title: Zeeman energy
text: # 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
  
      $E_{\rm {Zeeman}}=-\mu _{0}\int _{V}\,{\textbf {M}}\cdot {\textbf {H}}_{\rm {Ext}}\,\mathrm {d} V$
  
  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:
  
      $H=-{\textbf {m}}\cdot {\textbf {B}}$
  