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Concept
Demagnetizing field
Summary
The demagnetizing field, also called the stray field (outside the magnet), is the magnetic field (H-field) generated by the magnetization in a magnet. The total magnetic field in a region containing magnets is the sum of the demagnetizing fields of the magnets and the magnetic field due to any free currents or displacement currents. The term demagnetizing field reflects its tendency to act on the magnetization so as to reduce the total magnetic moment. It gives rise to shape anisotropy in ferromagnets with a single magnetic domain and to magnetic domains in larger ferromagnets.
The demagnetizing field of an arbitrarily shaped object requires a numerical solution of Poisson's equation even for the simple case of uniform magnetization. For the special case of ellipsoids (including infinite cylinders) the demagnetization field is linearly related to the magnetization by a geometry dependent constant called the demagnetizing factor. Since the magnetization of a sample at a given location depends on the total magnetic field at that point, the demagnetization factor must be used in order to accurately determine how a magnetic material responds to a magnetic field. (See magnetic hysteresis.)
Maxwell's equations
In general the demagnetizing field is a function of position H(r). It is derived from the magnetostatic equations for a body with no electric currents. These are Ampère's law
and Gauss's law
The magnetic field and flux density are related by
where is the permeability of vacuum and M is the magnetisation.
magnetic scalar potential
The general solution of the first equation can be expressed as the gradient of a scalar potential U(r):
Inside the magnetic body, the potential Uin is determined by substituting () and () in ():
Outside the body, where the magnetization is zero,
At the surface of the magnet, there are two continuity requirements:
The component of H parallel to the surface must be continuous (no jump in value at the surface).
The component of B perpendicular to the surface must be continuous.
Official source
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