Electrostatic Fields in Matter

12 SummaryThe state of a dielectric is characterised by three vector quantities:The electric field ⃗ EThe polarisation ⃗ P (= total dipole moment per unit volume).The displacement ⃗ D defined by ⃗ D = ɛ 0⃗ E + ⃗ P .There are relations between these quantities.⃗D = ɛ ⃗ E = ɛ r ɛ 0⃗ E and ⃗ P = ɛ0 χ e⃗ EThe polarisation gives rise to bound charges:σ b = ⃗ P · ˆn and ρ b = −∇ · ⃗PThe displacement D ⃗ is determined by the free charges.∮∇ · ⃗D = ρ f (in integral form this is ⃗D · ⃗da = Q fenc )The field E ⃗ is determined by ALL the charges (i.e.bound)free plusAt a dielectric boundary the normal component of ⃗ D and thetangential component of ⃗ E are continuous.The energy density in a polarised dielectric is 1 2 ⃗ D · ⃗E.17