25.11: Susceptibility, Permittivity and Dielectric Constant

When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.

The polarization is proportional to the electric field for the linear dielectrics. This introduces a new proportionality constant called the electric susceptibility, a dimensionless quantity. The electric susceptibility is the tendency of any material to get polarized and is zero for free space.

These expressions can be solved to give the second proportionality constant, or the permittivity of the material.

The ratio between the material's permittivity and the free space's permeability gives the third proportionality constant, called the relative permittivity or the dielectric constant.

This is the same proportionality constant that gives the relationship between the capacitance of a capacitor with and without a dielectric medium. The value of the dielectric constant for free space is 1. The presence of a dielectric medium in a capacitor always increases the energy storage, thereby increasing the capacitance. Hence, the dielectric constant for any medium is always greater than 1.

In a polarized dielectric, the total charge density is the sum of the bound and free charge densities. Recalling the expression for bound charge density and rewriting the total charge density in terms of the total electric field gives the expression for electric displacement in terms of polarization.

In the case of linear dielectrics, the polarization is proportional to the total electric field. The constant of proportionality is called the electric susceptibility of the material, and the permittivity of free space makes the electric susceptibility dimensionless.

For an applied electric field, if electric susceptibility increases, the polarization increases.

Substituting the expression for polarization implies that the electric displacement is also proportional to the total electric field.

The new constant of proportionality is the permittivity of the material. The ratio of the material's permittivity to the permittivity of free space gives the relative permittivity, also known as the dielectric constant.

This estimates the ability to store charge for a given electric field. Materials with higher dielectric constants are used in capacitors to increase energy storage.