Electric displacement (D), also known as electric flux density, is the charge per unit area that would be displaced across a layer of conductor placed across an electric field. This describes also the charge density on an extended surface that could be causing the field.
E = σ/ε0
where ±σ are the surface densities of free charges on the plates and ε0 is the permittivity of free space. Introducing the dielectric causes the field to decrease to the value
E = (σ - σP)/ε0 (1)
reflecting the fact that σP coulombs/m2 of the free charges on the plates are now neutralized by the polarization charges on the surface of the dielectric. Rewriting equation (1), we have
σ = ε0E + σP = ε0E + P (2)
The left-hand side of this equation, and consequently the right-hand side as well, depends only on the density of free charges on the capacitor plates. The right-hand side is defined as the electric displacement, D. Thus
D = ε0E + P
or, in vector form,
D = ε0E + P (3)
Since the value of D depends only upon the density of free charges, it is not altered by the introduction of the dielectric. For this reason, it is a particularly useful quantity.
An alternative expression to equation (1) for the intensity between the plates of the dielectric-filled capacitor is given by the equation
E = σ/ε
Recognizing from equation (2) and (3) that D = σ, we see that
D = εE
D = εE
Thus, the factor of proportionality relating electric displacement and electric field strength is simply the dielectric constant of the medium.
The preceding relationships apply only to isotropic dielectrics. In such materials D, E, and P all have the same direction, and the value of ε is usually independent of the strength of the field. For anisotropic dielectrics, such as quartz, where the electrical properties depend on direction, D, E, and P are rarely parallel.
See also displacement current.