Question

An electron having charge $e$ is moving with a constant speed $v$ along a circle of radius $r$. Its magnetic moment will be

• A. e v r
• B. $\frac{evr}{2}$
• C. $2\pi rev$
• D. Zero

Answer 1

Answer: (B)

An electron moving in a circular motion is shown in figure below

Current due to circular motion
$i=\frac{e}{t}$, where $t=$ time period
So, the magnetic moment of electron
$m=i.A=\frac{e}{T}.\pi r^2$
$\Rightarrow m=e{r}^2\frac{2\pi }{2T}$
$=\frac{e\omega r^2}{2}\left[\because \frac{2\pi }{t}=\omega \right]$
$\Rightarrow m=\frac{evr}{2}\left[\because \omega =\frac{v}{r}\right]$