Question

An electron of charge e and mass m is moving in circular path of radius r with a uniform angular speed . 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 velocoty of electron.

Answer 1

Answer: (B), (D)

The correct options are
B The magnetic moment due to circular current loop is independent of m
D The angular momentum of the particle is proportional to the areal velocoty of electron.

Given charge of the electron is $e$ ,

and mass of the electron is $m$ ,

Radius of circular path is $r$ ,

Say, Uniform linear velocity is $v$ .

So, Angular momentum is $L=mvr$ .

Thus, Angular momentum is directly proportional to the velocity of the electron.

Now, Time peroid, $T=\frac{2\pi r}{v}$

Current $I=\frac{e}{T}=\frac{e}{\frac{2\pi r}{v}}=\frac{ev}{2\pi r}$

So, The current is inversely proportional to $r$

Magnetic moment $\mu =$ current $\times$area $=\frac{ev}{2\pi r}\times \pi r^2=\frac{evr}{2}=\left(\frac{e}{2m}\right)\times mvr=\left(\frac{e}{2m}\right)\times L$

Thus, Magnetic moment is independent of mass $m$

So, Option B and D are the correct options.