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 effective current $i=\frac{q\, \omega}{2 \pi}$ and $A=\pi r^{2}$.
Magnetic moment $M=i A=\frac{1}{2} q \, \omega r^{2}$
Angular moment $L=I\, \omega=m r^{2} \, \omega$
$ \Rightarrow \frac{M}{L}=\frac{q}{2 m}$