Moving Charges and Magnetism

An electron moves in a circular orbit of radius R
and period T.
Step 1: Find the current due to orbital motion
The charge of the electron is e (magnitude).
In one complete revolution, the charge e passes a given point once in time T.
So,
current I=‌

e

T

Step 2: Magnetic moment due to a current loop
Magnetic moment of a current loop is given by
µ=I× area of the loop
The area of a circular loop of radius R is
A=πR2
Thus,
µ=I×A=‌

e

T

×πR2=‌

πeR2

T