Consider a non-conducting ring of radius r and mass m which has a total charge q distributed uniformly on it. The ring is rotated about its axis with an angular speed ω.

(a) Find the equivalent electric current in the ring.

(b) Find the magnetic moment μ of the ring.

(c) Show that ℓ where ℓ is the angular momentum of the ring about its axis of rotation.

Given-
Radius of the ring = r

Mass of the ring = m

Total charge enclosed on the ring = q

(a) Angular speed-

We know that angular speed is given by-

now frequency f

Current in the ring,

(b)For a ring of area A with current i flowing through it, magnetic moment,

where,

A= area of cross section

i=current flowing through it

n = number of turns

for number of turns n = 1

From (1)

× =

(d) Angular momentum l,

where

I is moment of inertia of the ring about its axis of rotation.

is angular velocity

Where

m is the mass

r is the radius of gyration.

So,

Putting this value in equation (2), we get-