Question

What is the magnetic moment of an electron orbiting in a circular orbit of radius r with a speed v?

Answer 1

The magnetic momentum can be given as

M = I A

_ _ _ _ _ _ _ _ _ _ (1)

Where

I is a current flowing through the circular loop

i.e.

I = e / T

T is a time period=1 / f

Therefore

1 / T = f

I = e f

_ _ _ _ _ _ _ _ _ _ (2)

And

A is a area of circular loop

i.e.

A = π r2

_ _ _ _ _ _ _ _ _ _ (3)

From equation (1) (2) and (3) we get

M = e f π r2