Question

A thin circular disk of radius $R$ is uniformly charged with density $\rho >0$ per unit area. The disk rotates about its axis with a uniform angular speed $\omega$ The magnetic moment of the disk is

• A. $2\pi R^{4}\omega\rho $
• B. $\pi R^{4} \omega \rho$
• C. $\frac{\pi R^{4}}{2}\omega\rho $
• D. $\frac{\pi R^{4}}{4}\omega \rho$

Answer 1

Answer: (D)

$\frac{M}{L}=\frac{q}{2 m}$
$M=\frac{q}{2 m}L$
$M=\frac{\rho \pi R^{2}}{2 m}\times I\omega $
$M=\frac{\rho \pi R^{2}}{2 m}\times \frac{m R^{2}}{2}\omega $
$M=\frac{1}{4}\pi R^{4}\rho \omega $