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(C) Consider an electron of charge $e$ and mass $m$ revolving in a circular orbit of radius $r$ with a speed $v$ and time period $T$.The current $I$ a

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$\frac{eL}{2m}$

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(C) Consider an electron of charge $e$ and mass $m$ revolving in a circular orbit of radius $r$ with a speed $v$ and time period $T$.The current $I$ associated with this revolving electron is $I = \frac{e}{T} = \frac{e}{2\pi r / v} = \frac{ev}{2\pi r}$.The magnetic moment $M$ is given by $M = I 	imes A = I 	imes (\pi r^2)$.Substituting the value of $I$,we get $M = \left(\frac{ev}{2\pi r}ight) 	imes (\pi r^2) = \frac{evr}{2}$.The angular momentum $L$ of the electron is $L = mvr$.Thus,$vr = \frac{L}{m}$.Substituting this into the expression for $M$,we get $M = \frac{e}{2} 	imes \left(\frac{L}{m}ight) = \frac{eL}{2m}$.

The magnetic moment of a revolving electron of charge $e$ and mass $m$ in terms of the angular momentum $L$ of the electron is:

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