1. Christopher Crawford PHY 311 2014-03-07
§4.2–3 Displacement
Christopher Crawford
PHY 311

2. Outline
Review – D=ε0E+P New Gauss’ law – displacement field boundary conditions – obtained as usual
Consititutive equation – ε = ε0εr = ε0(1+χe) Electric susceptibility – P vs E, compare: polarizability Dielectric constant – amplification of free charge [relative] permittivity – D vs E
Examples parallel plate capacitor polarized sphere – HW 7 dielectric sphere in an external field

3. 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

4. Summary

5. Constitutive relation
Connects E and D so we can apply the Helmholtz theorem to the mixed Maxwell equations (if E and D !)

6. Example: Parallel plates w/dielectric

7. Example: Polarized dielectric

8. Example: dielectric sphere in external E