# Energy conservation: electromagnetic wave in matter

happyparticle
Homework Statement:
An electromagnetic wave passes through a material with conductivity ##\sigma##. The wave is attenuated, and the amplitude exponentially decreases with the distance traveled. Show that the total energy is conserved and what happen with the energy lost by the wave.
Relevant Equations:
$$u = u_e + e_m$$
$$\tilde{E} (z,t) = \hat{E}_0 e^{i(\tilde{k}z - \omega t)} \hat{x}$$
$$\tilde{B} (z,t) = \hat{E}_0 \frac{\tilde{k}}{\omega}e^{i(\tilde{k}z - \omega t)} \hat{y}$$
Hi,
I completely failed this homework. I mean I think I know what happen, but I don't know how to show it mathematically. The energy lost by the wave is used to oscillate the electrons inside the conductor. Thus, the electrons acts like some damped driven oscillators.
I guess I have to find ##e_m, u_e##, but I don't know with what to compare. That's pretty all I know.

Any help will me appreciate, thanks.