Solving Plane Wave Equation: Ex, Ey & Maxwell's Wave Equation

[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!

 

[quantumdude]

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?

 

[mycroft]

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

 

[Galileo]

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

 

[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...

 

[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).

 

[mycroft]

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