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 $m$

Magnetic moment, $\mu =iA$

$\mu =\frac{q}{2\pi /\omega }\times \pi r^2=\frac{\omega q{r}^2}{2}$

$\because T=\frac{2\pi }{\omega }$ and $I=\frac{q}{T}$

Angular momentum,

$L=mvr=m\left(r\omega \right)r=m{r}^2\omega$

So,

$\frac{L}{\mu }=\frac{m{r}^2\omega }{\omega q{r}^2/2}=\frac{2m}{q}$