The magnetic moment of a circular orbit of radius $‘r’$ carrying a charge $‘q’$ and rotating with velocity $v$ is given by
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The convection current is
$I=\frac{q \omega}{2 \pi}=\frac{q v}{2 \pi r}$
$\therefore$ The magnetic moment is
$\mathrm{M}=\mathrm{I} \pi \mathrm{r}^{2}=\frac{\mathrm{qv}}{2 \pi \mathrm{r}} \pi \mathrm{r}^{2}$
$M=\frac{q v r}{2}$
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