Physics - Magnetism Question with Solution | TestHub

The electron moving with a speed $v$ in the circular Bohr orbit of radius $r$ constitutes a current of magnitude.

$i=\frac{e}{T}.$ where $T$ is the orbital period of the electron.

$T=2\pi r/v$

$i=\frac{ev}{2\pi r}$

By definition of atomic dipole moment ${\mu }_i,$ its magnitude is given by

${\mu }_i=iA=\frac{eV}{2\pi r}·\pi r^2=\frac{evr}{2}$

$\therefore$ Angular momentum, $L=mvr$
$\therefore$ $\frac{L}{{\mu }_i}=\frac{2mvr}{evr}=\frac{2m}{e}=\text{ constant }$