Magnetic susceptibility

In electrical engineering, the magnetic susceptibility is the degree of magnetization of a material in response to a magnetic field. The dimensionless volume magnetic susceptibility is represented by the symbol χ (lowercase Greek letter chi).

<math>

\chi = \frac {M} {H}, <math>

where M is the magnetization of the material (the magnetic dipole moment per unit volume) and H is the magnetic field strength.

If χ is positive the material is called paramagnetic, and the magnetic field is strengthened by the presence of the material. If χ is negative then the material is diamagnetic and 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 accomidate 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{dM_j}{dH_i}<math>

called the differential susceptibility describes ferromagnetic materials. 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>\mu_0<math> is the permeability of vacuum (see table of physical constants).