# electric displacement (*D*)
Also known as **electric flux density**, 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 deind as the electric displacement, *D*. Thus
*D* = *ε*_{0}*E* + *P*
or, in vector form,
**D** = *ε*_{0}**E**
+ **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*
or
**D** = *ε***E**
Thus, the factor of proprtionality 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.
## Related category
• ELECTRICITY
AND MAGNETISM
Source: Duckworth, Henry E. *Electricity and Magnetism*,
pp. 92-93. New York: Holt, Rinehart and Winston (1960). |