An electron revolving in circular orbit of radius 'r' with velocity 'V' and frequency 'v' has orbital…
An electron revolving in circular orbit of radius 'r' with velocity 'V' and frequency 'v' has orbital magnetic moment 'M'. If the frequency of revolution is doubled then the new magnetic moment will be
$\frac{\mathrm{M}}{4}$
$2 \mathrm{~M}$
$\mathrm{M}$
$\frac{M}{2}$
Solution
$M=i A=\frac{e}{t} \times \pi r^{2}$
$=\frac{e V}{2 \pi r} \times \pi r^{2}$
$=\frac{e V r}{2}=\frac{e r^{2} \omega}{2}$
$M \propto \omega$ $\therefore$ if $\omega$ is doubled, $M$ will be doubled.