Understanding Electromagnetic Wave at a Perfect Conducting Wall

[Mppl]

I am having a problem understanding a thing in a electrodynamics problem.
Imagine we have a wall at x=0 made of a perfect conducting material. Imagine now we have an electromagnetic wave traveling perpendicular to the wall with the electric field polarized in the y direction and the magnetic field polarized in the z direction. The wave is an electromagnetic plane wave such that E=Eo cos(wt-kx). My question is when the wave hits the wall, the electrical field must be continuous at the interface between the air and the wall since it is zero on the wall it must be zero at x=0 and that gives us the condition that the reflected wave in th eplane x=0 must be Er=Eor.cos(-wt) but as far as I know there is no reason to guess what will be the dependence on x, I mean why should I assume it will be a plane wave like the incident one? Do I have any reason to believe that?

Thank you for your time.

 

[chrisbaird]

You seem to have several jumbled thoughts here. Let's see if we can straighten them out. First, for a perfect conductor (which is unphysical but a good approximation), there is zero electric field inside the conductor, and right at the surface of the conductor but outside it, the tangential components of the electric field are zero, and the normal component of the electric field is typically non-zero. The standard infinite transverse em plane wave is really only a special case of em wave that exists in unbounded free space. Obviously, as the plane wave approaches the conductor, there is an interaction with the conductor (induced currents which re-radiate), so a simple transverse plane wave solution is not sufficient anymore. But you can show that the reflected wave off a flat perfect conductor will become a transverse plane wave again far from the conductor. The symmetry of the problem is what dictates this.

 

[Meir Achuz]

In order for E to be zero at x=0, the reflected wave must be the negative of the incident wave at every instant. This makes the reflected wave exactly the negative of the incident wave, but moving to the left.

 

[Mppl]

Well what I mean is for example if the reflected wave was Er=-Eo cos(wt)*e^23x which is indeed diffrent from a plane wave the continuity condition would still be valid so why not saying that that one is the reflected wave, I mean in what should I base the assumption that the reflected wave is still a plane wave? So chrisbaird the assumption that the reflected wave is a plane wave is An Aproximation?
Thank you for your help

 

[Meir Achuz]

The reflected wave has to satisfy the same wave equation as the incident wave.

 

[Mppl]

Well but that doesn't tell me much about the wave... Then the reflected wave just has to let the total field be zero at the interface and it has to satisfy the wave equation... And it let's me with a lot of possibilities...so I don't really know how the reflected wave is right? I just know it has to obbey the conditions I mentioned right?

 

[kimkimkim]

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