An electron of charge e and mass m is moving | vedclass

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(C) The current $I$ is given by $I = \frac{e}{T} = \frac{e \omega}{2 \pi}$. This is independent of $r$.The magnetic moment $\mu = I A = \left( \frac{e

Vedclass · Accepted Answer

The magnetic moment due to the circular current loop is equal to $e / (2m)$ times the angular momentum of the electron.

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(C) The current $I$ is given by $I = \frac{e}{T} = \frac{e \omega}{2 \pi}$. This is independent of $r$.The magnetic moment $\mu = I A = \left( \frac{e \omega}{2 \pi} \right) (\pi r^2) = \frac{e \omega r^2}{2}$.The angular momentum $L = m v r = m (\omega r) r = m \omega r^2$.Comparing $\mu$ and $L$, we get $\mu = \frac{e}{2m} L$.Thus, the magnetic moment is proportional to the angular momentum, and the ratio $\mu / L = e / (2m)$ is known as the gyromagnetic ratio. Statement $C$ is correct as it relates $\mu$ and $L$ via the factor $e / (2m)$.

An electron of charge $e$ and mass $m$ is moving in a circular path of radius $r$ with a uniform angular speed $\omega$. Which of the following statements are correct?

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