Q. 605.0( 2 Votes )
Consider a non-conducting plate of radius r and mass m which has a charge q distributed uniformly over it. The plate is rotated about its axis with an angular speed ω. Show that the magnetic moment μ and the angular momentum ℓ of the plate are related as 
Answer :
Given-
Radius of the ring = r
Mass of the ring = m
Total charge of the ring = q
Angular speed,
Where
F is the frequency
Now frequency f
Where,
T is the time period
Magnetic moment, 
where,
A= area of cross section
i=current flowing through it
n = number of turns
for number of turns n = 1
Current in the ring,
For the ring of area A with current i, magnetic moment,m is given by
Where A is the area of the loop
Angular momentum,
where
I is the moment of inertia of the ring about its axis of rotation.
is the angular moment
Moment of inertia, I is given by-
where,
m is the mass of the object
r is the radius of the circular object
So, substituting in (2)
Putting this value 
in equation (1),
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