Question

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

• A. The equivalent current flowing in the circular path is proportional to $r^2$
• B. The magnetic moment due to circular current loop is independent of $m$
• C. The magnetic moment due to circular current loop is equal to $2e/m$ time the angular momentum of the electron
• D. The angular momentum of the particle is proportional to the areal velocity of electron.

Answer 1

Answer: (D)

The angular momentum of the particle is proportional to the areal velocity of electron.

Answer 2

Magnetic moment, $m=l A$
$=\frac{e V}{2 \pi r} \times \pi r^{2}=\frac{e v r}{2}$
Angular momentum $=2 m \frac{d A}{d t}$