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. `1/12 piqfl^2`
B. ` piqfl^2`
C. `1/6 piqfl^2`
D. `1/3 piqfl^2`

Answer

a

Explanation

At a distance x consider a small element of width dx. Magnetic
moment of the small element is:

`dm=IA=(dq)fpix^2=q/l d pi rx^2`
`M=(qfpi)/lint_(-l//2)^(l//2) x^2dx=(qpifl^2)/12`