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How do EM waves propagate inside waveguides made of conductors and how does current flow inside a conductor from a high voltage to a low voltage if the Electric field inside a perfect conductor is = 0 ? What is the driving force that causes the charges to move ?

Andrea Escalante
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    The electric field is zero if the charges do not move = electrostatics. When there is an electric field mobile charge carrier move. – Farcher Feb 02 '18 at 20:44
  • @Andrea Escalante - Could you, please, clarify whether you generally see the problem in conductors or whether your question is restricted to "perfect" conductors, like superconductors? – freecharly Feb 04 '18 at 02:40

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The electric field in a conductor is only zero in a static situation where the charges on the surface of the conductor can rearrange so that the electric field in the interior and tangentially at the surface become zero. This is a consequence of the high concentration of electrons and thus conductance of the metal. If you apply a voltage between two points of a conductor, there will be an electric field in the metal that produces a current. That's how all electric wires work.

Inside a hollow conductor (wave guide) EM waves can propagate while the boundary conditions to the metal produce surface currents in the metal.

freecharly
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  • The thing that keeps a simple circuit from being static is that the battery or other power supply keeps pushing on the circuit. The steady state will only be reached when the batter comes to chemical equilibrium. – dmckee --- ex-moderator kitten Feb 02 '18 at 21:21
  • "The electric field in a conductor is only zero in a static situation" - Doesn't the OP specifically mention the case that the conductor is a perfect conductor? A perfect conductor, by definition, has zero electric field inside. – Alfred Centauri Feb 03 '18 at 02:41
  • @AlfredCentauri - The OP only mentions a "conductor". For the electric field to be zero inside a conductor under "static conditions", you only need a conductor with sufficiently high conductivity $\sigma$ so that Maxwell's relaxation time $\tau=\frac {\epsilon}{\sigma}$ is short compared to the time scale of the experiment. – freecharly Feb 03 '18 at 02:58
  • I quote the OP: "how does current flow inside a conductor from a high voltage to a low voltage if the Electric field inside a perfect* conductor is = 0 "* – Alfred Centauri Feb 03 '18 at 03:07
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    @AlfredCentauri - You are right, there he put the adjective "perfect" in. However, it doesn't appear in the title of the question: How does current flow in a conductor if the electric field in a conductor is always 0? Obviously, he assumes that the electric field is always zero inside a conductor (not only in an electrostatic situation) and thus sees a contradiction to the case where a current flows when an external EMF is applied to a conductor. I think that a superconductor was not on his mind in this question. – freecharly Feb 03 '18 at 03:35
  • @AlfredCentauri I got curious about the link. I do not see anything inside it which contradicts the fact that current flows between two points kept at different potential in a conductor and whatever a superconductor is. All the discussion is relevant to the magnetic properties. If I had understood correctly. – Alchimista Feb 03 '18 at 22:00
  • "Obviously, he assumes that the electric field is always zero inside a conductor (not only in an electrostatic situation)" - freecharly, the mere fact that the OP mentions perfect conductor does not justify your conclusion at all (in my judgment). It seems to me that, given the mention of a perfect conductor, one might consider addressing the perfect conductor case in one's answer rather than glossing over it entirely. Perhaps I will do that should I find the inclination. – Alfred Centauri Feb 04 '18 at 00:39
  • @Alfred Centauri - It would only be an enrichment for everybody if you could spare the time to expound on the special case of a "perfect conductor". – freecharly Feb 04 '18 at 02:30
  • freecharly, not bad. Have you been practicing? – Alfred Centauri Feb 04 '18 at 05:20