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The linear permittivity of a homogeneous material is usually given relative to that of free space, as a relative permittivity ε r (also called dielectric constant, although this term is deprecated and sometimes only refers to the static, zero-frequency relative permittivity).
Definition for linear dielectrics [ edit ] 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 ] P = ε 0 χ e E , {\displaystyle \mathbf {P ...
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
The electric displacement field "D" is defined as +, where is the vacuum permittivity (also called permittivity of free space), E is the electric field, and P is the (macroscopic) density of the permanent and induced electric dipole moments in the material, called the polarization density.
The definitions of charge, ... In materials with relative permittivity, ... For linear algebraic equations, one can make 'nice' rules to rewrite the equations and ...
6 Equation for linear ... ε 0 is the vacuum permittivity and ... The first equation is true by definition, and therefore the second equation is true if and only if ...
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field.
The distinction is irrelevant for an unattenuated wave, but becomes relevant in some cases below. For example, there are two definitions of complex refractive index, one with a positive imaginary part and one with a negative imaginary part, derived from the two different conventions. [2] The two definitions are complex conjugates of each other.