An electron of charge e and mas m is moving in a circular path of radius r with a unifrom angular speed `omega` . Then which of the following statementa are correct?

Options

A. The equivalent current flowing in the circular path is proprotional 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` times the angular momentum of the electron:
D. The angular momentum of the particle is proportional to the areal velocity of electron.

Answer

B, D

Explanation

An electron moving in a circular orbit acts like a current loop.
`therefore` The current flowing in the loop.
`I = e/T = e/(2pi//omega)=(eomega)/(2pi)`
Hence, statement (a) is incorrect.
Area of the loop, `A = pir^(2)`
Magnetic moment of the loop,
`M = IA= (eomega)/(2pi)pi r^(2) = (er^(2)omega)/2`
Hence, statement (b) is correct.
As `M = e/(2m)L`
where L is the angular momentum of the electron.
Hence. statement (c) is incorrect.
Angular momentum `=2m(dA)/dt`
where `(dA)/dt` is the area velocity.
Hence, statement (d) is correct.