Traffic congestion: Reconstruction with Kerner's three-phase theory

Zeeman energy, or the external field energy, is the potential energy of a magnetised body in an external magnetic field. It is named after the Dutch physicist Pieter Zeeman, primarily known by the Zeeman effect. In SI units, it is given by

$E_{Zeeman}=-{\mu }_0\underset{V}{\int }\mathbf{\text{<mi fromhbox="1">M</mi>}}\cdot {\mathbf{\text{<mi fromhbox="1">H</mi>}}}_{Ext}\mathrm{d}V$

where H_Ext is the external field, M the local magnetisation, and the integral is done over the volume of the body. This is the statistical average (over a unit volume macroscopic sample) of a corresponding microscopic Hamiltonial (energy) for each individual magnetic moment m, which is however experiencing a local induction B:

$H=-\mathbf{\text{<mi fromhbox="1">m</mi>}}\cdot \mathbf{\text{<mi fromhbox="1">B</mi>}}$

References

• d'Aquino, M, Phd thesis, http://wpage.unina.it/mdaquino/PhD_thesis/main/node16.html
• Hubert, A. and Schäfer, R. Magnetic domains: the analysis of magnetic microstructures, Springer-Verlag, 1998