I have some doubts about the electric field inside an ideal conductor (let's call it E). Precisely, I have read two different descriptions
1) On physics books I read that the electric field inside in a conductor in electrostatic equilibrium is equal to 0. The physical reason of this is the fact that all charges, at equilibrium, are distributed in the external surface of the conductor since only this distribution can reduce their repulsion forces. A mathematical view of this is given by the equation J = sigma * E. In fact, since sigma = infinite and J = 0 (since equilibrium means that charge do not move), necessarily we must have E = 0.
According to this explanation, E = 0 only in electrostatic equilibrium.
2) On Electromagnetic Fields books I read an explanation which is similar, but not identical. I read that, since J must have a finite value, and J = sigma * E and sigma = infinite, we get E = 0.
According to this explanation, there is not any mention of electrostatic equilibrium. It seems that inside a conductor in any condition we have E = 0. Also if there is a voltage source applied on it or something similar.
Now I have two questions:
Which is the correct description?
It is known that a metal is able to reflect EM waves. Is it due to the fact that E = 0 in its inner points?