Solution
= Solution
An annulus of radius $s$ and width $ds$ has charge $dQ=2\pi s\sigma\,ds$, current
$$
dI=\frac{\omega}{2\pi}dQ=\sigma\omega s\,ds,
$$
and dipole moment $dm=\pi s^2dI\,\hat n$. Therefore the <magnetic dipole moment of a rigidly rotating charge distribution> is
$$
\boxed{
m=\pi\sigma\omega\int_0^R s^3\,ds\,\hat n
=\frac{\pi\sigma\omega R^4}{4}\hat n}.
$$