Question 1

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 magnitude of the magnetic field midway between the two wires? (μ₀ = 4π × 10^-7 T ∙ m/A)

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Question 2

A rectangular loop of wire carrying a 4.0-A current is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire 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?

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Question 3

Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field 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)

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Question 4

A rigid rectangular loop, which measures 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 negative x direction is present. Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. Find the magnitude of the external torque needed to keep the loop in static equilibrium.

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Question 5

A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field  = 0.30 T  . The normal to the loop is parallel to a unit vector  = -0.60  - 0.80  . Calculate the magnitude of the torque on the loop due to the magnetic field.

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Question 6

A rigid circular loop has a radius of 0.20 m and is in the xy-plane. A clockwise current I is carried by the loop, as shown. The magnitude of the magnetic moment of the loop is 0.75 A · m². A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present. (a) What is the current in the loop? (b) Find the magnitude of the magnetic torque exerted on the loop. (c) If the loop is released from rest, in what direction will points a and c initially move?

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Question 7

The figure shows two long, parallel current-carrying wires. The wires carry equal currents I₁ = I₂ = 20 A in the directions indicated and are located a distance d = 0.5 m apart. Calculate the magnitude and direction of the magnetic field at the point P that is located an equal distance d from each wire. (μ₀ = 4π × 10^-7 T ∙ m/A)

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Question 8

A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 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 magnetic torque on the coil?

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Question 9

At what distance from the central axis of a long straight thin wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of the Earth's magnetic field of about 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T ∙ m/A)

Accepted Answer

We use the equation for the magnetic field due to a current-carrying wire at a distance r from the central axis:

μ0I/2πr = B

where μ0 is the permeability of free space, I is the current, and B is the magnetic field.

Rearranging for r, we get:

r = μ0I/2πB

Plugging in the given values, we get:

r = (4π × 10^-7 T∙m/A)(5.0 A)/(2π(5.0 × 10^-5 T))
r = 2.0 × 10^-2 m
r = 2.0 cm

Therefore, the magnetic field due to the wire is equal to the strength of Earth's magnetic field at a distance of 2.0 cm from the central axis of the wire.

Question 10

The magnetic field at a distance of 2 cm from a current carrying wire is 4 μT. What is the magnetic field at a distance of 4 cm from the wire?

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Question 11

A straight 15.0-g wire that is 2.00 m long carries a current of 8.00 A. This wire is aligned horizontally along the west-east direction with the current going from west to east. You want to support the wire against gravity using the weakest possible uniform external magnetic field.
(a) Which way should the magnetic field point?
(b) What is the magnitude of the weakest possible magnetic field you could use?

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Question 12

Three very long, straight, parallel wires each carry currents of 4.00 A, directed out of the page as shown in the figure. The wires pass through the vertices of a right isosceles triangle of side 2.00 cm. What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle?

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Question 13

A wire segment 1.2 m long carries a current I = 3.5 A, and is oriented as shown in the figure. The +x-axis points directly into the page. A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown. What is the magnetic force vector on the wire segment?

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Question 14

A point charge Q moves on the x-axis in the positive direction with a speed of A point P is on the y-axis at The magnetic field produced at the point P, as the charge moves through the origin, is equal to What is the charge Q? (μ₀ = 4π × 10^-7 T ∙ m/A)

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Question 15

An L-shaped metal machine part is made of two equal-length segments that are perpendicular to each other and carry a 4.50-A current as shown in the figure. This part has a total mass of 3.80 kg and a total length of 3.00 m, and it is in an external 1.20-T magnetic field that is oriented perpendicular to the plane of the part, as shown. What is the magnitude of the NET magnetic force that the field exerts on the part?

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Question 16

A 15-turn rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, and the other two sides are perpendicular to the magnetic field.
(a) What is the magnitude of the magnetic moment of the loop?
(b) What torque does the magnetic field exert on the loop?

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Question 17

A wire segment 1.2 m long carries a current I = 3.5 A and is oriented as shown in the figure. A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown. The +z-axis points directly into the page. What is the magnetic force vector on the wire segment?

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Question 18

A point charge Q moves on the x-axis in the positive direction with a speed of A point P is on the y-axis at The magnetic field produced at point P, as the charge moves through the origin, is equal to When the charge is at what is the magnitude of the magnetic field at point P? (μ₀ = 4π × 10^-7 T ∙ m/A)

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Question 19

A wire along the z-axis carries a current of 6.8 A in the +z direction. Find the magnitude and direction of the force exerted on a 6.1-cm long length of the wire by a uniform magnetic field with magnitude 0.36 T in the -x direction.

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Question 20

A very long thin wire produces a magnetic field of at a distance of from the central axis of the wire. What is the magnitude of the current in the wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

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Quiz 29: The Magnetic Field

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 magnitude of the magnetic field midway between the two wires? (μ0 = 4π × 10-7 T ∙ m/A)

A rectangular loop of wire carrying a 4.0-A current is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire 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?

Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field 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 circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T . The normal to the loop is parallel to a unit vector = -0.60 - 0.80 . Calculate the magnitude of the torque on the loop due to the magnetic field.

A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 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 magnetic torque on the coil?

At what distance from the central axis of a long straight thin wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of the Earth's magnetic field of about 5.0 × 10-5 T? (μ0 = 4π × 10-7 T ∙ m/A)