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

AI Thread Summary
In a Fabry-Perot interferometer, light reflects between two highly reflective mirrors, resulting in electric and magnetic fields that are 90 degrees out of phase, unlike in free space where they are in phase. The discussion revolves around using Poynting's theorem to explain this phase difference. Initial attempts included calculating the magnetic field from the electric field and using the Poynting vector, but the focus shifted to the law of conservation of electromagnetic energy. The realization was made that the argument could be better framed using energy conservation principles rather than directly through Poynting's theorem. Ultimately, the discussion highlights the complexity of demonstrating the phase relationship in this context.
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Homework Statement


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.


Homework Equations



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.
 
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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?
 
Thanks. I just realized 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.
 
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