A charged particle of mass $m$ and charge $q$ is moving in a circular orbit of radius $R$ with a uni

Question

A charged particle of mass $m$ and charge $q$ is moving in a circular orbit of radius $R$ with a uniform speed $v$. The ratio of its associated magnetic moment $\mu$ to its angular momentum $L$ (known as the gyromagnetic ratio) is correctly given by

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(d) : The orbiting charge constitutes an electric current $I = \frac{q}{T} = \frac{qv}{2\pi R}$. The magnetic moment generated by this current loop is $\mu = IA = \left(\frac{qv}{2\pi R}ight) 	imes (\pi R^2) = \frac{qvR}{2}$. The angular momentum of the particle moving in a circle is $L = mvR$. The ratio of the magnetic moment to the angular momentum is $\frac{\mu}{L} = \frac{qvR/2}{mvR} = \frac{q}{2m}$.