question_answer

An insulating thin rod of length i has a linear charge density \[\rho (x)={{\rho }_{0}}\frac{x}{\ell }\]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:

A) \[\pi n\rho {{\ell }^{3}}\]

B) \[\frac{\pi }{3}n\rho {{\ell }^{3}}\]

C) \[\frac{\pi }{4}n\rho {{\ell }^{3}}\]

D) \[n\rho {{\ell }^{3}}\]