Demagnetization Fields

Generaly in the study of magnetism, and specifically for micromagnetics simulations, one needs to know the magnetic field ~ HM inside a macroscopic magnet, that is caused by the magnetization ~ M (the dipole moment per unit volume) of that magnet itself. Some aspects of how that demagnetization field can be found are discussed. There are two basic cases: (1) The demagnetization field ~ HM inside a finite element, that is caused by ~ M of that particular element; (2) The demagnetization field caused by one finite element, but measured at the position of another element. The discussion here is based on continuum description of the magnet and the field, although it can be connected to an alternative analysis that considers the superposition of many fields from a multitude of individual magnetic dipoles.