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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 Pieter Zeeman (; 25 May 1865 – 9 October 1943) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Hendrik Lorentz for his discovery of the Zeeman effect. Childhood and youth Pieter Zeeman was born in Zonnemaire, a small town ...
, primarily known for the
Zeeman effect The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel prize ...
. In SI units, it is given by :E_ =-\mu_ \int_V\,\textbf M\cdot \textbf H_{\rm Ext} \, \mathrm dV where HExt 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 In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...
m, which is however experiencing a ''local'' induction B: :H =-\textbf m \cdot \textbf B


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 Magnetism Physical phenomena