Question

A thin disc of radius R and mass M has charge q uniformly distributed on it. It rotates with angular velocity w. The ratio of magnetic moment and angular momentum for the disc is
(1) q/2M (2) R/2M (3) q^2/2M (4) 2M/q

Answer 1

The formula to get  angular momentum (L) is

 L=Iw or L= $\frac{mR^{2}w}{2}$

where

I= moment inertia for a disk which is $\frac{mR^{2}}{2}$

The formula for magnetic moment (M) is

$M=\frac{qR^{2}w}{4}$

Therefore the ratio of magnetic moment to angular moment is

M/L.

$\frac{\frac{qR^{2}w}{4}}{\frac{mR^{2}w}{2}}$

$(\frac{qR^{2}w }{2} )(\frac{2}{mR^{2} }w)$

$\frac{q}{2m}$

Therefore, the ratio is q/2m.