Electron magnetic dipole moment

In electron is caused by its intrinsic property of spin within a magnetic field.

Explanation of magnetic moment

The electron is a negatively charged particle with angular momentum. A rotating Lande g-factor.

The intrinsic magnetic moment μ of a particle with charge q, mass m, and spin s, is

$\mu = g \, \frac{q}{2m}\, \boldsymbol{s}$

where the dimensionless quantity g is called the g-factor.

The g-factor is an essential value related to the magnetic moment of the subatomic particles and corrects for the precession of the angular momentum. One of the triumphs of the theory of quantum electrodynamics. Reduction of the Dirac equation for an electron in a magnetic field to its non-relativistic limit yields the Schrödinger equation with a correction term which takes account of the interaction of the electron's intrinsic magnetic moment with the magnetic field giving the correct energy.

The total spin magnetic moment of the electron is

$\boldsymbol{\mu}_S=-g_S \mu_B (\boldsymbol{s}/\hbar)$

where $g s = 2$ in Dirac mechanics, but is slightly larger due to Bohr magneton and s is the electron spin.

The z component of the electron magnetic moment is

$\boldsymbol{\mu}_z=-g_S \mu_B m_s$

where m_s is the spin quantum number.

It is important to notice that $\boldsymbol{\mu}$ is a negative constant multiplied by the spin, so the magnetic moment is antiparallel to the spin angular momentum.

Orbital magnetic dipole moment

Generally, for a electron in state $Ψ n, l, m$ where $n, l$ and $m$ are the principal, azimuthal and magnetic quantum numbers respectively, the total magnetic dipole moment due to orbital angular momentum is given by

$\mu_L=-\frac{e}{2m_e}L=-\mu_B\sqrt{l(l+1)}$

where $μ B$ is the Bohr magneton.

The z-component of the orbital magnetic dipole moment for an electron with a magnetic quantum number m_l is given by

$\boldsymbol{\mu}_z=-\mu_B m_l$

Electron magnetic dipole moment

Explanation of magnetic moment

Orbital magnetic dipole moment

See also