Electrostatic Fields in Matter

11 Energy in a Dielectric.The following represents a simple derivation, although the result obtainedis quite general.We know that the energy stored in a charged capacitor isW = 1 2 CV 2 (30)For a parallel plate capacitor C = Kɛ o A/d and V = Ed.Thus W = 1 2 Kɛ oAdE 2 (31)The energy per unit volume stored in the capacitor is thus:U = 1 2 Kɛ 0E 2 = 1 2 ɛE2 = 1 2 ⃗ D · ⃗E (32)The energy stored in a dielectric, for a given field, is K times largerthen the energy stored in a vacuum. The extra energy comes fromthe polarization of the dielectric.16