## Electric Displacement

Dielectric may not be neutral even when unpolarised. If the dielectric carries a charge densityof free charges representing a net surplus or deficit of electrons in the atoms of the dielectric andis the charge density due to the polarizing effect of an electric field then the total charge density is given by

The macroscopic electric fieldis related to the total charge density, and in the presence of matter Gauss's Law becomes

We can rearrange this expression to giveIf we definethen this equation becomes

is a new vector field, called the electric displacement. Sincewe 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 becomeson 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