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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