= Magnetic field of a rotating charged spherical body
A uniformly charged solid sphere of total charge $Q$, radius $R$ and <angular velocity> $\boldsymbol\omega$ has <magnetic dipole moment>
$$
\mathbf m=\frac12\int\mathbf r\times(\rho\boldsymbol\omega\times\mathbf r)\,d^3r=\frac{QR^2}{5}\boldsymbol\omega.
$$
For 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.
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