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I know that for an air-filled parallel plate capacitor with applied voltage, there exist the relation $E=V/d$, where d is the separation distance. Does this relation still hold when the parallel plate capacitor is filled with a dielectric material? (Say, a dielectric material is anisotropic and is placed at 45 degree angle?)

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  • $\begingroup$ What do you mean by saying the dielectric is placed at an angle? $\endgroup$ Commented Oct 17, 2018 at 22:36
  • $\begingroup$ I was talking about the dielectric orientation angle. The capacitor is filled with dielectric, but the orientation of the dielectric tensor is not the same as the capacitor plates. $\endgroup$
    – Alalalala
    Commented Oct 17, 2018 at 22:41

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Does this relation still hold when the parallel plate capacitor is filled with a dielectric material?

Yes, this relationship is true, as long as the electric field could be considered constant, which is approximately the case for a parallel plate capacitor, as long as the dielectric between the plates is uniform.

If the dielectric was not uniform, the formula would be still be applicable, but, since the electric field would not be constant, it would yield the average field.

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  • $\begingroup$ Doesn't the E field become weaker when it is in the dielectric? $\endgroup$
    – Alalalala
    Commented Oct 18, 2018 at 0:54
  • $\begingroup$ @Alalalala If an air capacitor is charged to a certain voltage and then a dielectric is introduced into the gap, while the charge on the plates remains the same, both the strength of the electric field and the voltage will decrease, proportionally. $\endgroup$
    – V.F.
    Commented Oct 18, 2018 at 1:03
  • $\begingroup$ @Alalalala The electric field does not get weaker if the capacitor plates are kept at the same potential difference. What happens is that more charge is stored on the plates and the D-field increases. $\endgroup$
    – ProfRob
    Commented Oct 18, 2018 at 6:35
  • $\begingroup$ @Alalalala That is correct as well. Either way, $E=\frac V d$ relationship holds, because it follows from the basic definitions of electric field and voltage. $\endgroup$
    – V.F.
    Commented Oct 18, 2018 at 12:32
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You can't calculate electric field in a parallel plate capacitor with the relation E=V/d if dielectric has orientation angle. For static electric fields and conductors the electric field must be perpendicular to the surface of any conductor.

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