Question

You have a circular loop carrying wire in a large uniform magnetic field because it's a current-carrying loop in a magnetic field, there will be a torque acting on it. Your friend wants to increase the torque by doubling the loop over itself so that it now makes two circular loops on top of each other by using the same length of wire.
What is the new torque in terms of the old torque?

Answer 1

Answer:

The torque experienced by the new loop is 1/4 of that experienced by the old loop.

Explanation:

The torque τ = IBASinΦ

Assuming the direction of current flow through the loop is perpendicular to that of the magnetic field, SinΦ = Sin90° = 1 and

τ = IBA. With the current flowing through the loop and the magnetic field remaining the same for both cases, then

τ ∝ A. The area is equal to πD² where D is the diameter so

τ ∝ D². Let the old loop have a diameter D. Using the same length of wire, the act of doubling the loop (making 2 turns of wire) reduces the diameter by a factor of 1/2. So the new diameter is D/2

τ ∝ (D/2)² which means that τ ∝ D²/4. So the new torque is 1/4 the old torque.