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Another common term encountered for both absolute and relative permittivity is the dielectric constant which has been deprecated in physics and engineering [2] as well as in chemistry. [ 3 ] By definition, a perfect vacuum has a relative permittivity of exactly 1 whereas at standard temperature and pressure , air has a relative permittivity of ...
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 derivation of the Helmholtz equation from the Maxwell's equations is an approximation as one neglects the spatial and temporal derivatives of the permittivity and permeability of the medium. A new formalism of light beam optics has been developed, starting with the Maxwell's equations in a matrix form: a single entity containing all the ...
For linear algebraic equations, one can make 'nice' rules to rewrite the equations and unknowns. The equations can be linearly dependent. But in differential equations, and especially partial differential equations (PDEs), one needs appropriate boundary conditions, which depend in not so obvious ways on the equations.
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
In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem , and it relates the distribution of electric charge to the resulting electric field .
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
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.