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Parallel plate capacitor with two dielectric materials?

  1. May 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Use Gauss' law to find an expression for the electric field within a charged parallel plate capacitor with two layers of dielectric materials (?r1 and ?r2).
    (See attached image, this is for question 2a).

    3. The attempt at a solution
    My approach would be to split the capacitor into two capacitors, each with r1 and r2 dielectrics - connected in series. Then the electric field across them both would be the sum of the electric fields across each one?

    So:
    For The first dielectric:
    The integral of: E1.dA = Q/(e0*er1)
    E1 = Q/(e0*er1*A)
    E2 = Q/(e0*er2*A)

    Therefore
    Etotal = (Q/(?0*A)) * (1/?r1 + 1/?r2)

    Am I taking the right approach?

    Any help would be appreciated,

    Thanks.
     

    Attached Files:

  2. jcsd
  3. May 15, 2012 #2
    Just had a brain wave: is it possible to treat both dielectrics as a single material by averaging their respective permittivities divided by their proportion of the gap?

    So
    [itex]\epsilon_{T}=\epsilon_{r1}*1/3 + \epsilon_{r2}*2/3 = (\epsilon_{r1} +2\epsilon_{r2})/3[/itex]

    Therefore:
    [itex]E = 3Q/(A\epsilon_{0}(\epsilon_{r1}+2\epsilon_{r2}))[/itex]

    This seems more likely... I think...
     
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