Centre field of a rigidly rotating charged loop
= Centre field of a rigidly rotating charged loop
{title2=$B(0)=\frac{\mu_0\Omega}{4\pi}\int\frac{dq}{r}$}
For planar charge rotating rigidly about its centre, $\mathbf v=\boldsymbol\Omega\times\mathbf r$. The magnetic contribution at the centre is $dB=\mu_0\Omega\,dq/(4\pi r)$, along the rotation axis. Integrate over the actual charge distribution; charges on a rotating polygon do not follow the sides of a stationary wire circuit.