Given conductivity, calculate E, D, and P vectors

[aliaze1]

Homework Statement

The gap between a pair of parallel infinite copper plates extends from z = 0 to z = W > 0 and is originally occupied by vacuum (ε₀, μ₀). The plates carry equal and oppositely signed surface charge densities and as a consequence we have a constant electric field E = −4ˆz V/m in vacuum in the gap region.

What would be the new equilibrium values of E, D, and P in the gap region if some amount
of salt were dissolved in the fluid in the gap (64ε₀) to raise its conductivity to σ = 4 S/m (conductivity of sea water)?

State the values of E, D, and P after a steady-state equilibrium is reached and briey explain your answer.

Homework Equations

D=εE=ε₀*E₀+P

P=polarization vector

The Attempt at a Solution

I have the equation J = σE, but I do not know how to relate this to D and P, since I am not given J in the problem

Thanks!

 

[gabbagabbahey]

Try to look at this problem qualitatively first. What does Ohm's Law (\textbf{J}=\sigma\textbf{E}) tell you the current will be when the salt is first added? What does that current do to the amount of charge on each plate? What effect does that have on the electric field in the gap?...Can you guess what the electric field will be when equilibrium is reached?