Electrostatic Fields in Matter
Electrostatic Fields in Matter
Electrostatic Fields in Matter
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This could all get confus<strong>in</strong>g!Remember• ɛ will be a very small number (s<strong>in</strong>ce ɛ 0 = 8.84 × 10 −12 ).• Relative permittivity and dielectric constant are the same th<strong>in</strong>g,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 th<strong>in</strong>k 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 def<strong>in</strong>e a new quantity, the electric displacement vector⃗D, def<strong>in</strong>ed as⃗D = ɛ 0⃗ E + ⃗ P (19)(This also means that ⃗ D = ɛ ⃗ E) (20)We then have ∇ · ⃗D = ρ f (21)We can th<strong>in</strong>k of equation (21) as Gauss’s law <strong>in</strong> a dielectric.9