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

$\frac{πR^4}{4}σω$

$\text{Consider a small element of radius r and thickness dr}$

$\text{Charge on the element is } = \sigma 2\pi rdr$ 

$\text{ Current on the element is } dI = \frac{dq}{T} = \frac{dq\omega}{2\pi} =\sigma  \omega rdr $

$\text{Its magnetic moment is } dM =\sigma  \omega rdr \times \pi r^2$

$\text{Total Magnetic moment is }M = \int_0^R{\pi \sigma  \omega r^3dr = \frac{\sigma \omega \pi R^4}{4}}$