Gce Model Questions Vol1 2018 Physics Question 16

A long solenoid of length \(0.50\ \text{m}\) and radius \(0.04\ \text{m}\) has \(800\) turns and carries a current \(I\). It is placed in a uniform external magnetic field of magnitude \(1.2\times10^{-3}\ \text{T}\) directed parallel to the solenoid axis. (a) Determine the current required so that the magnetic field at the centre of the solenoid is exactly twice the external field. (b) A small magnetic dipole with moment \(\mu =5.0\times10^{-3}\ \text{A·m}^2\) is placed at the centre, initially making an angle of \(30^{\circ}\) with the combined field direction. Calculate the magnitude of the torque acting on the dipole. (c) Assuming the dipole can rotate freely about the axis, find its angular acceleration if its moment of inertia about that axis is \(2.0\times10^{-4}\ \text{kg·m}^2\).