An insulating, thin rod of length $\ell$ has a x linear charge density $\rho \left(x\right)={\rho }_0\frac{x}{\ell }$ on it. The rod is  rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is :