Question

Magnetic dipole moment of a uniformly charged square plate of side $l$ and charge $Q$ rotating about an axis passing through center of mass and perpendicular to plane with angular velocity $\omega$ is

• A. $\frac{Q\omega l^2}{2}$
• B. $\frac{Q\omega l^2}{4}$
• C. $\frac{Q\omega l^2}{12}$
• D. $\frac{Q\omega l^2}{3}$

Answer 1

The correct option is C $\frac{Q\omega l^2}{12}$

By relation, $\frac{M}{L}=\frac{Q}{2m}$

where $L=\frac{m{l}^2\omega }{6}\Rightarrow M=\frac{Q}{2m}\frac{m{l}^2\omega }{6}$
$M=\frac{Q\omega l^2}{12}$