Magnetic susceptibility
From Freepedia
In electrical engineering, the magnetic susceptibility is the degree of magnetization of a material in response to a magnetic field. The dimensionless mass magnetic susceptibility, represented by the symbol <math>\ \chi</math>, is defined by the relationship
- <math>
\mathbf{M} = \chi \mathbf{H} </math>
where
- M is the magnetization of the material (the magnetic dipole moment per unit mass), measured in amperes per meter, and
- H is the applied field, also measured in amperes per meter.
The magnetic induction B is related to H by the relationship
- <math>\mathbf{B} \ = \ \mu_0(\mathbf{H} + \mathbf{M}) \ = \ \mu_0(1+\chi) \mathbf{H} \ = \ \mu \mathbf{H} </math>
where μ0 is the permeability of free space (see table of physical constants), and <math> \ (1+\chi) </math> is the relative permeability of the material.
If χ is positive, then (1+χ) > 1 and the material is called paramagnetic. In this case, the magnetic field is strengthened by the presence of the material. Alternatively, if χ is negative, then (1+χ) < 1, and the material is diamagnetic. As a result, the magnetic field is weakened in the presence of the material.
The magnetic susceptibility of a ferromagnetic substance is not linear. Response is dependent upon the state of sample and can occur in directions other than that of the applied field. To accommodate this, a more general definition using a tensor derived from derivatives of components of M with respect to components of H
- <math>\chi_{ij} = \frac{\part M_j}{\part H_i}</math>
called the differential susceptibility describes ferromagnetic materials,
- where i = {1,2,3} and j = {1,2,3} represent the x-, y-, and z- components of H and M respectively. The tensor is thus rank 2, dimension (3,3).
When the coercivity of the material parallel to an applied field is the smaller of the two, the differential susceptibility is merely a function of the applied field.
The magnetic susceptibility and the magnetic permeability (μ) are related by the following formula:
- <math>\mu = \mu_0(1+\chi) \,</math>
where <math> \ (1+\chi) </math> is the relative permeability of the material.
