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The relative permittivity of a medium is related to its electric susceptibility, χ e, as ε r (ω) = 1 + χ e. In anisotropic media (such as non cubic crystals) the relative permittivity is a second rank tensor. The relative permittivity of a material for a frequency of zero is known as its static relative permittivity.
Relative permittivity is directly related to electric susceptibility ... In an anisotropic material, the relative permittivity may be a tensor, causing birefringence.
If a dielectric material is a linear dielectric, then electric susceptibility is defined as the constant of proportionality (which may be a tensor) relating an electric field E to the induced dielectric polarization density P such that [3] [4] =, where
Here ε is known as the relative permittivity tensor or dielectric tensor. Consequently, the refractive index of the medium must also be a tensor. Consider a light wave propagating along the z principal axis polarised such the electric field of the wave is parallel to the x-axis. The wave experiences a susceptibility χ xx and a permittivity ε ...
Thus = (+) = = where ε r = 1 + χ is the relative permittivity of the material, and ε is the permittivity. In linear, homogeneous, isotropic media, ε is a constant. However, in linear anisotropic media it is a tensor , and in nonhomogeneous media it is a function of position inside the medium.
In terms of relative permeability, the magnetic susceptibility is χ m = μ r − 1. {\displaystyle \chi _{m}=\mu _{r}-1.} The number χ m is a dimensionless quantity , sometimes called volumetric or bulk susceptibility, to distinguish it from χ p ( magnetic mass or specific susceptibility) and χ M ( molar or molar mass susceptibility).
The refractive index of electromagnetic radiation equals =, where ε r is the material's relative permittivity, and μ r is its relative permeability. [ 47 ] : 229 The refractive index is used for optics in Fresnel equations and Snell's law ; while the relative permittivity and permeability are used in Maxwell's equations and electronics.
In electromagnetism, the Clausius–Mossotti relation, named for O. F. Mossotti and Rudolf Clausius, expresses the dielectric constant (relative permittivity, ε r) of a material in terms of the atomic polarizability, α, of the material's constituent atoms and/or molecules, or a homogeneous mixture thereof.