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Susceptibility, Permittivity and Dielectric Constant

### 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. X 