A charge q is distributed uniformly around a thin ring of radius r. The ring is rotating about an axis through the centre and perpendicular to its plane at an angular speed . We have to show that the magnetic moment due to the rotating charge is

(b) If L is the angular momentum of the ring, we have to show that .

Solution:             Click For PDF Version

We will first calculate the current in a ring of radius r containing charge q which is uniformly distributed when the ring is rotating about an axis through the centre and perpendicular to its plane at an angular speed . Current at a location is defined as the charge flowing per second. An amount of charge flows through at any point on the ring in time

Therefore, the current in the rotating ring is

As the current is flowing in a closed loop of area the magnetic moment will be

(b)

Let m be the mass of the charge contained in the ring. As the ring is rotating with angular speed , the angular momentum of the rotating charge will be