## Mastering Physics Solutions: Interaction of a Current Loop with a Magnetic Field

Interaction of a Current Loop with a Magnetic Field

Part A = Yes, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle theta (counterclockwise).
Part B = 0.000104 N*m
Part C = The net torque acting on the loop is zero, but the loop continues to rotate in a counterclockwise direction.
Part D = Yes, the net torque acting on the loop is negative and tends to rotate the loop in the direction of decreasing angle θ (clockwise).

Solutions Below:

The effects due to the interaction of a current-carrying loop with a magnetic field have many applications, some as common as the electric motor. This problem illustrates the basic principles of this interaction.

Part A

Consider a current I that flows in a plane rectangular current loop with height a = 4.00 cm and horizontal sides b = 2.00 cm. (Intro 1 figure) The loop is placed into a uniform magnetic field B in such a way that the sides of length a are perpendicular to B, and there is an angle θ between the sides of length b and B, as shown in the figures. (Intro 2 figure)

Will the interaction of the current through the loop with the magnetic field cause the loop to rotate?

• Yes, the net torque acting on the loop is negative and tends to rotate the loop in the direction of decreasing angle θ (clockwise).
• Yes, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle θ(counterclockwise).
• No, the net torque acting on the loop is zero and the loop is in equilibrium.
• No, the net force acting on the loop is zero and the loop is in equilibrium.
• Yes, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle theta (counterclockwise).

For parts B and C, the loop is initially positioned at θ = 30°.

Part B

Assume that the current flowing into the loop is 0.500 A. If the magnitude of the magnetic field is 0.300 T, what is τ, the net torque about the vertical axis of the current loop due to the interaction of the current with the magnetic field?

The torque on the loop follows the formula:

τ = IBAsin(φ)

φ is the angle between the normal (to the loop) and the magnetic field.

Since θ = 30 degrees, φ = 90 – 30 = 60°

τ = 0.5 * 0.3 * 0.04 * 0.02 * sin(60°)

0.000104 N*m

Part C

What happens to the loop when it reaches the position for which θ = 90°, that is, when its horizontal sides of length b are perpendicular to B (see the figure)? (Part C figure)

• The direction of rotation changes because the net torque acting on the loop causes the loop to rotate in a clockwise direction.
• The net torque acting on the loop is zero, but the loop continues to rotate in a counterclockwise direction.
• The net torque acting on the loop is zero; therefore it stops rotating.
• The net force acting on the loop is zero, so the loop must be in equilibrium.

The net torque acting on the loop is zero, but the loop continues to rotate in a counterclockwise direction.

Part D

Now suppose that you change the initial angular position of the loop relative to B, and assume that the loop is placed in such a way that initially the angle between the sides of length b and B is θ = 120°, as shown in the figure. (Part D figure) Will the interaction of the current through the loop with the magnetic field cause the loop to rotate?

• Yes, the net torque acting on the loop is negative and tends to rotate the loop in the direction of decreasing angle θ (clockwise).
• Yes, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle θ (counterclockwise).
• No, the net torque acting on the loop is zero and the loop is in equilibrium.
• No, the net force acting on the loop is zero and the loop is in equilibrium.

Yes, the net torque acting on the loop is negative and tends to rotate the loop in the direction of decreasing angle θ (clockwise).

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### 2 Responses to Mastering Physics Solutions: Interaction of a Current Loop with a Magnetic Field

1. zulfiqar ali says:

what happens with torque when the coil is tilted with an angle with respect to the field?

• Mastering Physics Solutions says:

The force from the magnetic field will decrease since the coil experiences the magnetic field at an angle.