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)

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