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Explain this statement: “In a static situation, the electric field at the surface of a conductor can have no component parallel to the surface because this would violate the condition that the charges on the surface are at rest.” Would this same statement be valid for the electric field at the surface of an insulator?

I think it'd be valid, because electric field parallel to the surface might cause surface currents. However, inside an insulator we can't use the fact that field inside is zero; which is key to proving the expression for electrostatic pressure in which we safely assume that field is only normal to the surface of the conductor

I'm slightly confused, does this have something to do with polarisation? Please explain.

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You are right, the essential reason because you can find a nonzero parallel components of the electric field on the surface, is that you will have a polarization charge. It is given by the divergence of the Polarization field. In a conductor, the field must "touch" its surface perpendicularly, but in an insulator it is no necessary. This is because the molecules of the media will polarize, this is, the positive and negative charges will "separate" without breaking the molecule. There is no reason to restrict the shape of the field at the surface. More else, it is a condition that the parallel and normal components of the electric field must be continuous. I mean, the more general case for the insulator is in which you have both components, but you can always have the particular case in which the parallel component vanishes.

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  • $\begingroup$ If there is indeed a parallel component as you say, won't it lead to surface currents on the insulator? That is something we do not desire as the problem concerns electrostatics $\endgroup$ Dec 8 '17 at 7:43
  • $\begingroup$ @user28968 Insulators don't have currents just because there's an electric field. That's what makes them different from conductors. $\endgroup$
    – Chris
    Dec 8 '17 at 7:47
  • $\begingroup$ Could you please elaborate a bit on that? $\endgroup$ Dec 8 '17 at 7:47
  • $\begingroup$ @user28968 I didn't say that a parallel component is needed, I said that the continuity of the parallel component is needed. That component vanishes without problem. For example if the field is perpendicular to a face of an insulator cube, the only component that you can find at the surface is the normal. As you can see the parallel component vanishes. $\endgroup$
    – Amadeus
    Dec 8 '17 at 7:52
  • $\begingroup$ So in general even for insulators there is no parallel component of electric field? $\endgroup$ Dec 8 '17 at 7:53

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