Chapter 24 3 How Much Currentis Flowing Through The Wire

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47) In the figure, the rectangular loop is pivoted about one side (of length 0.060 m), that

coincides with the y-axis. The end (length 0.020 m) of the loop that lies in the xz-plane makes an

angle of 37° with the x-axis as shown. The loop carries a current of I = 69 A in the direction

shown. (In the side of the loop that is along the y-axis the current is in the +y direction.) If there

is a uniform magnetic field of magnitude 9.7 T in the –x direction, find the magnitude of the

torque that this magnetic field exerts on the loop.

48) A rigid rectangular loop, measuring 0.30 m by 0.40 m, carries a current of 5.5 A, as shown in

the figure. A uniform external magnetic field of magnitude 2.9 T in the –x direction is present.

Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. What is the

magnitude of the torque that the magnetic field exerts on the loop?

A) 1.1 N ∙ m

B) 0.73 N ∙ m

C) 1.3 N ∙ m

D) 1.4 N ∙ m

E) 1.6 N ∙ m

49) A flat rectangular loop of wire is placed between the poles of a magnet, as shown in the

figure. It has dimensions w = 0.60 m and L = 1.0 m, and carries a current I = 2.0 A in the

direction shown. The magnetic field due to the magnet is uniform and of magnitude 0.80 T. The

loop rotates in the magnetic field and at one point the plane of the loop makes a 30° angle with

the field. At that instant, what is the magnitude of the torque acting on the wire due to the

magnetic field?

A) 0.30 N ∙ m

B) 0.40 N ∙ m

C) 0.48 N ∙ m

D) 0.83 N ∙ m

E) 0.96 N ∙ m

50) A flat rectangular loop of wire is placed between the poles of a magnet, as shown in the

figure. It has dimensions w = 0.60 m and L = 1.0 m, and carries a current I = 2.0 A in the

direction shown. The magnetic field due to the magnet is uniform and of magnitude 0.80 T. The

loop rotates in the magnetic field and at one point the plane of the loop is parallel to the field. At

that instant, what is the magnitude of the torque acting on the wire due to the magnetic field?

A) 0.00 N ∙ m

B) 0.40 N ∙ m

C) 0.48 N ∙ m

D) 0.83 N ∙ m

E) 0.96 N ∙ m

51) A flat rectangular loop of wire is placed between the poles of a magnet, as shown in the

figure. It has dimensions w = 0.60 m and L = 1.0 m, and carries a current I = 2.0 A in the

direction shown. The magnetic field due to the magnet is uniform and of magnitude 0.80 T. The

loop rotates in the magnetic field and at one point the plane of the loop is perpendicular to the

field. At that instant, what is the magnitude of the torque acting on the wire due to the magnetic

field?

A) 0.00 N ∙ m

B) 0.40 N ∙ m

C) 0.48 N ∙ m

D) 0.83 N ∙ m

E) 0.96 N ∙ m

52) A flat circular coil of wire having 200 turns and diameter 6.0 cm carries a current of 7.0 A. It

is placed in a magnetic field of with the plane of the coil making an angle of 30° with the

magnetic field. What is the magnitude of the magnetic torque on the coil?

A) 2.1 N ∙ m

B) 1.2 N ∙ m

C) 3.9 N ∙ m

D) 5.4 N ∙ m

E) 1.0 N ∙ m

53) A flat circular coil has 200 identical loops of very thin wire. Each loop has an area of 0.12

m2 and carries 0.50 A of current. This coil is placed in a magnetic field of 0.050 T oriented at

30° to the plane of the loop. What is the magnitude of the magnetic torque on the coil?

A) 0.25 N ∙ m

B) 0.52 N ∙ m

C) 2.5 N ∙ m

D) 5.2 N ∙ m

54) A flat circular loop carrying a current of 2.0 A is in a magnetic field of 3.5 T. The loop has

an area of 0.12 m2 and its plane is oriented at a 37° angle to the field. What is the magnitude of

the magnetic torque on the loop?

A) 0.10 N ∙ m

B) 0.51 N ∙ m

C) 0.67 N ∙ m

D) 46 N ∙ m

55) A flat circular loop of wire is in a uniform magnetic field of 0.30 T. The diameter of the

loop is 1.0 m, and a 2.0-A current flows in it. What is the magnitude of the magnetic torque on

the loop when the plane of the loop is parallel to the magnetic field?

