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(B) The magnetic moment $M$ of a circulating electron is given by $M = I A$,where $I$ is the current and $A$ is the area of the loop.For an electron o

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$\frac{eJ}{2m}$

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(B) The magnetic moment $M$ of a circulating electron is given by $M = I A$,where $I$ is the current and $A$ is the area of the loop.For an electron of charge $e$ moving with velocity $v$ in a circular orbit of radius $r$,the current is $I = \frac{e}{T} = \frac{ev}{2\pi r}$.The area of the orbit is $A = \pi r^2$.Therefore,$M = \left(\frac{ev}{2\pi r}\right) (\pi r^2) = \frac{1}{2} evr$.We know that the angular momentum $J$ of the electron is $J = mvr$.From this,we can write $vr = \frac{J}{m}$.Substituting this into the expression for $M$,we get $M = \frac{1}{2} e \left(\frac{J}{m}\right) = \frac{eJ}{2m}$.

If the angular momentum of an electron is $\overrightarrow{J}$,then the magnitude of the magnetic moment will be

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