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Fully filled capacitors with parallel dielectrics problem

  1. Dec 4, 2017 #1
    consider that we have two dielectrics inside a capacitor as shown in the picture, let0s consider also that Q is the charge of the capacitor and d the distance between the two plates , the first dielectric occupy a surface of S/3 with a dielectric constant of er1 and the second a surface of 2S/3 with a dielectric constant of er2, the question is calculate the electric field inside the capacitor and the surface density of the induced charge (see the uploaded image)
    During the calculation I faced the following doubts: I applied gauss theorem to the flux density in both areas of the dielectrics and I got: QEAJg.gif

    σ is the surface density of the free charges =Q/S,

    8YAxA.gif

    doing the same with the second surface I got that y48Zg.gif

    and because my two dielectric are in parallel so E1=E2

    this gives me MHZ6c.gif

    BUT this not true!!! so where did my logic fails??

    Many thanks in advance!! dielectric.png dielectric.png dielectric.png
     
  2. jcsd
  3. Dec 4, 2017 #2

    cnh1995

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    Charge density on the plates will not be uniform.
     
  4. Dec 4, 2017 #3
    Thanks for your prompt reply, it makes sens but can you elborate more?
     
  5. Dec 4, 2017 #4
    I just go why the charge density is different from dielectric to dielectric
    many thanks !!!
     
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