Question

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

• A. $\frac{q\omega l^2}{12}$
• B. $\frac{q\omega l^2}{3}$
• C. $\frac{q\omega l^2}{24}$
• D. $\frac{q\omega l^2}{6}$

Answer 1

The correct option is C $\frac{q\omega l^2}{24}$

The gyro-magnetic ratio is,
$\frac{M}{L}=\frac{q}{2m}$ ($L=I\omega :$ Angular momentum)
$\Rightarrow M=\frac{q}{2m}L$
$M=\frac{q}{2m}\times \frac{m{l}^2}{12}\times \omega$
$M=\frac{q\omega l^2}{24}$