Question

If the angular momentum of an electron of charge $e$, revolving in a circular orbit is $L$, then its magnetic moment is (Given mass of electron $=m$)

• A. $eLm$
• B. $\frac{eL}{m}$
• C. $\frac{eL}{2m}$
• D. $0$

Answer 1

Answer: (C)

$\frac{eL}{2m}$

angular momentum
$L=mVr\Rightarrow \frac{L}{m}=Vr=\omega r^2$
magnetic moment $=iA$
$=\frac{e}{T}\pi r^2$

$=\frac{e\omega }{2\pi }\pi r^2$ $(\because T=\frac{2\pi }{\omega })$

$=\frac{e\omega r^2}{2}$

$=\frac{e}{2}\times \frac{L}{m}$

$=\frac{eL}{2m}$