Question

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

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

Answer 1

Answer: (C)

$\frac{\pi R^{4}}{4}\sigma\omega$

Answer 2

$\frac{q}{2M} = \frac{Magnetic \,dipole \,moment}{Angular \,momentum}$ $\therefore\quad$ Magnetic dipole moment (M) $M = \frac{q}{2M}. \left(\frac{MR^{2}}{2}\right)\omega$ $= \frac{1}{4}\sigma.\pi R^{4}\omega$