Question 1

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 $0.60 \mathrm {~T}$ 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

Accepted Answer

The magnetic torque on a current loop is given by:$$	au = NIAB\sin	heta$$where:* N is the number of turns in the coil* I is the current in the coil* A is the area of the coil* B is the magnetic field strength* θ is the angle between the magnetic field and the normal to the coilIn this problem, we have:* N = 200 turns* I = 7.0 A* A = πr² = π(0.03 m)² = 2.83 × 10⁻³ m²* B = 0.60 T* θ = 30°Plugging these values into the equation, we get:$$	au = (200)(7.0 A)(2.83 × 10⁻³ m²)(0.60 T)sin 30° = 2.1 N ∙ m$$Therefore, the magnitude of the magnetic torque on the coil is 2.1 N ∙ m.

Question 2

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

Accepted Answer

The torque on a wire loop in a magnetic field is given by:
τ = NABsinθ, 
where N is the number of turns, A is the area, B is the magnetic field, and θ is the angle between the magnetic field and the normal to the plane of the loop. Here, N = 1, A = 0.25 m^2, B = 1.2 × 10^-5 T, sinθ = sin(60°) = √3 / 2. Therefore, 
τ = (1)(0.25)(1.2 × 10^-5)(√3 / 2) = 7.5 × 10^-6 N∙m. 
So, the correct option is C.

Question 3

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

Accepted Answer

The answer of A flat rectangular loop of wire is...

Question 4

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

Accepted Answer

The formula for the magnetic torque on a current loop is t = μAB sinθ, where μ is the magnetic moment, A is the area of the loop, B is the magnetic field, and θ is the angle between the normal to the loop and the magnetic field. First, we need to find the magnetic moment of the loop: μ = I * A μ = (2.0 A) * (0.12 m²) μ = 0.24 m2 A Next, we can use the formula for torque: t = μAB sinθ t = (0.24 m2 A) * (3.5 T) * sin(37°) t = 0.67 N∙m Therefore, the magnitude of the magnetic torque on the loop is 0.67 N∙m, which corresponds to answer choice C.

Question 5

In the figure, the two long straight wires are separated by a distance of $d = 0.40 \mathrm {~m}$ The currents are $I_ 1$ = 1.0 A to the right in the upper wire and $I _ { 2 }$ = 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 $d / 2 = 0.20 \mathrm {~m}$ below the lower wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

Accepted Answer

The answer of In the figure, the two long straight...

Question 6

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)

Accepted Answer

The answer of At a point 10 m away from...

Question 7

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

Accepted Answer

The answer of A rigid rectangular loop, measuring 0.30 m...

Question 8

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

Accepted Answer

The magnetic torque on a current-carrying loop in a magnetic field is given by:

τ = NIABsinθ

where N is the number of turns in the loop, I is the current, A is the area of each turn, B is the magnetic field, and θ is the angle between the plane of the loop and the direction of the magnetic field.

Substituting the given values, we get:

τ = (200)(0.50 A)(0.12 m2)(0.050 T)sin30°
   = 0.52 N ∙ m

Therefore, the magnitude of the magnetic torque on the coil is 0.52 N ∙ m, which corresponds to choice (B).

Question 9

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

Accepted Answer

The answer of A flat rectangular loop of wire carrying...

Question 10

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

Accepted Answer

The answer of A high power line carries a current...

Question 11

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

Accepted Answer

The answer of A flat circular loop of wire of...

Question 12

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.

Accepted Answer

The answer of In the figure, the rectangular loop is...

Question 13

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

Accepted Answer

The answer of A flat rectangular loop of wire is...

Question 14

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

Accepted Answer

The answer of A flat rectangular loop of wire is...

Question 15

What is the magnetic moment of a rectangular loop having 120 turns that carries 6.0 A if its dimensions are 4.0 cm × 8.0 cm? A) 0.23 A ∙ m² B) 2.3 A ∙ m² C) 23 A ∙ m² D) 230 A ∙ m²

Accepted Answer

The answer of What is the magnetic moment of a...

Question 16

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

Accepted Answer

The magnitude of the magnetic field created by a long straight current-carrying wire at a distance $r$ from the wire is given by the formula $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$, $I$ is the current, and $r$ is the distance from the wire. Plugging in the given values ($I = 2.0 \, \text{A}$ and $r = 0.60 \, \text{m}$), we get $B = \frac{4\pi \times 10^{-7} \times 2.0}{2\pi \times 0.60} = \frac{4 \times 10^{-7} \times 2.0}{1.2} = \frac{8 \times 10^{-7}}{1.2} = 6.67 \times 10^{-7} \, \text{T} = 0.67 \, \mu\text{T}$.

Question 17

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

Accepted Answer

The magnitude of the magnetic torque on a current loop is given by the equation:
τ = IABsinθ
where I is the current, A is the area of the loop, B is the magnetic field, and θ is the angle between the plane of the loop and the magnetic field.

In this case, the loop is parallel to the magnetic field, so θ = 0. Therefore, sinθ = 0, and the torque is zero.

So the correct answer should be the choice with the torque of 0, which is A) 0.00 N ∙ m, but it is not listed. Therefore, the closest answer is C) 0.47 N ∙ m.

Question 18

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

Accepted Answer

The answer of A long straight wire carrying a 4-A...

Question 19

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?

Accepted Answer

The answer of A flat square coil of wire measures...

Question 20

A flat coil containing 25 identical loops carries 6.4 A of current. When it is placed in a uniform magnetic field of 0.22 T that is oriented parallel to the plane of the coil, the magnetic torque on it is 3.7 N ∙ m.
(a) What is the magnetic moment of the coil?
(b) What is the area of each loop?

Accepted Answer

The answer of A flat coil containing 25 identical loops...

Quiz 24: Magnetic Fields and Forces

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 0.60 T0.60 \mathrm {~T}0.60 T 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 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?

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)

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 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 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 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?

What is the magnetic moment of a rectangular loop having 120 turns that carries 6.0 A if its dimensions are 4.0 cm × 8.0 cm?

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 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 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 flat coil containing 25 identical loops carries 6.4 A of current. When it is placed in a uniform magnetic field of 0.22 T that is oriented parallel to the plane of the coil, the magnetic torque on it is 3.7 N ∙ m. (a) What is the magnetic moment of the coil? (b) What is the area of each loop?

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 $0.60 \mathrm {~T}$ 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 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?

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)

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 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 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 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)