(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The question given is an electromagnetic wave incident on a vacuum metal interface. The wave is incident normally. We're given that the metal is a good conductor i.e. [tex]\omega \tau <<1 [/tex] where [tex]\tau[/tex] is the collision time of the metal and omega is the angular frequency. The metal is also non-magnetic and the conductivity is of the order of [tex] 10^8 [/tex] Siemens per metre

The first part is easy enough it's just to show that T the transmissivity is equal to 2/n where n is the real part of N the refractive index.

The part that has me stumped is to find the value of [tex]\omega[/tex] so that the fraction of incident power deposited beyond a depth d is maximised

2. Relevant equations

I think the relevant equation is the poynting vector.

I'm taking the time averaged poynting vector for a wave in vacuum as [tex] S_{avg} = \frac{1}{2} \sqrt{\frac{\epsilon}{\mu}} E_{i}^{2}[/tex] and inside the metal I assume the form[tex] S_{avg} = \frac{1}{4} \sigma_{0} \delta E_{t}^{2} e^{\frac{-2 z}{\delta}[/tex]

Where delta is given as[tex]\sqrt{\frac{2}{\mu \omega \sigma_{0}}}[/tex]

I'm also taking[tex]n=\frac{c}{\omega \delta}[/tex]

3. The attempt at a solution

I started by saying that since the time averaged poynting vectors is independent of x and y in both case we can say

[tex]\int S_{avg} dA=S_{avg} A[/tex]

Using this I divided the power incident on the surface by the power incident on hte same area but at a distance d below the surface to obtain

[tex]\frac{\delta \sigma_{0}}{2}\sqrt{\frac{\mu}{\epsilon}}\frac{E_{t}}{E_{i}}\frac{E_{t}}{E_{i}}e^{\frac{-2 d}{\delta}}[/tex]

but with this I differentiate w.r.t. omega and I can't obtain an answer? It's been bugging me for a while so I hope someone can help me out. Hope the format of the question is ok It's my first time posting here. =D

edit: I forgot to say that I replaced {E_{t}/E_{i}}^2 with 2/n I tried changing the latex code but it won't edit for some reason.

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# Homework Help: Classical electrodynamics -Good conductor

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