Electrostatic Fields in Matter
Electrostatic Fields in Matter
Electrostatic Fields in Matter
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11 Energy <strong>in</strong> a Dielectric.The follow<strong>in</strong>g represents a simple derivation, although the result obta<strong>in</strong>edis quite general.We know that the energy stored <strong>in</strong> 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 <strong>in</strong> the capacitor is thus:U = 1 2 Kɛ 0E 2 = 1 2 ɛE2 = 1 2 ⃗ D · ⃗E (32)The energy stored <strong>in</strong> a dielectric, for a given field, is K times largerthen the energy stored <strong>in</strong> a vacuum. The extra energy comes fromthe polarization of the dielectric.16