= Magnetic moment of a rotating charged spherical shell
{title2=$\mathbf m=Qa^2\boldsymbol\omega/3$}
For a uniformly charged spherical shell rotating rigidly in the quasistatic nonrelativistic model, a latitude strip carries current $dI=\sigma\omega a^2\sin\theta\,d\theta$. Its loop area is $\pi a^2\sin^2\theta$, so integration uses $\int_0^\pi\sin^3\theta\,d\theta=4/3$ and gives $\mathbf m=Qa^2\boldsymbol\omega/3$. For an isolated conducting shell, $Q=4\pi\epsilon_0aV$. Clockwise and counterclockwise descriptions require a viewing direction; the vector formula fixes the sign without that ambiguity.
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