Christopher Crawford PHY

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Presentation transcript:

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

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

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

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

Comparison and contrast Electric flux Polarization chains

Field due to a polarization distribution

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

Example: polarized dielectric sphere