Question

A hollow disk of inner radius R and outer radius 2R is uniformly charged to charge Q and is rotating at angular velocity $\omega$ as shown in figure. Magnitude of magnetic dipole moment is

• A. $Q\omega R^2$
• B. $\frac{Q\omega R^2}{2}$
• C. $\frac{5}{4}Q\omega R^2$
• D. $\frac{2}{3}Q\omega R^2$

Answer 1

The correct option is C $\frac{5}{4}Q\omega R^2$

$\sigma =\frac{Q}{3\pi R^2}$

$dq=\sigma 2\pi rdr$

$dM=\left(di\right)\pi r^2=\frac{dq}{T}\pi r^2=\frac{\sigma 2\pi rdrw}{2\pi }\pi r^2$

$M=\int d\mu =\sigma \pi w{\int }_R^{2R}{r}^{3}dr=\frac{Q\pi w}{3\pi R^2}{\left(\frac{r^4}{4}\right)}_R^{2R}=\frac{5}{4}Qw{R}^2$