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Electric charge of capacitor

  1. Jun 21, 2013 #1
    1. The problem statement, all variables and given/known data

    Dielectric medium inside capacitor consists of two types (check the pic). Capacitor's plates are connected to a source of constant tension U. Distance between the plates is d and their area is S. Find the electric charge of capacitor's plates.

    Data given: U=500 V, d=2cm, S=80cm^2, εr1=2.5, εr2=1.0.
    (ε1=εr1*ε0 ^ ε2 = εr2*ε0)

    3. The attempt at a solution

    By applying Gauss's Law for a surface around the capacitor's plate, I manage to get the electric field intensity which is [itex]E=\frac{Q}{ε0εr1S1+ε0εr2S2}[/itex]

    [itex]U=\frac{Qd}{ε0εr1S1+ε0εr2S2}=500[/itex]

    which implies

    [itex]Q=\frac{500(ε0εr1S1+ε0εr2S2)}{d}[/itex]

    I don't know how to continue after this because I don't know S1 and S2 separately.

    Help me!
     

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  3. Jun 21, 2013 #2

    gneill

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    Staff: Mentor

    If there's a variable left unspecified then your result will be an expression in that variable. Suppose you let r specify the division of the plate areas so that S1 = r*S and S2 = (1-r)*S.
     
  4. Jun 21, 2013 #3
    Yes gneill, but still that doesn't solve the problem. Does this mean the book didn't give enough data?
     
  5. Jun 21, 2013 #4

    gneill

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    Staff: Mentor

    It would seem that there are two possibilities:
    1. The book mistakenly failed to provide enough data to solve the problem numerically.
    2. The book intentionally did not provide enough data to solve the problem numerically and expects an expression for an answer.

    A third but unlikely possibility is that the missing data doesn't matter if its variable somehow cancels out of the problem.

    If this is a homework problem to be handed in, make note of the fact that there is not enough information for a complete numerical solution and provide a simplified expression for a result.
     
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