Susceptibility, Permittivity and Dielectric Constant

Electric susceptibility is a dimensionless constant that describes a material's tendency to become polarized in an external electric field. For linear dielectrics, polarization is directly proportional to the applied electric field, with electric susceptibility as the constant of proportionality. Materials with higher electric susceptibility exhibit greater polarization for the same electric field strength.

Permittivity is the proportionality constant between electric displacement and the total electric field in a material. The dielectric constant, or relative permittivity, is the ratio of the material's permittivity to the permittivity of free space. The dielectric constant is always greater than 1 for any medium, while free space has a dielectric constant of exactly 1.

The dielectric constant estimates a material's ability to store charge for a given electric field. Materials with higher dielectric constants are used in capacitors to increase energy storage capacity. The presence of a dielectric medium in a capacitor always increases the energy storage, thereby increasing the capacitance compared to a capacitor with no dielectric.

In a polarized dielectric, the total charge density is the sum of bound charge density and free charge density. The bound charge density can be expressed in terms of polarization, while the total charge density can also be written in terms of the total electric field. This relationship leads to the expression for electric displacement in terms of polarization.

Electric susceptibility is made dimensionless by dividing the proportionality constant between polarization and electric field by the permittivity of free space. This normalization allows for consistent comparison of material polarization tendencies across different systems. The dimensionless nature makes electric susceptibility a pure material property independent of unit systems.

When electric susceptibility increases for a given applied electric field, the polarization increases proportionally. Since electric displacement is also proportional to the total electric field through the material's permittivity, an increase in electric susceptibility results in increased electric displacement. This demonstrates how material properties directly affect the electric field behavior within dielectrics.

The dielectric constant is the same proportionality constant that relates the capacitance of a capacitor with a dielectric medium to its capacitance without one. A capacitor with a dielectric always has greater capacitance than the same capacitor with vacuum or air between its plates. The ratio of these capacitances equals the dielectric constant of the material used.