# Magnetic behavior of materials: definitions

## Definition

The macroscopic dependence linking the local values of the vector quantities magnetization M (or magnetic polarization J ) and the magnetic field strength H in any point of a material is called the law of material magnetic behavior.

This law renders the fact that the magnetization of matter is modified under the effect of a magnetic field.

This law is written in the form:

- with the magnetization vector
- with the polarization vector

where χ_{m} is the scalar or the tensor of magnetic susceptibility*

_{m}depends on H; χ

_{m}should be written in the form χ

_{m}(H) in all the relationships above.

## Notation

The magnetization law is written in the form:

⇒ ⇒ ⇒

where μ is the scalar or the tensor of permeability

_{m}, μ

_{r}, μ should be written in the form χ

_{m}(H), μ

_{r}(H), μ(H) in all the relationships above.

## Complex permeability

In the case of harmonic applications, a complex representation of permeability is used.

The quantity μ can be expressed by the complex permeability:

μ = μ' - j μ"

where:

- μ' corresponds to the real part of the complex permeability
- μ" corresponds to the imaginary part of the complex permeability