# Current density and skin depth

1. Dec 2, 2014

### beowulf.geata

1. The problem statement, all variables and given/known data
A thin metallic strip on a circuit board has length L, width a and thickness t, with L>>a>> t. Derive an expression for the resistance between the ends of the strip at frequency f, assuming that the skin depth is small compared with the thickness t.

2. Relevant equations
The book where I took this problem from explains that for an electromagnetic wave polarized in the x-direction and travelling in the z-direction through a conducting medium where ω << 1/τc (1/τc being the frequency of collisions between an electron and the lattice) the electric field is the real part of E = E0e-z/δei(z/δ-ωt)ex (where δ is the skin depth).

3. The attempt at a solution
What I am puzzled by is that the solution says that the current density is

J(z)= σE(z) = σE0e-z/δ,

so my question is: where has the real part of ei(z/δ-ωt) gone?

I'd be very grateful for any pointers on this.

2. Dec 7, 2014