Magnetic dipole moment of a rigidly rotating charge distribution
= Magnetic dipole moment of a rigidly rotating charge distribution
A circular charge distribution rotating with angular speed $\omega$ can be decomposed into current loops. A hoop of line density $\eta$ and radius $R$ has $m=\pi\eta\omega R^3\hat n$; a disc of surface density $\sigma$ has $m=\pi\sigma\omega R^4\hat n/4$.