A non-conducting rod $A B$ of length $\ell$ has a total charge $q$. The rod is rotated about an axis

Question

A non-conducting rod $A B$ of length $\ell$ has a total charge $q$. The rod is rotated about an axis passing through its centre of mass with a constant angular velocity $\omega$ as shown in the figure. The magnetic moment of the rod is

Professor PC Thomas Classes · Answer

Applying the gyromagnetic ratio ( $\mu=\frac{q}{2 m} L$ ) and using the angular momentum of a rod rotating about its center $\left(L=\frac{1}{12} m \ell^2 \omega\right)$, the magnetic moment is $\mu=\frac{q}{2 m}\left(\frac{1}{12} m \ell^2 \omega\right)=\frac{q \omega \ell^2}{24}$.