# Wave in a conductor

#### stunner5000pt

1. Homework Statement
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. Homework 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??

Related Advanced Physics Homework Help News on Phys.org