# Plane wave solution

1. Dec 12, 2005

### mycroft

I'm hoping that someone can descripe to me the steps involved in showing
E = (Ex,Ey,0),where Ex=f(z-ct)+g(z+ct) and Ey=F(z-ct)+G(z+ct),is a plane wave solution to the wave equation
(∇^2)E-[1/(c^2)](∂^2)E/∂(t^2) = 0
maxwell's wave equation if it's impossible to reat that!

2. Dec 12, 2005

### Tom Mattson

Staff Emeritus
What exactly are you trying to do? Are you trying to derive the general solution or are you trying to verify that your stated general solution satisfies the EM wave equation?

3. Dec 13, 2005

### mycroft

the latter, show that it is a plane wave solution for the wave equation, not derive a general solution. Thanks

4. Dec 13, 2005

### Galileo

In that case, just plug in the given field E in the wave equation and see if it satisfies it.

5. Dec 13, 2005

### mycroft

but will that prove it's a plane wave solution or simply that it's a solution? It was an exam question and that seems a little easy, but perhaps I'm just making things difficult for myself...

6. Dec 13, 2005

### HallsofIvy

Any solution to that equation is a wave function. It is a plane[\b] wave simply because it depends only on z (not x or y).

7. Dec 13, 2005

### mycroft

thanks, ment to say 'or simply that it's a wave solution?', but yea I see now!