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 $M=iA=\frac{1}{2}q\omega r^{2}$
Angular moment $L=I\omega =mr^{2}\omega \Rightarrow \frac{M}{L}=\frac{q}{2 m}$