Question

A magnetic moment of an electron orbiting in a circular orbit of radius $r$ with a speed $v$ is equal to:

• A. $\frac{evr}{2}$
• B. $evr$
• C. $\frac{er}{2v}$
• D. none of these

Answer 1

The correct option is A $\frac{evr}{2}$

Current flowing in the circular orbit : $I=e\nu$ where , $\nu$ is the frequency of revolution of electron

$\therefore$ $I=e\times \frac{v}{2\pi r}$

Area of the circular orbit: $A=\pi r^2$

Magnetic moment of an electron : $\mu =IA=\frac{ev}{2\pi r}\times \pi r^2=\frac{evr}{2}$