Practicing Success
a b c d |
d |
$\text{Consider a small element of radius r and thickness dr}$ $\text{Charge on the element is } = \sigma 2\pi rdr$ $\text{ Current on the element is } dI = \frac{dq}{T} = \frac{dq\omega}{2\pi} =\sigma \omega rdr $ $\text{Its magnetic moment is } dM =\sigma \omega rdr \times \pi r^2$ $\text{Total Magnetic moment is }M = \int_0^R{\pi \sigma \omega r^3dr = \frac{\sigma \omega \pi R^4}{4}}$ |