This site says that if the field at the surface at the conductor has a parallel component, then the surface charge will move, which is impossible if the conductor is at equilibrium.
But I learnt that positive ions can't move in a conductor, only electrons can.
I asked my prof and he said that if the field has a parallel component, the parallel components will cause the electrons to move, which will result in movement of positive charge.
1) But an electric field is a vector field, so each point has a different vector associated with it. So what would happen if the vector field had parallel components where positive ions are located but is completely perpendicular where electrons are located (look at the above image)? Isn't this a scenario where the entire field isn't perpendicular but there is no movement?
2) If a perpendicular field is acting on the electron, what's stopping it from leaving the conductor? Normally, if an electron tries to leave because of a field, the positive charges redistribute themselves to cancel out the field, preventing it from leaving. But if the field isn't cancelled out, theres nothing holding the electron back is there?