Question

If the angular momentum of an electron of mass $m$ is $J$ then the magnitude of the magnetic moment will be

• A. $\frac{eJ}{m}$
• B. $\frac{eJ}{2m}$
• C. $2eJm$
• D. $\frac{2m}{eJ}$

Answer 1

The correct option is B $\frac{eJ}{2m}$

Magnetic moment, $M=I\times A...........\left(1\right)$ where I is current and A is area

$I=\frac{e}{T}=\frac{e}{\frac{2\pi r}{v}}=\frac{ev}{2\pi r}$

$A=\pi r^2$

Angular Momentum $J=mvr.......\left(2\right)$

Put values of $I$ and $A$ in equation (1)

$M=\frac{ev}{2\pi r}\pi r^2$

$M=\frac{evr}{2}$

$M=\frac{eJ}{2m}(\because vr=\frac{J}{m})$