# Wave in a conductor

1. Jan 4, 2007

### stunner5000pt

1. The problem statement, all variables and given/known data
Wangsness exercise 24-12
A plane wave travels in the postiive z direction in a conductor with real conductivity.

a) Find the instantaeous and time average power loss per unit volume due to resisitive heating for any z

b) Find the total power loss per unit area between z= 0- and z approaching infinity

c) Find the time average Poynting vector at any z

2. Relevant equations
Poynting vector is given by
$$\vec{S} = \frac{1}{2} \Re (\vec{E} \times \vec{H*})$$
For a conducting medium

$$E = E_{0a} e^{-\beta z} e^{i(az-\omega t+ \upsilon}$$
$$B= \frac{|k|}{\omega} \hat{z} \times E_{0a} e^{-\beta z} \cos (\alpha z-\omega t + \upsilon + \Omega)$$

3. The attempt at a solution
Im a little stumped here

per unit area it would be the $$<S> \bullet \vec{n}$$

but per unit volume??

The instantaneous would simply the derivative of the prveious quantity with respect to time.. right/

FOr total power loss we need to integrate the power oss per unit volume over hte whole volume. What is the shape of the condutor though??