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(B) The magnetic field $B$ at the center of a circular current loop is given by $B = \frac{\mu_{0} I}{2r}$.Here, the current $I$ is due to the revolvi

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$\frac{\mu_{0} eL}{4 \pi m r^{3}}$

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(B) The magnetic field $B$ at the center of a circular current loop is given by $B = \frac{\mu_{0} I}{2r}$.Here, the current $I$ is due to the revolving electron: $I = \frac{e}{T} = \frac{e}{2 \pi r / v} = \frac{ev}{2 \pi r}$.Substituting $I$ into the magnetic field formula: $B = \frac{\mu_{0}}{2r} \left( \frac{ev}{2 \pi r} \right) = \frac{\mu_{0} ev}{4 \pi r^{2}}$.The angular momentum $L$ of the electron is $L = mvr$, which implies $v = \frac{L}{mr}$.Substituting $v$ into the expression for $B$: $B = \frac{\mu_{0} e}{4 \pi r^{2}} \left( \frac{L}{mr} \right) = \frac{\mu_{0} eL}{4 \pi m r^{3}}$.

An electron of mass $m$ is revolving around the nucleus in a circular orbit of radius $r$ and has angular momentum $L$. The magnetic field produced by the electron at the centre of the orbit is ($e = \text{electric charge}$, $\mu_{0} = \text{permeability of free space}$)

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