A nonconducting ring of radius r and mass m carries a total charge q that is uniformly distributed over it. The ring is rotated about its axis with an angular speed . If l represents the angular momentum of the ring about its axis of rotation, which of the following gives the correct relation between its magnetic moment and l ?

Step-by-step solution

The equivalent current due to the rotating charge is given by I = q T = q 2 . The magnetic moment of the ring is = I A = ( q 2 ) ( r^2) = 1 2 q r^2 . The angular momentum of the ring about its axis of rotation is l = m r^2 . Taking the ratio of magnetic moment to angular momentum, we get: l = 1 2 q r^2 m r^2 = q 2m Therefore, = q 2m l .