Zeeman energy

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 for the Zeeman effect. In SI units, it is given by

$E_{\mathrm{Z}\mathrm{e}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{n}}=-{\mu }_0\underset{V}{\int }\text{<mi fromhbox="1">M</mi>}\cdot {\text{<mi fromhbox="1">H</mi>}}_{\mathrm{E}\mathrm{x}\mathrm{t}}\mathrm{d}V$

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:

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

References

• F. Barozzi, F. Gasparini, Fondamenti di Elettrotecnica: Elettromagnetismo, UTET Torino, 1989
• Hubert, A. and Schäfer, R. Magnetic domains: the analysis of magnetic microstructures, Springer-Verlag, 1998