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 its angular momentum depends on

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

Answer 1

Answer: (C)

The angular momentum L of the particle is given by
$L=m{r}^{2}w$ where $w=2\pi n$.
$\therefore$ Frequency $n=\frac{w}{2\pi }$;
Further $i=q\times n=\frac{wq}{2\pi }$
Magnetic Moment, $M=iA=\frac{wq}{2\pi }\times \pi r^2$;
$\therefore M=\frac{wq{r}^2}{2}$
So, $\frac{M}{L}=\frac{wq{r}^2}{2m{r}^{2}w}=\frac{q}{2m}$

Thus the required ratio depends upon both q and m.