Assume we have a plane of oscillating charges described by x=x(adsbygoogle = window.adsbygoogle || []).push({}); _{o}e^{i(omega)t}.

The total field is given by E=- [tex]\frac{\etaq}{2\epsilonc}[/tex]i[tex]\omega[/tex]x_{o}e^{i[tex]\omega[/tex](t-z/c)}. (Can someone point me to a website where I can learn to type in these formulas and not not have them suck?)

Ignore that weird looking x^o looking thingy. Those symbols on top of each other is supposed to be a fraction. i = sqrt(-1) as usual.

Can someone please explain the physical origin of the 90 degree phase shift from the oscillators. I.e. why there is an i in front of the term. If I put z=0 shouldn't I get radiation that is in phase with the oscillators? If a EM wave comes in from infinity and hits a plane of charges the charges oscillate and produce more EM waves. The new waves will not be 90 degrees out of phase with the incoming radiation, right? Is there a difference in these two situations?

Why I'm thinking about this:

The origin of the index of refraction seems to lay squarely on the relationship between the phases of the incoming radiation and the radiation produced by the charges that are oscillating because of the radiation. If it's not 90 degrees different then em waves won't be delayed in speed in a medium.

Reference: Volume 1 lecture 31, Feynman lectures on physics.

EDIT: Okay that above formula now looks even more screwed up. It's supposed to be this:

E = -eta*q/(2*epsilon_nought*c) * i omega x_o * exp(i omega (t-z/c))

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# Index of refraction and planes of oscillating charges

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