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(B) The magnetic moment $M$ of an electron revolving in a circular orbit is given by $M = I A$,where $I$ is the current and $A$ is the area of the orb

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$\frac{eJ}{2m}$

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(B) The magnetic moment $M$ of an electron revolving in a circular orbit is given by $M = I A$,where $I$ is the current and $A$ is the area of the orbit.Since $I = \frac{e}{T}$ and $T = \frac{2\pi r}{v}$,we have $I = \frac{ev}{2\pi r}$.The area $A = \pi r^2$.Thus,$M = \left(\frac{ev}{2\pi r}\right) (\pi r^2) = \frac{1}{2} evr$.We know that the angular momentum $J = mvr$.Substituting $vr = \frac{J}{m}$ 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 $\vec{J}$,then the magnitude of the magnetic moment will be:

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