Electron Magnetic Dipole Moment - Magnetic Moment of An Electron

Magnetic Moment of An Electron

The electron is a charged particle of charge (−e), where e is the elementary charge. Its angular momentum comes from two types of rotation: spin and orbital motion. From classical electrodynamics, a rotating electrically charged body creates a magnetic dipole with magnetic poles of equal magnitude but opposite polarity. This analogy holds as an electron indeed behaves like a tiny bar magnet. One consequence is that an external magnetic field exerts a torque on the electron magnetic moment depending on its orientation with respect to the field.

If the electron is visualized as a classical charged particle literally rotating about an axis with angular momentum L, its magnetic dipole moment μ is given by:

where m_e is the electron rest mass. Note that the angular momentum L in this equation may be the spin angular momentum, the orbital angular momentum, or the total angular momentum. It turns out the classical result is off by a proportional factor for the spin magnetic moment. As a result, the classical result is corrected by multiplying it with a dimensionless correction factor g is known as the g-factor;

It is usual to express the magnetic moment in terms of the reduced Planck constant ħ and the Bohr magneton μ_B:

since the magnetic moment is quantized in units of μ_B, correspondingly the angular momentum is quantized in units of ħ.