2 and 4 d. 1 and 2 e. None of these

59. Which diagram correctly shows the magnetic field lines created by a circular current loop in which current flows in the direction shown?

I I I I

IB B BB

(a) (b) (c) (d) (e)

B


60. Gauss’s Law states that the net electric flux, ∫E · dA, through any closed surface

is proportional to the charge enclosed: ∫E · dA = 0ε

q. The analogous formula for

magnetic fields is:

a. ∫B · dA = 0.

b. ∫B · dA = 0

mag

εq

.

c. ∫B · dA = 0μ

I.

d. ∫B · dA = 00εμ

I.

e. ∫B · dA = – dtdΦ

.

61. When the number of turns in a solenoid and its length are both doubled, the ratio of the magnitude of the new magnetic field inside to the magnitude of the original magnetic field inside is:

a. 0.25 b. 0.50 c. 1 d. 2 e. 4

62. By using a compass to measure the magnetic field direction at various points adjacent to a long straight wire, you can show that the wire’s magnetic field lines are

a. straight lines in space that go from one magnetic charge to another. b. straight lines in space that are parallel to the wire. c. straight lines in space that are perpendicular to the wire. d. circles that have their centers on the wire and lie in planes perpendicular to

the wire. e. circles that have the wire lying along a diameter of the circle.

63. The reason the north pole of a bar magnet free to rotate points north is because

a. the south geographic pole of the earth is the earth’s magnetic north pole. b. the south geographic pole of the earth is the earth’s magnetic south pole. c. there is a net accumulation of negative magnetic charge at the earth’s south

geographic pole. d. there is a net accumulation of positive magnetic charge at the earth’s north

geographic pole. e. the north geographic pole of the earth is the earth’s magnetic north pole.

176 CHAPTER 30

64. The following statements all refer to the human brain when mental activity is occurring. Which statement is correct?

a. In order to detect electric currents in the brain, you must open the skull and make direct electrical contact with the brain.

b. The electric currents in the brain can be detected outside the brain by detecting the magnetic fields they produce.

c. The electric currents in the brain can be mapped by shaving a person’s head and dropping iron filings on the head.

d. The electric currents in the brain produce an aura that can be detected visually.

e. The electric currents in the brain cannot be detected by any means.

65. At a point in space where the magnetic field is measured, the magnetic field produced by a current element

a. points radially away in the direction from the current element to the point in space.

b. points radially in the direction from the point in space towards the current element.

c. points in a direction parallel to the current element. d. points in a direction parallel to but opposite in direction to the current

element. e. points in a direction that is perpendicular to the current element and

perpendicular to the radial direction.

66. A long wire lies in a tangle on the surface of a table, as shown below. When a current is run through the wire as shown, the largest component of the magnetic field at X points

x

I

a. into the table. b. out of the table. c. parallel to the nearest segment of wire. d. antiparallel to the nearest segment of wire. e. along a circle which has its center at the center of the overall loop.


67. A solenoid consists of 100 circular turns of copper wire. Parts of three turns, A, B and C, are shown below.

A B C

I

When a current flows through the coil,

a. both A and C are repelled by B. b. A is attracted to B; C is repelled by B. c. neither A nor C is attracted to or repelled by B. d. A is repelled by B; C is attracted to B. e. both A and C are attracted to B.

68. When a microwave filter consisting of vertical parallel metal rods is in the absorbing position, oscillating currents are set up in the rods. At any one instant, the current in each rod has the same magnitude and direction. At that instant

a. the rods will try to move apart horizontally. b. the rods will try to move together horizontally. c. the rods will try to shift vertically upwards. d. the rods will try to shift vertically downwards. e. the rods will not be affected because the source of current is not a battery.

69. A toroid is made of 2000 turns of wire of radius 2.00 cm formed into a donut shape of inner radius 10.0 cm and outer radius 14.0 cm. When a 30.0-A current is present in the toroid, the magnetic field at a distance of 11.0 cm from the center of the toroid is

a. 0.0857 T. b. 0.109 T. c. 0.120 T. d. 0.600 T. e. 0.685 T.

70. Two solenoids are each made of 2000 turns of copper wire per meter. Solenoid I is 2 m long, while solenoid II is 1 m long. When equal currents are present in the two solenoids, the ratio of the magnetic field BI along the axis of solenoid I to the magnetic field BII along the axis of solenoid II, BI/BII, is

a. 1/4. b. 1/2. c. 1. d. 2 e. 4.

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71. A 0.50-m long solenoid consists of 1000 turns of copper wire wound with a 4.0 cm radius. When the current in the solenoid is 18 A, the magnetic field at a point 1.0 cm from the central axis of the solenoid is

a. 0.090 mT. b. 0.36 mT. c. 23 mT. d. 36 mT. e. 45 mT.

