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

The correct option is C

q and m

The angular momentum L of the particle is given by $L=m{r}^2\omega$

$\to$ where $\omega =2\pi n$

$\therefore$ Frequency $n=\frac{\omega }{2\pi }$

Further $i\times q\times n=\frac{\omega q}{2\pi }$

Magnetic moment, $M=iA=\frac{\omega q}{2\pi }\times \pi r^2$

$\therefore M=\frac{\omega q{r}^2}{2}\Rightarrow \frac{M}{L}=\frac{\omega q{r}^2}{2m{r}^2\omega }=\frac{q}{2m}$