A square and a circular loop with the same area lie in the xy-plane, where there is a uniform magnetic field vector B pointing at some angle θ with respect to the positive z-direction. Each loop carries the same current, in the same direction. Which magnetic torque is larger?

The torques in the two loops are the same.

Explanation:

The magnetic torque, τ = μB sin θ

μ = magnetic moment

B = magnetic field

θ = angle between the magnetic field and the loop

The magnetic moment is given as

μ = INA

where I = current

N = number of turns

A = Area of the loop

τ = NIA B sin θ

For the two loops given, all of these conditions are the same.

Hence, the magnetic torque for the two loops are the same.

The magnetic torque depends on the number of turns, the area of the loop, the current, magnetic field and angle between the field and the loop, but never on the shape of the loop.

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