Electric Flux Density (D-Field)

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The Electric Flux Density (usually written as the vector quantity D) is often used in electromagnetics. While we won't give it a rigorous definition here, it can be sufficiently understood for the purposes of antenna theory as being proportional to the Electric Field. The proportionality constant depends on the medium being analyzed, and is known as the permittivity:

electric flux density equals permittivity times E-field

The electric flux density has units of charge/area (Coulombs/meter-squared or [C/m^2]). The permittivity is often frequency-dependent, and is sometimes anisotropic (implying the permittivity depends on which direction the fields are in):

permittivity is anisotropic, electric flux density

In the most general case the E-field is related to the the electric flux density by a 3x3 matrix, which is also frequency-dependent.

The only other major result in relation to the electric flux density involves the continuitiy of fields across boundaries. Consider two materials as shown in the figure below.

surface charge density and the normal D vector across a material discontinuity

The normal component of the electric flux density will be discontinuous at the boundary by an amount equal to the surface charge density surface charge density, which has units of charge/area (Coulombs/meter-squared). This can be written mathematically as:

discontinuity of the electric flux density across a medium

This relation holds at every point along the interface of a material discontinuity (medium change).

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