A) 0.00 N ∙ m

B) 0.41 N ∙ m

C) 0.47 N ∙ m

D) 0.52 N ∙ m

56) A flat rectangular loop of wire carrying a 4.0-A current is placed in a uniform 0.60-T

magnetic field. The magnitude of the torque acting on this loop when the plane of the loop makes

a 30° angle with the field is measured to be 1.1 N ∙ m. What is the area of this loop?

A) 0.20 m2

B) 0.40 m2

C) 0.26 m2

D) 0.80 m2

E) 0.53 m2

57) A flat circular loop of wire of radius 0.50 m that is carrying a 2.0-A current is in a uniform

magnetic field of 0.30 T. What is the magnitude of the magnetic torque on the loop when the

plane of its area is perpendicular to the magnetic field?

A) 0.00 N ∙ m

B) 0.41 N ∙ m

C) 0.47 N ∙ m

D) 0.52 N ∙ m

E) 0.58 N ∙ m

58) A flat square coil of wire measures 9.5 cm on each side and contains 175 turns of very thin

wire. It carries a current of 6.3 A in a uniform 0.84-T magnetic field. What angle less than 90°

should the plane of this coil make with the magnetic field direction so that the magnitude of the

magnetic torque on it is 6.5 N ∙ m?

59) A flat circular wire loop of area 0.25 m2 carries a current of 5.0 A. This coil lies on a

horizontal table with the current flowing in the counterclockwise direction when viewed from

above. At this point, the earth’s magnetic field is 1.2 × 10-5 T directed 60° below the horizontal.

What is the magnitude of the torque that the earth’s magnetic field exerts on this loop?

A) 2.5 × 10-6 N ∙ m

B) 5.0 × 10-6 N ∙ m

C) 7.5 × 10-6 N ∙ m

D) 1.0 × 10-5 N ∙ m

60) At a point 10 m away from a long straight thin wire, the magnetic field due to the wire is

0.10 mT. What current flows through the wire? (μ0 = 4π × 10-7 T ∙ m/A)

61) In the figure, the two long straight wires are separated by a distance of The

currents are = 1.0 A to the right in the upper wire and = 8.0 A to the left in the lower wire.

What are the magnitude and direction of the magnetic field at point P, that is a distance

below the lower wire? (μ0 = 4π × 10-7 T ∙ m/A)

62) A high power line carries a current of 1.0 kA. What is the strength of the magnetic field this

line produces at the ground, 10 m away? (μ0 = 4π × 10-7 T ∙ m/A)

A) 4.7 µT

B) 6.4 µT

C) 20 µT

D) 56 µT

63) A long wire carrying a 2.0-A current is placed along the y-axis. What is the magnitude of the

magnetic field at a point that is 0.60 m from the origin along the x-axis? (μ0 = 4π × 10-7 T ∙

m/A)

A) 0.67 µT

B) 1.3 µT

C) 0.12 µT

D) 6.7 T

E) 12 T

64) A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure.

What is the magnitude of the magnetic field at a point P, located at y = 2 cm, due to the current in

this wire? (μ0 = 4π × 10-7 T ∙ m/A)

A) 20 μT

B) 30 μT

C) 40 μT

D) 50 μT

E) 60 μT

65) At point P the magnetic field due to a long straight wire carrying a current of 2.0 A is 1.2 µT.

How far is P from the wire? (μ0 = 4π × 10-7 T ∙ m/A)

A) 11 cm

B) 22 cm

C) 33 cm

D) 44 cm

E) 55 cm

66) The magnetic field due to the current in a long, straight wire is 8.0 μT at a distance of 4.0 cm

from the center of the wire. What is the current in the wire? (μ0 = 4π × 10-7 T ∙ m/A)

A) 0.20 A

B) 0.40 A

C) 0.80 A

D) 3.2 A

E) 1.6 A

67) The magnetic field at point P due to a 2.0-A current flowing in a long, straight, thin wire is

8.0 μT. How far is point P from the wire? (μ0 = 4π × 10-7 T ∙ m/A)

A) 2.0 cm

B) 2.5 cm

C) 4.0 cm

D) 5.0 cm

E) 10 cm

68) The magnitude of the magnetic field that a long and extremely thin current-carrying wire

produces at a distance of 3.0 µm from the center of the wire is 2.0 × 10-3 T. How much current

is flowing through the wire? (μ0 = 4π × 10-7 T ∙ m/A)

