1. Christopher Crawford PHY 416 2014-12-01
§4.2–3 Displacement
Christopher Crawford
PHY 416

2. Outline
Review – E, P fields Polarization chains – polarization flux E vs. P fields – comparison and contrast Field of dipole distribution – bound charge density
Displacement field – D New Gauss’ law – free charge ρf only Old flow equation – voltage stays the same Boundary conditions – same prescription as before Examples – dielectric sphere with constant P – polarized sphere in electric field Eext

3. Review: Polarization chain
Dipole density P = dp/dτ = dq/da = σ (l=1)
Versus charge density ρ = dq/dτ (l=0)
Units: C/m2
Dipole chain – polarization flux dΦP = P  da
Gauss-type law
Units: C
Back-field -ε0Eb
Charge screening
Geometry-dependent
Example: sphere
Displacement flux D
Between free change
Continuity between E-flux and P-chains

4. Polarization density
Recall: field of spherical dipole distribution: dipole density
Same problem: pepper dipole all throughout sphere!
Dipole density is naturally treated as a flux

5. Comparison and contrast
Electric flux
Polarization chains

6. Field due to a polarization distribution

7. New Gauss’ (flux) law: Old (flow) law:
New field: D = ε0E + P (electric displacement)
Derived from E, P Gauss’ laws
Corresponding boundary condition
Old (flow) law:
E field still responsible for force -> potential energy
V is still defined in terms of E
Boundary conditions: potential still continuous

8. Example: polarized dielectric sphere