# Magnetic susceptibility

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 is represented by the symbol χ (lowercase Greek letter chi).

[itex]

\chi = \frac {M} {H} [itex]

where

M is the magnetization of the material (the magnetic dipole moment per unit mass), measured in A/m (i.e. Amperes per metre)

H is the applied field, measured in A/m (where the magnetic induction B is related to H by the relationship [itex]B = \mu_0(H + J)[itex] where μ0 is the permeability of vacuum (see table of physical constants).)

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 accommodate this, a more general definition using a tensor derived from derivatives of components of M with respect to components of H

[itex]\chi_{ij} = \frac{\part M_j}{\part H_i}[itex]

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:

[itex]\mu = \mu_0(1+\chi) \,[itex]de:Suszeptibilität

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