Question

An electron of charge $e$ is orbiting in a circular path of radius $r$ with a uniform speed $v$. Its magnetic moment will be

• A. $\frac{evr}{2}$
• B. $evr$
• C. $\frac{er}{2v}$
• D. $2evr$

Answer 1

Answer: (A)

$\frac{evr}{2}$

Answer 2

An orbiting electron behaves as a current loop. The current due to motion of electron is $I=\frac{e}{T}=\frac{e}{\left(2\pi r/v\right)}=\frac{ev}{2\pi r}$ Area of the loop, $A=\pi r^{2}$ $\therefore$ Magnetic moment $= IA=\frac{ev}{2\pi r}\pi r^{2}$ $=\frac{evr}{2}$