## Derivation of the gyromagnetic ratio of electron

*By: Argielou A. Flores, MSU-IIT*

Derive the gyromagnetic ratio, , of electron

Solution:

The magnitude of the magnetic moment of a current loop,

where is the current, is the area enclosed

For an electron with frequency , in a circular orbit of radius , it has a current

and area of,

Substituting these, we have

Its velocity and for its angular momentum ,

Therefore, the magnitude of magnetic moment,

and since

From this we can finally say that our gyromagnetic ratio is,