How to get capacitance from potential FEM

[rinale84]

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?

 

[maajdl]

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

 

[rinale84]

Excuse my silly question I don't remember why the electric filed at the surface gives the surface charge density..thank u very much

 

[Delta2]

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 don't remember how to calculate the laplacian for numerical data.

 

[rinale84]

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?

 

[jtbell]

I don't remember why the electric filed at the surface gives the surface charge density

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gausur.html#c3

 

[rinale84]

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...