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Dielectric Problem

  1. Oct 31, 2013 #1
    1. The problem statement, all variables and given/known data
    A parallel plate capacitor has a capacitance C when there is no dielectric inside of it. Suppose a wedge
    of material with dielectric constant K is inserted in between the plates of the capacitor (see figure). The
    bottom face of the wedge has the same area as the plate of the capacitor. The height of the wedge is
    equal to the thickness of the capacitor, t on the left edge and varies linearly until the height is zero on
    the right edge. What is the new capacitance with this dielectric inserted?
    HINT: See if you can split up the capacitor into small capacitors that each have a dielectric in them that
    you know how to deal with.




    2. Relevant equations
    C = KC0

    C = εA/d


    3. The attempt at a solution
    Well, I first started with slicing the capacitor vertically into n small slices and from here to set up an integral, but I'm not sure how to set up the integral...
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

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  2. jcsd
  3. Oct 31, 2013 #2

    UltrafastPED

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    Science Advisor
    Gold Member

    The "mini capacitors" all share the same bus, so they are parallel ... so to get the total capacitance you just add them up.

    For each little bit, the amount of dielectric present is proportional to the distance from the edge, so you just need to express this relationship.
     
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