Q.A bar magnet of dipole moment $m$ is free to rotate in a uniform magnetic field $B$. State, with reasons, the angle $\theta$ (between $\vec{m}$ and $\vec{B}$) at which the magnet is in stable equilibrium and the angle at which it is in unstable equilibrium.

At both $\theta=0^\circ$ and $\theta=180^\circ$, the torque $\tau=mB\sin\theta$ is exactly zero ($\sin0^\circ=\sin180^\circ=0$), so both are equilibrium positions; which one is STABLE is decided by the potential energy $U(\theta)=-mB\cos\theta$ (Section 1.7).

At $\theta=0^\circ$: $U=-mB$, the MINIMUM possible value of $U$. Any small displacement away from $\theta=0^\circ$ raises $U$, and the resulting torque acts to restore the magnet back toward $\theta=0^\circ$ -- a stable equilibrium. …

Find the zero-torque angles first, then use the potential-energy curve's minimum/maximum to dec …

• Assuming zero torque alone means stability -- both equilibrium angles have zero torque; only the energy curvature (or a displa …