 Magnetic field of a rotating charged spherical body

A uniformly charged solid sphere of total charge $Q$, radius $R$ and angular velocity $\mathbf{\omega }$ has magnetic dipole momentFor a uniformly charged thin spherical shell the coefficient is $1/3$ instead of $1/5$. At large distances the magnetic field is a magnetic dipole field, $\mathbf{B}={\mu }_0[3(\mathbf{m}\cdot \hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{m}]/(4\pi r^3)$. Its angularly averaged magnitude and root mean square magnitude both scale as $r^{-3}$; its angularly averaged vector is zero. Steady rotation of this axisymmetric charge distribution produces magnetostatics, not radiation.