A rod of length $\ell$ having uniformly distributed charge Q is rotated about one end with constant frequency ' f '. Its magnetic moment.

Charge on the differential element dx, $dq=\frac{Q}{\ell }\cdot dx$

equivalent current di = f dq
$\therefore$magnetic moment of this element $d\mu =\left(di\right)NA$   (N=1)

$d\mu =\left(\pi x^2\right)f\frac{Q}{\ell }dx$

$\Rightarrow \mu =\frac{\pi \mathrm{fQ}}{\ell }{\int }_0^{\ell } x^{2}dx;\mu =\frac{\pi \mathrm{fQ}{\ell }^2}{3}$