Physics - Magnetism Question with Solution | TestHub

As $\overrightarrow{\mathrm{M}}=\mathrm{IA}$
$\Rightarrow |\overrightarrow{\mathrm{M}}|=\frac{\mathrm{e}}{\frac{2\pi \mathrm{R}}{\mathrm{v}}}\pi {\mathrm{R}}^2$ $\left[\because \mathrm{I}=\frac{\mathrm{Q}}{\mathrm{T}}=\frac{\mathrm{e}}{\frac{2\pi \mathrm{R}}{\mathrm{V}}}\right]$
$\Rightarrow |\vec{M}|=\frac{1}{2}evR\Rightarrow |\vec{M}|=\frac{\mathrm{mvR}}{1}\cdot \frac{\mathrm{e}}{2\mathrm{m}}$
$\Rightarrow |\overrightarrow{\mathrm{M}}|=\frac{\mathrm{eL}}{2\mathrm{m}}\Rightarrow |\overrightarrow{\mathrm{M}}|=-\frac{\mathrm{e}\overrightarrow{\mathrm{L}}}{2\mathrm{m}}$
[ $\because$ Here $\overrightarrow{\mathrm{M}}$ and $\overrightarrow{\mathrm{L}}$ will always be opposite]