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