# Time for a DC electric field to penetrate copper

1. Nov 12, 2011

### burkleyp

1. The problem statement, all variables and given/known data
Using the differential equation for a resistive medium $\frac{\delta^{2}E}{\delta x^2}=\frac{\mu_o}{\eta}\frac{\delta E}{\delta t}$
estimate the time for a dc electric field to penetrate fully into a copper slab 2cm thick.

2. Relevant equations/ information
The electric field can be zero by the time it reaches the end of the copper to minimally satisfy the time requirement, so E(0.02)=0 and $\frac{\delta E}{\delta x}=\frac{-E_o}{0.02}$

3. The attempt at a solution
I'm at a loss here. The diffusion equation relates the change in the change of the magnitude of the electric field in space to the change in the electric field in time, but I'm not sure what to do with this. My instinct was to plug in a value for $\frac{\delta^{2}E}{\delta x^2}$ then integrate and solve for t, but I am not sure what value I should substitute.