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Given conductivity, calculate E, D, and P vectors

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

    9048aa1e501c7b9e6f7f758b10c490f7.png

    57619c6a86c79e56ac806faf21502c90.png

    9cab6787646062d6e658cd1e83ad468f.png

    39adeb66b53fc1be92dda9c01386c3a9.png

    DE0*E0+P

    P=polarization vector


    3. 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!!!
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Feb 15, 2010 #2

    gabbagabbahey

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    Homework Helper
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    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?
     
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