Small-angle magnetic dipole oscillation
= Small-angle magnetic dipole oscillation
{title2=$T=2\pi\sqrt{J/(m_BB)}$}
A <magnetic dipole> of fixed magnitude $m_B$, free to rotate about an axis with <moment of inertia> $J$, has <potential energy> $-m_BB\cos\theta$ in a uniform <magnetic field>. Near stable alignment, $J\ddot\theta=-m_BB\theta$, so its small-angle period is $2\pi\sqrt{J/(m_BB)}$. This neglects damping, bearing friction and any other restoring <torque>.