Question

A rectangular loop of sides \(a\) and \(b\) carrying current \(I\) is placed in a magnetic field \(\vec B\) such that its area vector \(\vec A\) makes an angle \(\theta\) with \(\vec B\). With the help of a suitable diagram, show that the torque \(\vec \tau\) acting on the loop is given by \[ \vec \tau=\vec m\times \vec B, \] where \[ \vec m=I\vec A \] is the magnetic dipole moment of the loop.

Hint:

For a current loop in a magnetic field: \[ \vec\tau=\vec m\times\vec B \] and \[ m=NIA. \] Maximum torque occurs when \[ \theta=90^\circ. \]

Answer 1