An insulating rod of length I carries a charge q distrubuted uniformly on it. The rod is pivoted at its mid-point and is rotated at a frequency f about a fixed axis perpendicular to the the rod and passing through the pivot . The magnetic moment of the rod system is

Options

A. zero
B. `pi qfl^(2)`
C. `(1)/(2)piqfl^(2)`
D. `(1)/(3)pi q fl^(2)`

Answer

D

Explanation

`(d)` `dM=iA=fdq(pil^(2)),dM=flambdadlpil^(2)`
`M=intdM=flambdapiint_(0)^(l)l^(2)dl=flambda pi (l^(3))/(3)=f((q)/(l))pi(l^(3))/(3)`
`dq=lambda dl=(q)/(l)dl`