# electric displacement (*D*)

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.

If we consider a parallel-plate capacitor before introducing a dielectric into the space between the plates, the electric field strength is:

*E* = *σ*/*ε*_{0}

where ±*σ* are the surface densities of free charges on
the plates and *ε*_{0} is the permittivity of free space. Introducing the dielectric causes the field to decrease to
the value

*E* = (*σ* - *σ _{P}*)/

*ε*

_{0}(1)

reflecting the fact that *σ _{P}* coulombs/m

^{2}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* = *ε*_{0}*E* + *σ _{P}* =

*ε*

_{0}

*E*+

*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* = *ε*_{0}*E* + *P*

or, in vector form,

* D* =

*ε*

_{0}

*+*

**E***(3)*

**P**

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*

or

* D* =

*ε*

**E**

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*,

*, and*

**E***all have the same direction, and the value of*

**P***ε*is usually independent of the strength of the field. For anisotropic dielectrics, such as quartz, where the electrical properties depend on direction,

*,*

**D***, and*

**E***are rarely parallel.*

**P**

See also displacement current.