In electrostatics, inside a metal there are no charges (electric field equals zero, thus one can find the potential using Laplace equation (together with the proper boundary conditions). Is it still true when I apply current through the metal? Are the charges still moving only at the surface (in order to keep zero electric field insode?) or do I need now to solve the poisson equation instead (or some other equations) and to determine somehow the charges?
Do you remember the law of Ohm, I=V/R ?
Do you remember that the resistance R decreases when the transversal section through the conductor increases, R ~ 1/S?
If the charges would flow only through the external surface of a conductor, the perimeter of the transversal section would matter, not the surface.
Now, the situation that in a metal the charges are spread only on the external surface, is correct only in an equilibrium state. If, for instance, there are electrical discharges in the close vicinity of the metal, transient currents may cross the metal.
Band theory is good, to explain. Metals are having no forbidden band between valence and conduction band, semiconductor with 1 to 2 ev forbidden band and insulating material with higher than 2ev. Conduction in material could be carried out by exciting(applying potential(voltage)) electrons in outer most orbit(valance band). For semiconductor, measurable(0.3 to0.7V), and for insulator considerable, potential different is needed and almost nil(depending on resistivity, R=(resistivity)(length)/(cross sec. area) for conducting material......
Dear colleague,
inside of metal conductors is free of negative charges just in the statical case when all the free electrons are gathered on the conductor surface.
For the case of direct current we have uniform current density, i.e. uniform distribution of electrons (charges) in conductor's cross-section. For the case of alternating current the distribution of electrons (charges) is determined by skin-effect. Thus, in the presence of a voltage source compensating for Joule losses in the directed motion of electrons, charges inside the conductor will exist.
You may see the corresponding chapters in the courses of Landau or Feynman.
Regards
The charges in the metal is neutral. The metal has an equal number of negative and positive. When current flows on it, the charges move because of the flow of electron. Remember, opposite charges attract and similar charges repel.
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