# Electromagnetic wave

1. Oct 19, 2011

### 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.

2. Oct 19, 2011

### 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.

3. Oct 19, 2011

### clem

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.

4. Oct 21, 2011

### Mppl

Well what I mean is for example if the reflected wave was Er=-Eo cos(wt)*e^23x wich 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

5. Oct 21, 2011

### clem

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

6. Oct 23, 2011

### Mppl

Well but that doesnt 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 lets me with a lot of possibilities...so I dont really know how the reflected wave is right? I just know it has to obbey the conditions I mentioned right?

7. Oct 23, 2011

### kimkimkim

The magnetic flux through one face of a cube is +0.120 Wb. (a) What must the total
magnetic flux through the other five faces of the cube be? (b) Why didnâ€™t you need to
know the dimensions of the cube in order to answer part (a).

Lightning bolt can carry current up to approximately 20kA. We can model such a current as the equivalent of a very long, straight wire. (a) If you were unfortunate enough to be 5.0m away from such a lightning bolt, how large a magnetic field would you experience? (b) How does this field compare to one you would experience by being 5.0cm from a long, straight household current of 10A?

A metal ring 4.50 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.250T/s. (a) What is the magnitude of the electric field induced in the ring? (b) In which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?