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www.GOALias.blogspot.comPhysicsand the potential difference V 0isV 0= E 0dThe capacitance C 0in this case isCQ A= = εd(2.46)0 0V0Consider next a dielectric inserted between the plates fully occupyingthe intervening region. The dielectric is polarised by the field and, asexplained in Section 2.10, the effect is equivalent to two charged sheets(at the surfaces of the dielectric normal to the field) with surface chargedensities σ pand –σ p. The electric field in the dielectric then correspondsto the case when the net surface charge density on the plates is ±(σ – σ p).That is,E σ − σ P= (2.47)ε0so that the potential difference across the plates isσ − σ= = (2.48)PV Ed dε0For linear dielectrics, we expect σ pto be proportional to E 0, i.e., to σ.Thus, (σ – σ p) is proportional to σ and we can writeσσ − σP= (2.49)Kwhere K is a constant characteristic of the dielectric. Clearly, K > 1. Wethen haved QdV = σε0K = Aε0K(2.50)The capacitance C, with dielectric between the plates, is thenQ ε KA 0C = = (2.51)V d76The product ε 0K is called the permittivity of the medium and isdenoted by εε = ε 0K (2.52)For vacuum K = 1 and ε = ε 0; ε 0is called the permittivity of the vacuum.The dimensionless ratioεK = (2.53)ε0is called the dielectric constant of the substance. As remarked before,from Eq. (2.49), it is clear that K is greater than 1. From Eqs. (2.46) and(2. 51)CK = C(2.54)0Thus, the dielectric constant of a substance is the factor (>1) by whichthe capacitance increases from its vacuum value, when the dielectric isinserted fully between the plates of a capacitor. Though we arrived at