Question

A non-conducting thin disc of radius R charged uniformly over one side with surface density σ rotates about its axis with an angular velocity ω. Find: 

(a) the magnetic induction at the centre of the disc; 

(b) the magnetic moment of the disc.

Answer 1

(a) Let us take a ring element of radius r and thickness dr, then charge on the ring element., d q = σ 2 π r dr

and current, due to this element, 

So, magnetic induction at the centre, due to this element : 

and hence, from symmetry :

(b) Magnetic moment of the element, considered,