Q. 594.3( 4 Votes )
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.
Answer :
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-
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