So according to my notes, the field inside a conductor is zero. But what, exactl

Question

So according to my notes, the field inside a conductor is zero. But what, exactly, is meant by inside?

I think we are in electrostatics for the purpose of this question.

The reason it is zero is because all the electrons are pushed to the edge of the conductor. So are these electrons assumed to be no longer inside the conductor (i.e. not strictly inside the conductor). If this is the case, does this mean that Gauss' Law applies to charges strictly inside a surface, and considers charges on the surface to be "outside" the surface, or more precisely, not strictly inside the surface?

Please let me know if I should write this more clearly.

physics

Explanation / Answer

Adding a bit of detail to Pygmalion's answer (at the risk of going down a rabbit hole):

1) The math definition of an "inside" point is that it is surrounded by other "inside" points, so the surface is not inside. (I like your "not strictly inside".) However, the surface charge electrons are still part of the conductor, and they can and do adjust so that the conductor surface is an equipotential (tangential electric field = 0). (In short, the conductor is composed of its inside plus its surface, and these two sets are disjoint.)

2) Gauss' law ??E=? applies everywhere: in its differential form, ??E=0 both inside the conductor (where E=0) and outside. On the surface the divergence is non-zero (in fact a nasty discontinuous delta-function-type thingey). More tractably, you can use the integral version and consider Gaussian pill-boxes with one side inside and the other outside. I am not responsible if you put a pill-box side precisely on the surface.

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