Everyone does know that the surface of a conductor is at equipotential during equilibrium.
I was reading Feynman's lectures where I found this (bold)line:
Suppose that we have a situation in which a total charge Q is placed on an arbitrary conductor. Now we will not be able to say exactly where the charges are. They will spread out in some way on the surface. How can we know how the charges have distributed themselves on the surface? They must distribute themselves so that the potential of the surface is constant. If the surface were not an equipotential, there would be an electric field inside the conductor, and the charges would keep moving until it became zero.
This is a much good reasoning for the surface to be an equipotential one; if there were any region to be in higher potential, charges would flow towards them to neutralize and again make the surface equipotential.
To understand his explanation, I thought of a positively charged surface that is not in equipotential status; so there would be an electric field which would prompt the free electrons inside the conductor to go there & nullify the field to make the surface equipotential, right? But what about the positive charges that are now inside the conductor? Okay, they would by repulsion move towards the surface. But what is the GUARANTEE that they would form the equipotential surface? What really happens when they go on the surface that compels them to make an equipotential surface??
[After all, you can't say:" since you are studying electrostatics, there must be equipotential region on the surface no matter what happens; that's it"-this is what my school-teacher said when I asked him.]
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