4 2 3 Displacement Christopher Crawford PHY 416

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§ 4. 2– 3 Displacement 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.

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 2

Review: Polarization chain • Dipole density P = dp/dτ = dq/da = σ (l=1)

Review: Polarization chain • Dipole density P = dp/dτ = dq/da = σ (l=1) – Versus charge density – Units: C/m 2 ρ = dq/dτ (l=0) • Dipole chain – polarization flux dΦP = P da – Gauss-type law – Units: C • Back-field -ε 0 Eb – Charge screening – Geometry-dependent – Example: sphere • Displacement flux D – Between free change – Continuity between E-flux and P-chains 3

Polarization density • Recall: field of spherical dipole distribution: dipole density – Same problem:

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 4

Comparison and contrast Electric flux Polarization chains 5

Comparison and contrast Electric flux Polarization chains 5

Field due to a polarization distribution 6

Field due to a polarization distribution 6

New Gauss’ (flux) law: • New field: D = ε 0 E + P

New Gauss’ (flux) law: • New field: D = ε 0 E + P (electric displacement) • Derived from E, P Gauss’ laws • Corresponding boundary condition Old (flow) law: • E field still responsible force -> potential energy • V is still defined in terms of E • Boundary conditions: potential still continuous 7

Example: polarized dielectric sphere 8

Example: polarized dielectric sphere 8