of
free charges representing a net surplus or deficit of electrons in
the atoms of the dielectric and
is
the charge density due to the polarizing effect of an electric field
then the total charge density is given by
University Physics Notes: Electricity and Electromagnetism – Electric Displacement
Dielectric may not be neutral even when unpolarised. If the
dielectric carries a charge density
of
free charges representing a net surplus or deficit of electrons in
the atoms of the dielectric and
is
the charge density due to the polarizing effect of an electric field
then the total charge density is given by
The macroscopic electric field
is
related to the total charge density, and in the presence of matter
Gauss's Law becomes
We can rearrange this expression to give
If
we define
then
this equation becomes
is
a new vector field, called the electric displacement. Since
we
can write
The last equation is really Gauss's Law, apart from a constant factor, modified to include polarization charges. This can be further illustrated using the integral form of Gauss's Law:
which becomes
on
substituting (1).
has
no clear meaning, but is useful because it makes many problems very
easy to solve. It has the property that the normal component ofat
a dielectric boundary is continuous, as illustrated in the diagram
below.
so