Effect of a Dielectric

Relations obtained earlier for the capacitances hold only when the plates are in vacuum air. In actual capacitors, the regions between its two conductors are filled with an insulator (or dielectric) say mica or oil. Faraday found that the capacitance of a capacitor increases if a dielectric is placed between the plates.

It C is the capacitance of a capacitor with vacuum and C’ is its capacitance with dielectric, then the ratio C’/C = ε, is called the relative permittivity of the medium.
     C’ = ε, C

The capacitance of a capacitor with a medium of relative permittivity ε, between its two conductors is ε, times the value given by the above formulae. Therefore
   
     Cd = 4πε_rε_oab        for a sphereical capacitor (outer sphere earthed)
                 (b – a)
        = 2πε_oε_rl        for cylindrical capacitor
           loge (b/a)
       = ε_rε_oA        for parallel plate capacitor
             d