Question

A particle of charge ‘q’ and mass ‘m’ moves in a circular orbit of radius ‘r’ with angular speed $\omega$. The ratio of the magnitude of its magnetic moment to that of angular momentum depends on

• A. $\omega$ and q
• B. $\omega$, q and m
• C. q and m
• D. $\omega$ and m

Answer 1

The correct option is C q and m

Magnetic moment (M) = iA = $\frac{qV}{2\pi r}(\pi r{)}^2=\frac{qvr}{2}=\frac{qw{r}^2}{2}$
Angular momentum (L) = mvr = $m{r}^{2}w$
\(\therefore \frac{M}{L}=\frac{qwr^2}{2mr^2w}=\frac{q}{2m}\)