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Electric Displacement and Dielectric Materials in Physics

Explore displacement fields, constitutive equations, dielectric constants, polarization, and more in this comprehensive guide to electric properties in materials. Learn through examples and detailed explanations.

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Electric Displacement and Dielectric Materials in Physics

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

  2. Outline • Review – D=ε0E+PNew Gauss’ law – displacement fieldboundary conditions – obtained as usual • Constitutive equation –ε = ε0εr = ε0(1+χe)Electric susceptibility – P vs E, compare: polarizabilityDielectric constant – amplification of free charge[relative] permittivity – D vs E • Examplesparallel plate capacitorpolarized sphere dielectric sphere in an external field

  3. New Gauss’ (flux) law: • MACROSCOPIC formulation • 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. Polarizability vs. Susceptibility • Polarizability • Dipole moment of single atom in an electric field • Susceptibility • Polarization [density] of a material in an electric field • Relation between the two • Clausius-Mossotti relationship

  5. Dielectric material properties In general the polarization is an arbitrary function of: • Electric field, position(wavelength), time(frequency), temperature, … “Electrets” even have polarization independent of E However most materials satisfy the following properties which makes it much easier to calculate the fields: • Linear– χe independent of magnitude of E • Polarization proportional to electric field • Isotropic– χe independent of direction of E • Polarization in the same direction as electric field • Homogeneous– χe independent of position • Material doesn’t change from place to place

  6. Permittivity: constitutive equation • Link between D and E in Maxwell’s equations • Susceptibility • Relative permittivity (dielectric constant) • Permittivity of free space [vacuum] • Absolute permittivity • Relations between constants • Permittivity reflects the same material propertiesas susceptibility: linear, isotropic, homogeneous • In general it is a tensor (matrix) function ε(E,r,ω,…)

  7. Macroscopic potential formulation • Poisson’s equation  Laplace’s equation • Continuity boundary conditions

  8. Example: Parallel plates w/dielectric

  9. Example: Polarized dielectric

  10. Example: dielectric sphere in external E

  11. Example: dielectric sphere in external E

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