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In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field.
Electric displacement, auxiliary electric field or electric vector that represents that aspect of an electric field associated solely with the presence of separated free electric charges, purposely excluding the contribution of any electric charges bound together in neutral atoms or molecules.
This new vector is called the electric displacement D: D 0E+P (4) The units of D are those of polarization density, which is dipole moment per unit volume. The dipole moment has units of charge times distance, so the units of D are charge times distance over volume, or charge per unit area.
The differential form uses the vector del operator ∇: ∇ ≡ xˆ ∂ + yˆ ∂ + zˆ ∂ ∂x ∂y ∂z. (2.1.1) where xˆ, yˆ , and zˆ are defined as unit vectors in cartesian coordinates. Relations involving ∇ are summarized in Appendix D.
Dielectric Polarization, Bound Charges, and the Electric Displacement Field. Any kind of matter is full of positive and negative electric charges. In a dielectric, these charges are bound — they cannot move separately from each other through any macroscopic distance, — so when an electric field is applied there is no net electric current.
$D$ is the electric displacement field or commonly the flux density and $E$ is the field intensity. There is a fundamental difference between them which will be understood to certain extent as you go through the following answer.
Theory of Electromagnetic Fields. I shall assume some familiarity with the following topics: vector calculus in Cartesian and polar coordinate systems; Stokes' and Gauss' theorems; Maxwell's equations and their physical signi cance; types of cavities and waveguides commonly used in accelerators.
