Question

Derive the formula for the torque acting on a current-carrying loop in a uniform magnetic field and define the magnetic dipole moment with the help of it.

Hint:

The torque is maximum when the plane of the loop is perpendicular to the magnetic field.

Answer 1

Torque on a current-carrying loop: The torque \( \tau \) on a current loop in a uniform magnetic field is given by: \[ \tau = \vec{m} \times \vec{B} \] where \( \vec{m} \) is the magnetic dipole moment and \( \vec{B} \) is the magnetic field. 

Magnetic dipole moment: \[ m = N I A \] where:
- \( N \) is the number of turns,
- \( I \) is the current,
- \( A \) is the area of the loop. \[ \boxed{\tau = N I A B \sin \theta} \]