Question

An electron of charge e mass m moves in an orbit of radius r with an angular velocity $\omega$ . The ratio of the magnetic moment of the orbiting electron to its angular momentum is

• A. e/m
• B. 2e/m
• C. e/2m
• D. 2m/e

Answer 1

The correct option is C e/2m

angular momentum=mvr

=$m{r}^2\omega$

magnetic moment

=$i.\pi .r^2$

=$\left(\frac{dq}{dt}\right).\pi .r^2$

=$e.f.\pi .r^2$ =$e.\left(\frac{\omega }{2\pi }\right).\pi .r^2$

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

$\frac{Magneticmoment}{Angularmoment}=\frac{e}{2m}$