Question

Obtain an expression for the torque \( \tau \) acting on a current-carrying loop in a uniform magnetic field \( \vec{B} \). Draw the necessary diagram.

Hint:

The torque on a current loop in a magnetic field depends on the current, area of the loop, and the angle between the magnetic field and the loop's normal.

Answer 1

The torque on a current loop in a magnetic field is given by the expression: \[ \tau = I A B \sin \theta, \] where: - \( I \) is the current in the loop, - \( A \) is the area of the loop, - \( B \) is the magnetic field strength, - \( \theta \) is the angle between the normal to the loop and the magnetic field. The forces on arms BC and DA are equal and opposite and cancel each other out, while the forces on arms AB and CD form a couple, leading to a torque. \[ \tau = I A B \sin \theta. \]