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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