Metallic Mirrors: E Field, Power Loss, Energy Loss at Optical Freqs

[sachi]

We have to show that in a conductor an E field can exist but it decays according to the skin depth as follows:

Ex = Eo*exp[i(z/d - wt)exp(-z/d)

where d is the skin depth, w is the frequency etc.
I can answer this part. We are also asked to show that the power lost per unit area in this conductor is (H^2)/(2*sigma*d) where sigma is the conductivity. I got this answer by finding the H field, then taking the real parts of H and E, and finding the poynting vector and finding its average. I also set z=0.

I'm very confused about the physical results here, and am not too sure what approximations have been made. The result seems to indicate a constant rate of power dissipation in the conductor (i.e the energy just keeps flowing through the conductor) which contradicts the idea that the wave in the conductor is attenuated (and therefore absorbed). Was I therefore wrong in setting z=0 and perhaps have said that the result is only valid for z is v. small (i.e our result gives us the power dissipated at the surface, but this quickly gets absorbed by the conductor after a short distance), but we can still simplify the algebra by setting z=0 in our Poynting integrals?

Last of all we are asked to find the fractional energy loss at optical frequencies. If I was right about the energy being continually transported through the conductor, then the fractional loss is just the power lost per unit area in the conductor divided by the power incident from the vacuum (this will just be 1/2 * (H^2) *Z , where Z is the impedance of free space).

thanks very much for your help

 

[Physics Monkey]

Remember that the electromagnetic wave constantly delivers energy to the conductor. Since the conductor attenuates the field, the conductor must constantly carry off the dissipated energy.

 

[sachi]

by "constantly" carry off the energy, do you mean that if a particular quantity of energy (let's call it packet no. 1) enters the conductor, this packet of energy must continue flowing through the conductor until it reaches the other end, and not just that there is a constant flow of energy into the conductor from the surface?