2.13 E FFECT OF D IELECTRIC ON C APACITANCE

. E FFECT OF D IELECTRIC ON C APACITANCE With the understanding of the behavior of dielectrics in an external field developed in Section . , let us see how the capacitance of a parallel plate capacitor is modified when a dielectric is present. As before, we have two large plates, each of area A , separated by a distance d . The charge on the plates is ± Q , corresponding to the charge density ± σ (with σ = Q / A ). When there is vacuum between the plates, E σ Factors affecting capacitance, capacitors in action Interactive Java tutorial
            and the potential difference V is V = E d The capacitance C in this case is Q A ( . ) Consider next a dielectric inserted between the plates fully occupying the intervening region. The dielectric is polarised by the field and, as explained in Section . , the effect is equivalent to two charged sheets (at the surfaces of the dielectric normal to the field) with surface charge densities σ p and – σ p . The electric field in the dielectric then corresponds to the case when the net surface charge density on the plates is ±( σ – σ p ). That is, P E σ σ ( . ) so that the potential difference across the plates is P E d σ σ ( . ) For linear dielectrics, we expect σ p to be proportional to E , i.e., to σ . Thus, ( σ – σ p ) is proportional to σ and we can write P K σ σ σ ( . ) where K is a constant characteristic of the dielectric. Clearly, K > . We then have Qd K A K σ ( . ) The capacitance C, with dielectric between the plates, is then KA Q ( . ) The product ε K is called the permittivity of the medium and is denoted by ε ε = ε K ( . ) For vacuum K = and ε = ε ; ε is called the permittivity of the vacuum . The dimensionless ratio K ( . ) is called the dielectric constant of the substance. As remarked before, from Eq. ( . ), it is clear that K is greater than . From Eqs. ( . ) and ( . ) K ( . ) Thus, the dielectric constant of a substance is the factor (> ) by which the capacitance increases from its vacuum value, when the dielectric is inserted fully between the plates of a capacitor. Though we arrived at