Static dielectric constant

Definition: The ratio of the capacitance of a given capacitor (with the material filling the entire space between its plates) to the capacitance of the same capacitor in vacuum is called static dielectric constant or relative permittivity of the material.

A dielectric is characterized by its dielectric constant which is also called relative permittivity.

Derivation:

When a voltage V is applied across parallel plates of capacitor, let the charges on one plate be +q and on other be –q. The capacitance C is related to the quantity of charge stored on either plate q by relation

C = q/V

Now consider a parallel plate capacitor with a vacuum in the region between the plates.

So the capacitance for  the parallel plate capacitor is

C₀ =  ε₀A/d

Where A represents the area of the plates and d is the distance between them.

If a dielectric material is inserted into the region within the plates, then

C = εA/d

Then the static dielectric constant will be

ε_r = C/C₀

putting above two equations, we get

ε_r = ε/ ε₀

It is a dimensionless quantity and it is independent of the size or shape of the dielectrics. For dielectrics ε_r > 1.