List of top Physics Questions on The Magnetic Dipole Moment

A circular coil of 100 turns and radius \( \left(\frac{10}{\sqrt{\pi}}\right) \, \text{cm}\) carrying current of \( 5.0 \, \text{A} \) is suspended vertically in a uniform horizontal magnetic field of \( 2.0 \, \text{T} \). The field makes an angle \( 30^\circ \) with the normal to the coil. Calculate:
the magnetic dipole moment of the coil, and
the magnitude of the counter torque that must be applied to prevent the coil from turning.

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.