72. Two solenoids of equal length are each made of 2000 turns of copper wire per meter. Solenoid I has a 5.00 cm radius; solenoid II a 10.0 cm radius. When equal currents are present in the two solenoids, the ratio of the magnitude of the magnetic field BI along the axis of solenoid I to the magnitude of the magnetic field BII along the axis of solenoid II, BI/BII, is

a. 1/4. b. 1/2. c. 1. d. 2. e. 4.

73. A thin infinitely large current sheet lies in the y-z plane. Current of magnitude Js per unit length along the z axis travels in the y-axis direction, which is up out of the page. Which diagram below correctly represents the direction of the magnetic field on either side of the sheet?

x x x

x x

B B B B B B

B BB B

(a) (b) (c)

(d) (e)

74. The magnetic moment of an electron (charge = -e; mass = me) moving in a circular orbit of radius r with speed v about a nucleus of mass mN is proportional to

a. r. b. v. c. vr. d. evr. e. mNvr.


75. The magnetic field strength H within a solenoid with n turns per unit length (length = ) and current I has magnitude H equal to

a. nI. b. nI0μ . c. nI)1( 0μ+ .

d. nI

.

e. nI0μ .

76. On the average, in a ferromagnetic domain permanent atomic magnetic moments are aligned _____ to one another.

a. antiparallel b. parallel c. perpendicular d. alternately parallel and antiparallel e. randomly relative

77. Equal currents of magnitude I travel out of the page in wires M and N. Eight directions are indicated by letters A through H.

A

BC

D

E

FG

H

M N

P

The direction of the magnetic field at point P is

a. E. b. F. c. G. d. H. e. A.

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78. Equal currents of magnitude I travel out of the page in wire M and into the page in wire N. Eight directions are indicated by letters A through H.

A

BC

D

E

FG

H

M N

P


a. A. b. B. c. C. d. D. e. E.

79. Equal currents of magnitude I travel into the page in wire M and out of the page in wire N. Eight directions are indicated by letters A through H.

A

BC

D

E

FG

H

M N

P


a. C. b. E. c. F. d. G. e. H.

80. Equal currents of magnitude I travel into the page in wires M and N. Eight directions are indicated by letters A through H.

A E

FG

H

BC

D

M N

P


a. B. b. C. c. D. d. E. e. F.


81. Lara says that the magnetic field outside an infinitely long solenoid would be no larger than the field caused by a single winding. Meara says that it is zero, because the magnetic field is confined to the inside of an infinite solenoid. Which one, if either, is correct, and why?

a. Meara, because each loop in an adjacent pair of windings cancels out the magnetic field of the other.

b. Lara, because each loop in an adjacent pair of windings cancels out the magnetic field of the other.

c. Meara, because the magnetic fields from loops of wire at equal distances from a given loop cancel at the position of that loop.

d. Lara, because the magnetic fields from loops of wire at equal distances from a given loop cancel at the position of that loop.

e. Neither. They are both wrong because the field outside the solenoid is directly proportional to the distance between the windings.

82. If you were to travel parallel to an infinitely long straight wire with current I at the same velocity as the electrons in the wire at a distance a from the wire, the magnitude of the magnetic field (according to your measuring instruments) would be

a. 0. μ I

b.

0

2π a.

μ0Iπ a

c. .

2μ0Iπ a

d. .

e.

4μ0Iπ a

.

83. Two parallel and coaxial current loops of radius a are placed a distance L apart. The current in each ring circulates in the same direction. At a point on the axis half way between the loops the magnetic field in T has magnitude

a. 0.

μ0Ia2

4(a2 + L2 )3/2 . b.

μ0Ia2

2(a2 + L2 )3/2c. .

μ0Ia(a2 + L

2

2 )3/2d. .

e.

2μ0IL

.

182 CHAPTER 30

84. Two parallel and coaxial current loops of radius a are placed a distance L apart. When you look along the axis at the loops, the current in one is clockwise, and counterclockwise in the other. At a point on the axis half way between the loops the magnetic field in T has magnitude

a. 0.

b.

μ0Ia2

4(a2 + L2 )3/2 .

c.

μ0Ia2

2(a2 + L2 )3/2 .

d.

μ0Ia2

(a2 + L2 )3/2 .

e.

2μ0IL

.

85. Two current loops are coaxial and coplanar. One has radius a and the other has radius 2a. Current 2I in the outer loop is parallel to current I in the inner loop. The magnitude of the magnetic field at the center of the two loops is

a. 0. μ0I . b.

4a

c.

μ I0

2a.

d.

μ I0

a.

e.

2μ0Ia

.

86. Two current loops are coaxial and coplanar. One has radius a and the other has radius 2a. Current 2I in the outer loop is antiparallel to current I in the inner loop. The magnitude of the magnetic field at the center of the two loops is

a. 0.

μ0I4a

. b.

μ0I2a

c. .

μ0Ia

d. .

e.

2μ0Ia

.


