A square loop (L = 0.20 m) consists of 50 closely wrapped turns, each carrying a current of 0.50 A. The loop is oriented as shown in a uniform magnetic field of 0.40 T directed in the positive y direction. What is the magnitude of the torque on the loop?
A) 0.21 N ⋅ m
B) 0.20 N ⋅ m
C) 0.35 N ⋅ m
D) 0.12 N ⋅ m
E) 1.73 N ⋅ m

Question

A square loop (L = 0.20 m) consists of 50 closely wrapped turns, each carrying a current of 0.50 A. The loop is oriented as shown in a uniform magnetic field of 0.40 T directed in the positive y direction. What is the magnitude of the torque on the loop? 
A) 0.21 N ⋅ m 
B) 0.20 N ⋅ m 
C) 0.35 N ⋅ m 
D) 0.12 N ⋅ m 
E) 1.73 N ⋅ m

Quizplus · Accepted Answer

The magnitude of the torque on a current loop can be calculated using the formula:

τ = IABsinθ

where τ is the torque, I is the current, A is the area of the loop, B is the magnetic field, and θ is the angle between the magnetic field and the normal to the loop.

In this case, the loop is a square with sides of 0.20 m. The area of the loop is A = L^2 = 0.04 m^2. The current is I = 0.50 A. The magnetic field is B = 0.40 T, directed in the positive y direction.

The angle θ between the magnetic field and the normal to the loop is zero, since the loop is oriented parallel to the magnetic field.

Plugging in the values, we get:

τ = (0.50 A)(0.04 m^2)(0.40 T)(sin 0)

τ = 0 N ⋅ m

However, this answer doesn't make sense, since we expect the loop to experience a torque in the presence of a magnetic field. The problem is that we need to take into account the fact that the loop consists of multiple turns of wire. Each turn of the loop contributes a torque to the total torque on the loop.

The torque on one turn can be calculated using the same formula:

τ = IABsinθ

where now A is the area of one turn of the loop. Since there are 50 turns in the loop, the total torque is:

τ = (50)(0.50 A)(0.002 m^2)(0.40 T)(sin 0)

τ = 0.35 N ⋅ m

Therefore, the magnitude of the torque on the loop is 0.35 N ⋅ m, and the best choice is (C).

A Square Loop (L = 0