# Permittivity and Dielectric constant

We have mentioned about permittivity of free space and air but different medium have different absolute permittivities (E) and the Coulomb force F in the medium is given by, F_m=\frac1{4\pi\epsilon}\frac{q_1q_2}{r^2}

Whne they are placed in vaccum, F_0=\frac1{4\pi\epsilon_0}{q_1q_2}{r^2}

Dividing ,

\frac{F_0}{F_m}=\frac{\epsilon}{\epsilon_0}=\epsilon_r

or, \epsilon=\epsilon_0\epsilon_r or, \epsilon_0\kappa

Where E is called relative permittivity of the medium or also called dielectric constant of the medium and denoted by \kappa.
So, the dielectric constant or relative permittivity of a medium is the ratio of absolute permittivity of the medium to the absolute permittivity of free space. This can also be expressed in terms of ratio F0 / Fm It should be noted that although \epsilon_0 or \epsilon has unit C^2N^{-1} relative permittivity (\epsilon_r) and dielectric constant (\kappa) being ratio of two permittivities have no unit.
In general we have,

F=\frac1{4\pi\epsilon}{q_1q_2}{r^2}=\frac1{4\pi\epsilon_0\epsilon_r}.\frac{q_1q_2}{r^2}=\frac1{4\pi\epsilon_0\kappa}.\frac{q_1q_2}{r^2}