Write the equation for the orbital magnetic moment of an electron rotating about the nucleus in an atom.
(N/A) An electron of charge $e$ revolving in a circular orbit of radius $r$ with a speed $v$ constitutes a current $I = \frac{e}{T}$,where $T$ is the time period of revolution.
Since $T = \frac{2\pi r}{v}$,the current is $I = \frac{ev}{2\pi r}$.
The orbital magnetic moment $\mu_l$ is given by the product of current $I$ and the area of the orbit $A = \pi r^2$.
$\mu_l = I \times A = \left( \frac{ev}{2\pi r} \right) \times (\pi r^2) = \frac{evr}{2}$.
In terms of angular momentum $L = mvr$,we can write $\mu_l = \frac{e}{2m} L$.
Since $T = \frac{2\pi r}{v}$,the current is $I = \frac{ev}{2\pi r}$.
The orbital magnetic moment $\mu_l$ is given by the product of current $I$ and the area of the orbit $A = \pi r^2$.
$\mu_l = I \times A = \left( \frac{ev}{2\pi r} \right) \times (\pi r^2) = \frac{evr}{2}$.
In terms of angular momentum $L = mvr$,we can write $\mu_l = \frac{e}{2m} L$.
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