Question

Derive an expression for the torque acting on a rectangular current loop suspended in a uniform magnetic field.

Hint:

Torque on a current loop in a magnetic field is maximum when the angle between the magnetic moment and the field is 90 degrees.

Answer 1

The torque \( \tau \) on a current loop in a magnetic field is given by: \[ \tau = \mu B \sin \theta \] where:
\( \mu \) is the magnetic moment of the loop,
\( B \) is the magnetic field strength,
\( \theta \) is the angle between the magnetic moment and the magnetic field.
For a rectangular loop, the magnetic moment \( \mu \) is: \[ \mu = I \cdot A \] where \( I \) is the current and \( A \) is the area of the loop. The torque acts to rotate the loop until the magnetic moment aligns with the magnetic field.