$E(x,t)=E_0e^{i(kx-\omega t)}$ , $B(x,t)=B_0e^{i(kx-\omega t)}$
The wave falls perpendicular onto a metal. Compute the penetration depth $\delta$, meaning the length within the metal at which the amplitude reduces to 1/e of its initial value. Let $k=\frac{\omega}{c}(\bar{n}+i\kappa)$ within the metal.
This is the last part of a problem set I've been dealing with. I can't seem to find a right approach to this. I was thinking of looking at the intensity to get the depth,
$I(x)=I_0e^{-\alpha \Delta x}$.
And from that setting $\frac{I(x)}{I_0}=1/e$ and from that to infer that $\Delta x=1/\alpha$. I assume that $\Delta x=\delta$? I got the formula from wikipedia when trying to search for penetration depth. Is that the right approach? And if so, what would $\alpha$ be in that case?
Edit: For some reason my original post got deleted so here it is again.
The person who answered my original post suggested to use maxwell's equation in combination with the current density from Ohm's law somehow to get to the solution but I couldn't get to the penetration depth. Although it might be that I tried using the wrong one of maxwell's equations.
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