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The Permittivity

The Permittivity. LL 8 Section 7. Maxwell’s equations for a dielectric. Four equations for 6 unknowns Can’t be solved We need a relation between induction D and field E . External field is usually small compared to the internal molecular fields. Polarization is due to external field.

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The Permittivity

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  1. The Permittivity LL 8 Section 7

  2. Maxwell’s equations for a dielectric • Four equations for 6 unknowns • Can’t be solved • We need a relation between induction D and field E.

  3. External field is usually small compared to the internal molecular fields • Polarization is due to external field

  4. Isotropic dielectric • D||E • D= e E • e = permittivity (or dielectric constant) • Depends on substance and thermodynamic state

  5. Polarization is also proportional to the field For a rarified medium (gas), k is proportional to density e>1 k>0

  6. Boundary conditions at surface between two dielectrics

  7. Spatially uniform dielectrics can have no volume charge density

  8. Volume charge density of inhomogeneous dielectric

  9. What equation is satisfied by the potential in a dielectric?

  10. Boundary conditions on the potential

  11. Piecewise homogeneous dielectric (e.g. multilayer optical films)

  12. Conductor surrounded by homogeneous isotropic dielectric

  13. If the potential of the conductor is maintained as it is placed inside dielectric • fV = fDeD = eeV • Field is unchanged but the charge is increased by the factor e. • The extra charge is put there by the battery. + +++ v v e

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