# Electron magnetic dipole moment

Electron magnetic dipole moment

In atomic physics, the magnetic dipole moment of an 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 electrically charged body in classical electrodynamics causes a magnetic dipole effect creating magnetic poles of equal magnitude but opposite polarity like a bar magnet. For magnetic dipoles, the dipole moment points from the magnetic south to the magnetic north pole. The electron exists in a magnetic field which exerts a torque opposing its alignment creating a potential energy that depends on its orientation with respect to the field. The magnetic energy of an electron is approximately twice what it should be in classical mechanics. The factor of two multiplying the electron spin angular momentum comes from the fact that it is twice as effective in producing magnetic moment. This factor is called the electronic spin g-factor. The persistent early spectroscopists, such as Alfred Lande, worked out a way to calculate the effect of the various directions of angular momenta. The resulting geometric factor is called the Lande g-factor.

The intrinsic magnetic moment "&mu;" of a particle with charge "q", mass "m", and spin "s", is

:

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 is its accurate prediction of the electron "g"-factor, which has been experimentally determined to have the value 2.002319... The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of 0.002319..., called the anomalous magnetic dipole moment of the electron, arises from the electron's interaction with virtual photons in 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

:

where $g_s=2$ in Dirac mechanics, but is slightly larger due to Quantum Electrodynamic effects, $mu_\left\{B\right\}$ is the Bohr magneton, "s" is the electron spin, and $hbar,$ is the reduced Planck constant. An electron has an intrinsic magnetic dipole moment of approximately one Bohr magneton. [A. Mahajan and A. Rangwala. [http://books.google.com/books?id=_tXrjggX7WwC&pg=PA419&lpg=PA419&dq=%22intrinsic+dipole+moment%22+and+electron+%22Bohr+magneton%22&source=web&ots=87QUlLPdmD&sig=cmYr28QQJM75lI_ih4sS9UjGRE0 Electricity and Magnetism] , p. 419 (1989). Via Google Books.]

The "z" component of the electron magnetic moment is

:

where ms is the spin quantum number.

It is important to notice that 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 hydrogen atomic electron in state $Psi_\left\{n,l,m\right\}$ 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

:$mu_L=-frac\left\{e\right\}\left\{2m_e\right\}L=-mu_Bsqrt\left\{l\left(l+1\right)\right\}$

where $mu_\left\{B\right\}$ is the Bohr magneton.

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

:

* anomalous magnetic dipole moment
* Nuclear magnetic moment
* Fine structure
* Hyperfine structure
* g-factor

Footnotes

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Electron electric dipole moment — The electron electric dipole moment (EDM) d e is, roughly speaking, a measure of the charge distribution within an electron. Within the standard model of elementary particle physics, such a dipole is predicted to be of smaller than 10^{ 40}… …   Wikipedia

• magnetic dipole moment — n. A physical quantity associated with the magnetic field of a dundamental particle; as, An orbiting electron in an atom will have a magnetic dipole moment. [WordNet 1.5] …   The Collaborative International Dictionary of English

• magnetic dipole moment — noun (physics) a current loop gives rise to a magnetic field characteristic of a magnetic dipole An orbiting electron in an atom will have a magnetic dipole moment • Topics: ↑physics, ↑natural philosophy • Hypernyms: ↑dipole moment …   Useful english dictionary

• Dipole moment — can be defined as the product of magnitude of charge distance of separation between the charges. Dipole moment may refer to: Electric dipole moment, the measure of the electrical polarity of a system of charges Transition dipole moment, the… …   Wikipedia

• Anomalous magnetic dipole moment — In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. The Dirac magnetic moment, corresponding …   Wikipedia

• Magnetic dipole transition — The interaction of an electromagnetic wave with an electron bound in an atom or molecule can be described by time dependent perturbation theory. Magnetic dipole transitions describe the dominant effect of the coupling to the magnetic part of the… …   Wikipedia

• magnetic dipole — Tiny magnet with subatomic dimensions, equivalent to the flow of electric charge around a loop. Examples include electrons circulating around atomic nuclei, rotating atomic nuclei, and single subatomic particles with spin. On a large scale, these …   Universalium

• Anomalous electric dipole moment — In particle physics, the anomalous electric dipole moment, or the electric dipole moment of a particle in short, is the electric dipole moment of a particle. There is a symmetry, the CP symmetry, which if exact and unbroken will predict an… …   Wikipedia

• Electric dipole moment — In physics, the electric dipole moment (or electric dipole for short) is a measure of the polarity of a system of electric charges. In the simple case of two point charges, one with charge {+}q and one with charge { }q, the electric dipole moment …   Wikipedia

• Magnetic moment — Electromagnetism Electricity · …   Wikipedia