A) 30 mA

B) 190 mA

C) 19 mA

D) 380 mA

69) A very long thin wire produces a magnetic field of at a distance of from

the wire. What is the magnitude of the current? (μ0 = 4π × 10-7 T ∙ m/A)

A) 1.0 mA

B) 2.0 mA

C) 4000 mA

D) 3100 mA

70) How much current must flow through a long straight wire for the magnetic field strength to

be 1.0 mT at 1.0 cm from a wire? (μ0 = 4π × 10-7 T ∙ m/A)

A) 50 mA

B) 9.2 A

C) 16 A

D) 50 A

E) 5.0 mA

71) At what distance from a long straight wire carrying a current of 5.0 A is the magnitude of the

magnetic field due to the wire equal to the strength of Earth’s magnetic field of about 5.0 × 10-5

T? (μ0 = 4π × 10-7 T ∙ m/A)

A) 1.0 mm

B) 1.0 cm

C) 2.0 cm

D) 3.0 cm

E) 4.0 cm

72) Two long parallel wires that are 0.40 m apart carry currents of 10 A in opposite directions.

What is the magnetic field strength in the plane of the wires at a point that is 20 cm from one

wire and 60 cm from the other? (μ0 = 4π × 10-7 T ∙ m/A)

A) 3.3 µT

B) 6.7 µT

C) 33 µT

D) 67 µT

73) Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires

are separated by 0.20 m. What is the strength of the magnetic field midway between the two

wires? (μ0 = 4π × 10-7 T ∙ m/A)

A) 1.0 × 10-5 T

B) 2.0 × 10-5 T

C) 3.0 × 10-5 T

D) 4.0 × 10-5 T

E) 5.0 × 10-5 T

74) Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires

are separated by 20 cm. At what point between the two wires do they produce the same strength

magnetic field?

A) 4.0 cm from the 20 A wire

B) 8.0 cm from the 20 A wire

C) 12 cm from the 20 A wire

D) 16 cm from the 20 A wire

E) 18 cm from the 20 A wire

75) Three long parallel wires each carry 2.0-A currents in the same direction. The wires are

oriented vertically, and they pass through three of the corners of a horizontal square of side 4.0

cm. What is the magnitude of the magnetic field at the fourth (unoccupied) corner of the square

due to these wires? (μ0 = 4π × 10-7 T ∙ m/A)

A) 1.2 µT

B) 2.1 µT

C) 12 µT

D) 21 µT

E) 0 T

76) Three very long, straight, parallel wires each carry currents of 4.0 A, directed out of the page

as shown in the figure. These wires pass through the vertices of a right isosceles triangle as

shown. Assume that all the quantities shown in the figure are accurate to two significant figures.

What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the

triangle? (μ0 = 4π × 10-7 T ∙ m/A)

A) 4.4 µT

B) 18 µT

C) 57 µT

D) 130 µT

E) 1.8 µT

77) What is the strength of the magnetic field at the center of a circular loop of wire of diameter

8.0 cm when a current of 2.0 A flows in the wire? (μ0 = 4π × 10-7 T ∙ m/A)

78) A wire carrying a current is shaped in the form of a circular loop of radius 4.0 mm. If the

magnetic field strength at its center is with no external magnetic fields present, what is the

magnitude of the current flowing through the wire? (μ0 = 4π × 10-7 T ∙ m/A)

A) 7.0 A

B) 28 A

C) 14 A

D) 17 A

79) A circular metal loop of radius 10 cm and three long straight wires carry currents of

and as shown in the figure. Each of the straight wires is 20 cm from

the center of the loop. The axes are shown in the figure, with the +z-axis coming out of the paper.

What is the y component of the resultant magnetic field at the center of the loop? (μ0 = 4π × 10-7

T ∙ m/A)

A) –54 μT

B) –60 μT

C) –50 μT

D) +60 μT

E) +50 μT

80) A circular metal loop of radius 10 cm and three long straight wires carry currents of

and as shown in the figure. Each of the straight wires is 20 cm from

the center of the loop. The axes are shown in the figure, with the +z-axis coming out of the paper.

