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 expression for the torque on a current loop within a magnetic field is:\[\tau = I A B \sin \theta,\]with the following definitions:- \( I \) representing the current flowing through the loop,- \( A \) denoting the area enclosed by the loop,- \( B \) indicating the strength of the magnetic field,- \( \theta \) signifying the angle formed between the loop's normal vector and the magnetic field vector.Specifically, the forces acting on segments BC and DA are equal in magnitude and opposite in direction, resulting in their cancellation. Conversely, the forces on segments AB and CD create a rotational couple, which generates the described torque.\[\tau = I A B \sin \theta.\]