# Use Poynting's Theorem to show E and B fields are out of phase

1. May 9, 2009

### freesnow

1. The problem statement, all variables and given/known data
In a Fabry-perot interferometer, light is reflected back and forth between 2 highly reflecting parallel mirrors, with a nonconducting medium inside. The waves of magnetic and electric field are 90o out of phase, unlike the case of a wave in free space where they in phase. Develop an argument using Poynting's theorem for why this should be so.

2. Relevant equations

3. The attempt at a solution
I've thought of using E to calculate H and then say that they're out of phase, but then this method isn't based on Poynting's theorem.
Then I've thought of using the eq.:
E = E0exp((-kapper)z+i(kz-wt))
B = B0exp((-kapper)z+i(kz-wt+theta))
to calculate the Poynting vector, S = 1/mu * (E x B), then somehow show that theta is 90o, but then I don't really know how to do it.

2. May 9, 2009

### diazona

I was under the impression that Poynting's theorem was the law of conservation of electromagnetic energy,
$$\vec{J}\cdot\vec{E} + \frac{1}{2}\frac{\partial}{\partial t}\left(\epsilon_0 E^2 + \frac{1}{\mu_0}B^2\right) + \frac{1}{\mu_0}\vec{\nabla}\cdot(\vec{E}\times\vec{B}) = 0$$

Does that give you any ideas?

3. May 11, 2009

### freesnow

Thanks. I just realised that I was in the wrong direction from the start, I've just now finished the argument using the law of conservation of electromagnetic energy instead.