Magnetic Dipole Moment of Electron Orbit and Orbital Gyro magnetic Ratio

An electron moving in an orbit has orbital angular momentum, which is a vector quantity L. The L vector is perpendicular to the plane in which the orbital motion of electron takes place.

    L = Mvr = Mr² ω

Here, M is the mass of the electron, v is the linear velocity along the orbit, and r is the radius of the circular orbit, ω is the circular frequency of revolution.

Magnetic dipole moment associated with orbital motion is ml = current x area = (eω/ 2π) x πr² = eωr² /2

Direction of m1 is opposite moment to the angular momentum is
    m₁ /L = -eωr² /Mr²ω = -e/2M
This ratio, which involves only the charge and mass of the electron, is called the gyro magnetic ratio.