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Equal currents of magnitude I travel out of the page in wires M and N. Eight directions are indicated by letters A through H. Equal currents of magnitude I travel out of the page in wires M and N. Eight directions are indicated by letters A through H. The direction of the magnetic field at point P is A) E. B) F. C) G. D) H. E) A. The direction of the magnetic field at point P is


A) E.
B) F.
C) G.
D) H.
E) A.

F) C) and D)
G) B) and E)

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E

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? 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) 23 mN B) 64 mN C) 32 mN D) 46 mN E) 55 mN


A) 23 mN
B) 64 mN
C) 32 mN
D) 46 mN
E) 55 mN

F) B) and E)
G) All of the above

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An ideal solenoid of radius a has n turns per 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)
An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux Φ<sub>B</sub> through any circular area of radius a inside the solenoid, centered on and perpendicular to the solenoid axis is A) . B) . C) μ<sub>0</sub>πa<sup>2</sup>nI. D) 2μ<sub>0</sub>πa<sup>2</sup>nI. E) 0. .
B)
An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux Φ<sub>B</sub> through any circular area of radius a inside the solenoid, centered on and perpendicular to the solenoid axis is A) . B) . C) μ<sub>0</sub>πa<sup>2</sup>nI. D) 2μ<sub>0</sub>πa<sup>2</sup>nI. E) 0. .
C) μ0πa2nI.
D) 2μ0πa2nI.
E) 0.

F) C) and D)
G) A) and D)

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C

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? 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? A) 2.5 mN B) 3.3 mN C) 2.2 mN D) 2.9 mN E) 1.7 mN


A) 2.5 mN
B) 3.3 mN
C) 2.2 mN
D) 2.9 mN
E) 1.7 mN

F) None of the above
G) A) and B)

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A 0.50-m long solenoid consists of 1 000 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.

F) A) and B)
G) B) and E)

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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

F) None of the above
G) A) and E)

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An ideal solenoid of radius a has n turns per 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 An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux Φ<sub>B</sub> 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 A) . B) . C) μ<sub>0</sub>πa<sup>2</sup>nI. D) 2μ<sub>0</sub>πa<sup>2</sup>nI. E) 0.


A)
An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux Φ<sub>B</sub> 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 A) . B) . C) μ<sub>0</sub>πa<sup>2</sup>nI. D) 2μ<sub>0</sub>πa<sup>2</sup>nI. E) 0. .
B)
An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux Φ<sub>B</sub> 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 A) . B) . C) μ<sub>0</sub>πa<sup>2</sup>nI. D) 2μ<sub>0</sub>πa<sup>2</sup>nI. E) 0. .
C) μ0πa2nI.
D) 2μ0πa2nI.
E) 0.

F) A) and D)
G) C) and D)

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C

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?


A)
A thin infinitely large current sheet lies in the y-z plane. Current of magnitude J<sub>s</sub> 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? A) B) C) D) E)
B)
A thin infinitely large current sheet lies in the y-z plane. Current of magnitude J<sub>s</sub> 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? A) B) C) D) E)
C)
A thin infinitely large current sheet lies in the y-z plane. Current of magnitude J<sub>s</sub> 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? A) B) C) D) E)
D)
A thin infinitely large current sheet lies in the y-z plane. Current of magnitude J<sub>s</sub> 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? A) B) C) D) E)
E)
A thin infinitely large current sheet lies in the y-z plane. Current of magnitude J<sub>s</sub> 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? A) B) C) D) E)

F) A) and B)
G) A) and C)

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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

F) A) and D)
G) C) and D)

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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?


A) 78 μT
B) 55 μT
C) 48 μT
D) 68 μT
E) 2.0 μT

F) A) and D)
G) A) and C)

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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.

F) C) and D)
G) A) and B)

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

F) A) and C)
G) None of the above

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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

F) A) and B)
G) B) and D)

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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?


A) 1.1 mT
B) 1.4 mT
C) 1.7 mT
D) 2.0 mT
E) 0.2 mT

F) A) and B)
G) A) and E)

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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?


A) 57 μT
B) 80 μT
C) 64 μT
D) 48 μT
E) 40 μT

F) None of the above
G) B) and C)

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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

F) A) and E)
G) D) and E)

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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 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 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.


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.

F) A) and D)
G) All of the above

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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 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 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.


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.

F) A) and B)
G) A) and E)

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A long solenoid (n = 80 turns/cm) carries a current of 70 mA. Determine the magnitude of the magnetic field inside the solenoid.

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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.
B)
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. B) . C) . D) . E) . .
C)
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. B) . C) . D) . E) . .
D)
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. B) . C) . D) . E) . .
E)
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. B) . C) . D) . E) . .

F) A) and D)
G) A) and B)

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