Wave guides and induced free charges and currents

Question

Consider electromagnetic waves confined to the interior of a hollow pipe or waveguide. Assuming that the waveguide is a perfect conductor so that electric field and magnetic field inside the material itself is zero and the boundary conditions at the inner wall says that the tangential component of electric field and the perpendicular component of the magnetic field are zero.

Free charges and currents will be induced on the surface in such a way as to enforce these constraints. My doubt is how can there be any surface current on the equipotential surface of a conductor whose conductivity is infinite. Griffith tackles this by saying even though there can be no surface currents in an ohmic conductor with finite conductivity, there can be volume currents extending roughly to the skin depth. As the conductivity increases, they are squeezed into a thinner and thinner layer and in the limit of a perfect conductor, they become true surface currents. I don't understand what he meant by this.

Answer 1

I am beginning to conclude that there is a combination of free charge and polarization charge such that tangential $E$ components are zero. There is a $D$ field from free charge and somehow also $P$ charge. I read statements that there are $E$ fields in a conductor under non static nonequilibrium, like current flowing in a wire. Isn’t a waveguide always in such a state? David

Answer 2

Or.. there is no cause and effect. The currents in the waveguide walls are those required to make $E_\text{tangential}$ zero. $E_\text{tangential}$ does not cause the current. In a sense $E_\text{tangential} = 0$ causes the currents. $dE/dt$ and $dB/dt$ happen together. They do not cause each other might follow.

Answer 3

My understanding is that the boundary conditions are primarily enforced by a reflected and transmitted wave so that the sum cancels out the incident wave fields at the surface of the conductor. Equations show that a transmitted "evanescent" wave can indeed penetrate the material, but its amplitude exponentially decays hence the "skin effect". In the limit of an ideal conductor the depth of penetration goes to 0. Now the microscopic interpretation is that electrons in the skin depth are moved by the incident field and create in return a reflected wave cancelling out the incident field.