87. We find that N current loops are coplanar and coaxial. The first has radius a and current I. The second has radius 2a and current 2I, and the pattern is repeated up to the Nth, which has radius Na and current NI. The current in each loop is counterclockwise as seen from above. The magnitude of the magnetic field at the center of the loops is

a.

μ0I2Na

.

b.

μ0INa

.

c.

μ0I2a

.

d.

μ0NI2a

.

e.

μ0NIa

.

88. We find that 2N current loops are coplanar and coaxial. The first has radius a and current I. The second has radius 2a and current 2I, and the pattern is repeated up to the Nth, which has radius Na and current NI. The current in the loops alternates in direction from loop to loop as seen from above. Thus the current in the first loop is counterclockwise, in the next clockwise, up to the last loop where it is again clockwise. The magnitude of the magnetic field at the center of the loops is

a. 0.

μ0I2Na

. b.

μ0INa

c. .

μ0NI2a

d. .

e.

μ0NIa

.

184 CHAPTER 30

89. Three coplanar parallel straight wires carry equal currents I to the right as shown below. Each pair of wires is a distance a apart. The direction of the magnetic force on the middle wire

I

I

I

a. is up out of the plane of the wires. b. is down into the plane of the wires. c. is in the plane of the wires, directed upwards. d. is in the plane of the wires, directed downwards e. cannot be defined, because there is no magnetic force on the middle wire.

90. Three coplanar parallel straight wires carry equal currents I as shown below. The current in the outer wires is directed to the right, and that in the middle wire is directed to the left. Each pair of wires is a distance a apart. The direction of the magnetic force on the middle wire

I

I

I


91. Three coplanar parallel straight wires carry equal currents I to the right as shown below. The current in the upper two wires is directed to the right, but the current in the bottom wire is directed to the left. Each pair of wires is a distance a apart. The direction of the magnetic force on the middle wire

I

I

I



92. An ideal solenoid of radius a has n turns per unit unit length and current I. The magnetic flux ΦB through any circular area of radius a inside the solenoid, centered on and perpendicular to the solenoid axis is

a. μ0

π a2

4nI .

b. μ0

π a2

2nI .

c. μ0π a2nI .

d. 2μ0π a2nI . e. 0.

93. An ideal solenoid of radius a has n turns per unit unit length and current I. The magnetic flux ΦB through any area completely inside the solenoid, centered on the solenoid axis but at a 45° angle to the axis, so that it touches the inside of the solenoid, as shown below, is

μ0

π a2

4nIa. .

b. μ

π a2

. nI0 2c. μ0π a2nI .

d. 2μ0π a2nI . e. 0.

186 CHAPTER 30

Open-Ended Problems

94. A long solenoid (n = 80 turns/cm) carries a current of 70 mA. If the interior of the solenoid is filled with a ferromagnetic material having a permeability km of 650, determine the magnitude of the magnetic field before and after the ferromagnetic material is inserted.

95. Two wires, each having a weight per unit length of 10–4 N/m, are strung parallel, one 0.1 m above the other. If the wires carry the same current, though in opposite directions, how great must the current in each wire be for the magnetic field of the lower conductor to balance the weight of the upper conductor?

96. What current in a solenoid 15-cm long wound with 100 turns would produce a magnetic field equal to that of the Earth, 5 × 10–5 T?

97. A superconducting wire carries a current of 1.0 × 104 A. Find the magnetic field at a distance of 1.0 m from the wire.

98. The planetary model of the hydrogen atom consists of an electron in a circular orbit about a proton. The motion of the electron of charge 1.6 × 10–19 C creates an electric current. The radius of the electron orbit is 5.3 × 10–11 m and the electron’s velocity is 2.2 × 106 m/s. What is the magnetic field strength at the location of the proton?


Chapter 30

Sources of the Magnetic Field

1. b

2. c

3. a

4. c

5. d

6. b

7. d

8. c

9. b

10. c

11. a

12. b

13. c

14. d

15. c

16. b

17. c

18. d

19. d

20. c

21. b

22. a

23. a

24. b

25. a

26. d

27. a

28. c

29. b

30. c

31. d

32. b

33. d

34. c

35. d

36. b

37. c

38. d

39. c

40. b

41. a

42. c

43. b

44. a

45. c

46. c

47. d

48. b

49. c

50. d

51. a

52. b

53. c

54. a

55. a

56. b

57. c

58. a

59. c

60. a

61. c

62. d

188 CHAPTER 30

63. a

64. b

65. e

66. b

67. e

68. b

69. b

70. c

71. e

72. c

73. d

74. d

75. a

76. b

77. e

78. c

79. d

80. d

81. c

82. a

83. d

84. a

85. d

86. a

87. d

88. a

89. e

90. e

91. c

92. c

93. c

94. 7 gauss, 0.46 T

95. 7.1 A

96. 59.7 mA

97. 2 × 10–3 T

98. 12.5 T

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Chapter (30)