Electrostatic Fields in Matter

This could all get confusing!Remember• ɛ will be a very small number (since ɛ 0 = 8.84 × 10 −12 ).• Relative permittivity and dielectric constant are the same thing,with values usually between 1 and 100 (although 50,000 is possible).• χ e is one less than ɛ r . (So what is its value for free space?).8 Electric DisplacementThe differential form of Gauss’s law is:∇ · ⃗E = ρ ɛ 0(17)We now think of the charge as two parts: ρ = ρ f + ρ b .This means that ∇ · ⃗E = ρ f + ρ bɛ 0= ρ f − ∇ · ⃗Pɛ 0and this gives us ∇ · (ɛ 0⃗ E + ⃗ P ) = ρf (18)We now define a new quantity, the electric displacement vector⃗D, defined as⃗D = ɛ 0⃗ E + ⃗ P (19)(This also means that ⃗ D = ɛ ⃗ E) (20)We then have ∇ · ⃗D = ρ f (21)We can think of equation (21) as Gauss’s law in a dielectric.9