A solid conducting sphere of radius $R$ and total charge $q$ rotates about its diametric axis with c

Question

A solid conducting sphere of radius $R$ and total charge $q$ rotates about its diametric axis with constant angular speed $\omega$. The magnetic moment of the sphere is

Professor PC Thomas Classes · Answer

Since the charge of a conducting sphere resides entirely on its surface, applying the formula ( $\mu=\frac{q}{2 m} L$ ) requires using the angular momentum of a spherical shell ( $\left.L=\frac{2}{3} m R^2 \omega\right)$ rather than a solid body, resulting in $\mu=\frac{q}{2 m}\left(\frac{2}{3} m R^2 \omega\right)=\frac{1}{3} q R^2 \omega$.