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# §4.2–3 Displacement

§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

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## §4.2–3 Displacement

E N D

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

2. Outline • Review – E, P fieldsPolarization chains – polarization fluxE vs. P fields – comparison and contrastField of dipole distribution – bound charge density • Displacement field –DNew Gauss’ law – free charge ρf onlyOld flow equation – voltage stays the sameBoundary conditions – same prescription as beforeExamples – 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 betweenE-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: • 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

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