# How to get capacitance from potential FEM

1. Jul 8, 2014

### 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?

2. Jul 8, 2014

### 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

3. Jul 8, 2014

### 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

4. Jul 8, 2014

### 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 dont remember how to calculate the laplacian for numerical data.

Last edited: Jul 8, 2014
5. Jul 8, 2014

### 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?

6. Jul 8, 2014

7. Jul 8, 2014

### 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...

Last edited: Jul 8, 2014