What is the z component of the resultant magnetic field at the center of the loop? (μ0 = 4π × 10-7

T ∙ m/A)

A) –360 μT

B) +360 μT

C) –40 μT

D) +40 μT

E) –170 μT

81) A long straight wire on the z-axis carries a current of 8.0 A in the +z direction (out of the

paper). A circular loop of radius 10 cm lies in the xy-plane and carries a 3.0-A current, as shown

in the figure. Point P, at the center of the loop, is 25 cm from the z-axis. An electron is projected

from P with a velocity of 3.0 × 106 m/s in the –x direction. What is the y component of the

magnetic force on the electron? (e = 1.60 × 10-19, μ0 = 4π × 10-7 T ∙ m/A)

A) -9.0 × 10-18 N

B) 9.0 × 10-18 N

C) -4.5 × 10-18 N

D) 4.5 × 10-18 N

E) zero

82) A flat circular coil having 57 turns of very thin wire has a diameter of 9.5 cm and carries 7.2

A of current. (μ0 = 4π × 10-7 T ∙ m/A)

(a) What is the strength of the magnetic field at the center of the coil?

(b) If the same length of wire were used to make a coil with twice the original diameter, how

large would the magnetic field at the center be when it carried the same current as before?

83) An ideal solenoid having 200 turns and carrying a current of 2.0 A is 25 cm long. What is the

magnitude of the magnetic field at the center of the solenoid? (μ0 = 4π × 10-7 T ∙ m/A)

84) In order to trap the starship Enterprise, the diabolical Klingons build a huge ideal solenoid 10

light-years long with a diameter of 2.0 million kilometers. Every kilometer of length of the

solenoid contains 100 turns of wire. What magnetic field strength is produced near the center of

the solenoid using a current of 2.00 kA? (μ0 = 4π × 10-7 T ∙ m/A)

85) An ideal solenoid 20 cm long is wound with 5000 turns of very thin wire. What strength

magnetic field is produced at the center of the solenoid when a current of 10 A flows through it?

(μ0 = 4π × 10-7 T ∙ m/A)

A) 0.0063 T

B) 0.20 T

C) 3.2 T

D) 4.8 T

E) 0.31 T

86) An ideal solenoid having a coil density of 5000 turns per meter is 10 cm long and carries a

current of 4.0 A. What is the strength of the magnetic field at its center?

A) 3.1 mT

B) 6.2 mT

C) 13 mT

D) 25 mT

87) An ideal solenoid of length 10 cm consists of a wire wrapped tightly around a wooden core.

The magnetic field strength is inside the solenoid. If the solenoid is stretched to by

applying a force to it, what does the magnetic field become?

A) 1.6 T

B) 10.0 T

C) 20 T

D) 4.0 T

88) An ideal solenoid that is 34.0 cm long is carrying a current of 2.00 A. If the magnitude of the

magnetic field generated at the center of the solenoid is 9.00 mT, how many turns of wire does

this solenoid contain? (μ0 = 4π × 10-7 T ∙ m/A)

A) 860

B) 1590

C) 2320

D) 3180

E) 1220

89) How much current must pass through a 400-turn ideal solenoid that is 4.0 cm long to

generate a 1.0-T magnetic field at the center? (μ0 = 4π × 10-7 T ∙ m/A)

A) 0.013 A

B) 13 A

C) 22 A

D) 40 A

E) 80 A

90) How many turns should a 10-cm long ideal solenoid have if it is to generate a 1.5-mT

magnetic field when 1.0 A of current runs through it? (μ0 = 4π × 10-7 T ∙ m/A)

A) 12

B) 15

C) 120

D) 1200

E) 3200

91) An ideal solenoid with 400 turns has a radius of 0.040 m and is 40 cm long. If this solenoid

carries a current of 12 A, what is the magnitude of the magnetic field at the center of the

solenoid? (μ0 = 4π × 10-7 T ∙ m/A)

A) 16 mT

B) 4.9 mT

C) 15 mT

D) 6.0 mT

E) 9.0 mT

92) An ideal solenoid is wound with 470 turns on a wooden form that is 4.0 cm in diameter and

50 cm long. The windings carry a current in the sense shown in the figure. The current produces

a magnetic field of magnitude at the center of the solenoid. What is the current I in the

solenoid windings? (μ0 = 4π × 10-7 T ∙ m/A)

A) 3.5 A

B) 3.0 A

C) 2.6 A

D) 4.3 A

E) 3.9 A