Torque on a current loop

Intermediate

A loop rotates in a field.

Key relationτ = NBIA sinθ

A loop in a uniform field feels torque τ = NIAB sinθ, trying to align its moment with B. It's the principle of the motor and galvanometer.

Worked example

N = 100, I = 1 A, A = 0.01 m², B = 0.5 T: 0.5 N·m max.

Common mistake

No net force in a uniform field.

In more detail

A current loop in a magnetic field experiences a torque τ = NIAB sin θ, which tends to rotate it to align its magnetic moment with the field.

Moving-coil meters use this torque to deflect the needle.
Electric motors use continuous torque on coils.
A motor's coil rotates because the magnetic torque on the current loop turns it into the field.

Where is the torque zero?

When the loop's plane is parallel to the field, so the magnetic moment is aligned with the field.

What does N represent?

The number of turns in the coil, which multiplies the torque.

What makes the torque zero?

When the plane of the loop is parallel to the field, so the normal to the loop is perpendicular to it, the torque is zero.