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Capacitance capacitor parallel plate with dielectric (Gauss)

  1. May 5, 2017 #1
    1. The problem statement, all variables and given/known data
    I have an elementary doubt with the calculation of the capacitance of a capacitor of parallel plates that has a dielectric in the middle.

    https://ibb.co/b0W4BQ

    2. Relevant equations

    ∫D⋅ds=Q
    D=E+γP
    C=Q/V

    3. The attempt at a solution
    Suppose the top plate has a positive charge and the bottom plate has a negative charge.

    To calculate vector displacement in the upper plate, we occupy the gauss law, use a Gaussian box. On the outside of the top plate the polarization P is 0 and there is an electric field E. At the bottom of the plate there is an electric field E and a polarization P due to the dielectric.
    If we consider only the top plate:

    ∫D⋅ds=[D][/out]A+[D][/down]A=Q

    [D][/out]=E
    [D][/down]=E+γP

    If we consider the complete system (both plates)

    ∫D⋅ds=2*[D][/out]A+2*[D][/down]A=Q

    [D][/out]=E
    [D][/down]=E+γP

    The field inside is 2 E.

    What is the error, I do not understand. D is zero outside from capacitor?
    Thank you
     
    Last edited: May 5, 2017
  2. jcsd
  3. May 5, 2017 #2
    At a first glance I see some equation problems since D is not equal to E D=epsilonxE. On the other side the elctric field outside the plates is considered to be 0 since the infinite parallel plates asumption is used when Gauss Law is applied. You should check your relevant equations
     
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