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How to get capacitance from potential FEM

  1. Jul 8, 2014 #1
    Hi guys,
    I hope this is the correct section otherwise I apologize :).The goal is to find the capacity of a non linear capacitance composed by an upper plate which has a cup shape and the lower plate which is flat.
    The problem is the following: by means of a FEM simulation of the Poisson equation I was able to find the potential but once I got it how can I get the capacitance?
  2. jcsd
  3. Jul 8, 2014 #2


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    Gold Member

    C = Q/V

    You still need the charge.
    If it is not immediately available, you need to calculate it:
    - the field at the surface gives the charge density
    - summing over the whole surface will provide Q
  4. Jul 8, 2014 #3
    Excuse my silly question I don't remember why the electric filed at the surface gives the surface charge density..thank u very much
  5. Jul 8, 2014 #4


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    Homework Helper
    Gold Member

    Not exactly the electric field but the divergence of electric field. Thats the differential form of gauss law http://en.wikipedia.org/wiki/Gauss_law#Differential_form

    Since you have the potential, it is the laplacian of the potential that gives the charge density.

    PS i dont remember how to calculate the laplacian for numerical data.
    Last edited: Jul 8, 2014
  6. Jul 8, 2014 #5
    I think some function in matlab will be helpful... But the integration of the chrage density should be performed on the volume and not on the surface!Am i wrong?
  7. Jul 8, 2014 #6


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    Staff: Mentor

  8. Jul 8, 2014 #7
    I am not sure I am in this situation the plates of the capacitor are made of a polymer and inside the two plates we have water. Above the polymer there is a layer of conductive material on which we apply the potential...Besides how the charge will behave when i apply a potential difference among the plates? The water should polarize am I wrong? Sry if I forgot this fundamental detail before...
    Last edited: Jul 8, 2014
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