A charged particle (charge q) is moving in a circle of radius R with uniform speed v. The associated magnetic moment $\mu$ is given by

As revolving charge is equivalent to a current loop, so electric current corresponds to the revolution of electron is $\mathrm{I}=\mathrm{q}\mathrm{f}=\mathrm{q}\times \frac{\mathrm{\omega }}{2\mathrm{\pi }}$

But $\mathrm{\omega }=\frac{\mathrm{v}}{\mathrm{R}},$ where R is radius of circle and v is uniform speed of charged particle. 

Therefore, $\mathrm{I}=\frac{\mathrm{qv}}{2\mathrm{\pi R}}$

Now, magnetic moment associated with charged particle is given by

$\mathrm{or}\mathrm{\mu }=\frac{\mathrm{qv}}{2\mathrm{\pi R}}\times {\mathrm{\pi R}}^2=\frac{1}{2}\mathrm{qvR}$