Explanation of permeability.

In electromagnetism, the auxiliary magnetic field
H represents how a magnetic field B influences
the organization of magnetic dipoles in a given
medium, including dipole migration and
magnetic dipole reorientation. Its relation to
permeability is
where the permeability, μ, is a scalar if the
medium is isotropic or a second rank tensor for
an anisotropic medium.
In general, permeability is not a constant, as it
can vary with the position in the medium, the
frequency of the field applied, humidity ,
temperature, and other parameters. In a
nonlinear medium , the permeability can depend
on the strength of the magnetic field.
Permeability as a function of frequency can take
on real or complex values. In ferromagnetic
materials, the relationship between B and H
exhibits both non-linearity and hysteresis : B is
not a single-valued function of H , [2] but
depends also on the history of the material. For
these materials it is sometimes useful to
consider the incremental permeability defined as
This definition is useful in local linearizations of
non-linear material behavior, for example in a
Newton–Raphson iterative solution scheme that
computes the changing saturation of a magnetic
circuit.