- #1

happyparticle

- 405

- 20

- 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.

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.