Given conductivity, calculate E, D, and P vectors

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aliaze1
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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



Gauss's law in differential form: divergence of D equals rho sub f, written with nabla, vector D, and rho sub f.


Maxwell equation: divergence of the magnetic field B equals zero, written as ∇ · B = 0.


Maxwell-Faraday equation in differential form: curl of E equals negative partial derivative of B with respect to t.


Maxwell-Ampere law in differential form: curl of H equals J_f plus the partial derivative of D with respect to t.


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!
 
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Discussion

Try to look at this problem qualitatively first. What does Ohm's Law ([itex]\textbf{J}=\sigma\textbf{E}[/itex]) 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?