Q.A bar magnet of mass 120 g in the form of a rectangular parallelopiped, has dimensions l = 40 mm, b = 10 mm and h = 80 mm, with its dimension 'h' vertical, the magnet performs angular oscillations in the plane of the magnetic field with period $\pi$ seconds. If the magnetic moment is 3.4 A m², determine the influencing magnetic field.

A magnetic dipole disturbed slightly from its stable equilibrium orientation ($\vec m$ parallel to $\vec B$) and released performs angular simple harmonic motion about that equilibrium, with angular frequency $\omega=\sqrt{mB/I}$ and time period $T=2\pi\sqrt{\dfrac{I}{mB}}$, where I is the magnet's moment of inertia about the axis of oscillation. This result follows from combining the restoring torque $\tau=-mB\sin\theta\approx-mB\theta$ (for small $\theta$) with the rotational equation of motion $I\ddot\theta=\tau$, giving exactly the form of linear SHM's equation, $\ddot\theta=-\omega^2\theta$. …