Dielectrics

Insulators, known as dielectrics in the context of electromagnetic, behave the "opposite" way of conductors. That is, the electrons are tightly bound to the atom and cannot move over significant distances under the influence of an external electric field.

When we apply an external electric field to an insulator, the electrons in the atom still feel the force and are displaced towards one side. In this state, the insulator is said to be "polarized".

Polarization Vector

Polarization of dielectrics occurs due to the displacement of one or more electrons per atom over a subatomic distance. This induces a charge on the surface of the material.

This dipole is characterized by a dipole moment, , given as , where Q is the value of the charge and is the distance between the and charges.

where is the number of atoms per unit value, and represents the vector sum of the induced dipole moments in a very small volume.

The polarization vector, , is a function of the volume density of the dipole moment.

With this, we can calculate the induced charge densities on the surface and volume of the dielectric:

where is the normal unit vector to the surface pointing out of the dielectric.

Electric Flux Density and the Dielectric Constant

Gauss's law will be affected by dielectrics. First, we define the electric displacement field as:

And then we have to redefine Gauss Law for dielectrics:

Since many dielectrics are highly linear, we can assume is proportional to . We define as the electric susceptibility factor.

Then we can redefine the electric displacement vector: