 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 $m=\pi \sigma \omega R^4\hat{n}/4$.