Energy conservation: electromagnetic wave in matter

  • #1
happyparticle
360
19
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.
 

Answers and Replies

Suggested for: Energy conservation: electromagnetic wave in matter

Replies
1
Views
456
Replies
6
Views
972
Replies
8
Views
2K
Replies
2
Views
818
Replies
3
Views
644
Replies
6
Views
602
Replies
7
Views
644
Replies
5
Views
541
Top