- Electron magnetic dipole moment
In

atomic physics , the**magnetic dipole moment**of anelectron 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 inclassical 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 themagnetic north pole . The electron exists in a magnetic field which exerts atorque 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 sping-factor . The persistent early spectroscopists, such asAlfred Lande , worked out a way to calculate the effect of the various directions of angular momenta. The resulting geometric factor is called theLande g-factor .The intrinsic magnetic moment "μ" of a particle with charge "q", mass "m", and spin

**"s**", is:$mu\; =\; g\; ,\; frac\{q\}\{2m\},\; \backslash boldsymbol\{s\}$

where the

dimensionless quantity "g" is called theg-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 theDirac equation , a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of 0.002319..., called theanomalous magnetic dipole moment of the electron, arises from the electron's interaction with virtual photons inquantum 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:$\backslash boldsymbol\{mu\}\_S=-g\_S\; mu\_B\; (\backslash boldsymbol\{s\}/hbar)$

where $g\_s=2$ in

Dirac mechanics, but is slightly larger due to Quantum Electrodynamic effects, $mu\_\{B\}$ is theBohr magneton ,**"s**" is the electron spin, and $hbar,$ is thereduced 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

:$\backslash boldsymbol\{mu\}\_z=-g\_S\; mu\_B\; m\_s$

where m

_{s}is the spin quantum number.It is important to notice that $\backslash boldsymbol\{mu\}$ 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

hydrogen atomicelectron in state $Psi\_\{n,l,m\}$ where $n,\; l$ and $m$ are the principal, azimuthal and magneticquantum numbers respectively, the total magneticdipole moment due to orbitalangular momentum is given by:$mu\_L=-frac\{e\}\{2m\_e\}L=-mu\_Bsqrt\{l(l+1)\}$

where $mu\_\{B\}$ 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:$\backslash boldsymbol\{mu\}\_z=-mu\_B\; m\_l.$

**See also***

anomalous magnetic dipole moment

*Nuclear magnetic moment

*Fine structure

*Hyperfine structure

*g-factor **Footnotes**

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