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

${\displaystyle E_{\rm {Zeeman))=-\mu _{0}\int _{V}\,{\textbf {M))\cdot {\textbf {H))_{\rm {Ext))\,\mathrm {d} V}$

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:

${\displaystyle H=-{\textbf {m))\cdot {\textbf {B))}$