Question

A uniformly charged disc, whose total charge has a magnitude ‘q’, and whose radius is ‘r’, rotates with a constant angular velocity of magnitude 'ω'. The magnetic dipole moment of the ring is

(1) \(\frac{qωr^2}{4}\)

(2) \(\frac{qωr^2}{2}\)

(3) \(\frac{qωr^2}{8}\)

(4) \(qωr^2\)

Answer 1

 (1) \(\frac{qωr^2}{4}\)

Surface charge density = 9/πr²

∴ Charge within the ring of radius R and width dR

Hence magnetic moment contributed by this ring (dM) 

Total magnetic moment of the ring