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:
Answer & explanation
Correct answer: option 4
$\text{Consider a small element of radius r and thickness dr}$
$\text{Charge on the element is } = \sigma 2\pi rdr$
$\text{ Current on the element is } dI = \frac{dq}{T} = \frac{dq\omega}{2\pi} =\sigma \omega rdr $
$\text{Its magnetic moment is } dM =\sigma \omega rdr \times \pi r^2$
$\text{Total Magnetic moment is }M = \int_0^R{\pi \sigma \omega r^3dr = \frac{\sigma \omega \pi R^4}{4}}$