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Conceptual question on field/displacement

  1. Oct 12, 2011 #1
    I have a very basic problem in understanding the relationship between electric field and displacement. If a field is applied to a dielectric, it is clear that this will cause the material to polarize, and one can define the permittivity of the material to quantify the size of this effect. Since we can write [itex]D=\epsilon E[/itex], we can also define the inverse permittivity [itex]E=\kappa D[/itex]. But conceptually, I can't make sense of the displacement as the independent variable. How does a polarization give rise to a macroscopic field in the same direction? If anything, a polarization seems associated with a field in the opposite direction (by imagining the situation in the center of a dipole), although I know that macroscopic E&M says nothing about these microscopic fields.

    If I think about the case of stress and strain, I can easily imagine how either one gives rise to the other. Where is my problem?
  2. jcsd
  3. Oct 12, 2011 #2
    Ok, the answer is just to take the superposition of the fields from many dipoles. Everything should cancel except the field parallel to the polarization.
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