calculate the capacitance with PDE toolbox

Hello , 

I want PDE toolbox or any command to help me calculate the capacitance per length in attached problems.

The file named "1" is a co-axial cable with square cross section and I need to calculate capacitance per length between inner square and the outer one.

The file named "2" shows two sphere and I need to calculate capacitance per length between them.

Thank you.

Answer 1

[Bill Greene]

One of the simplest ways to calculate capacitance using PDE Toolbox is from the energy: C = 2*U/V^2 where U is the electrostatic energy and V is the potential across the electrodes.

The electrostatic energy can be calculated with this simple function

function energy=calcEnergy(p,t,permittivity,u)
[dudx,dudy] = pdegrad(p,t,u);
area=pdetrg(p,t);
energy = permittivity*sum(area.*(dudx.*dudx + dudy.*dudy))/2;
end

Since you are solving in the pdetool GUI, you will need to export the mesh and the solution to the MATLAB workspace before you can call this function and calculate the capacitance.

Another suggestion you might want to consider is turning on Adaptive mode on the Solver/Parameters dialog box. This option will refine the mesh (e.g. around sharp corners) to obtain a more accurate solution.

Regards,

Bill

Answer 2

[Alejandra]

Hello,

I am working on a similar problem, and I tried using this method, however, I get an answer that is way off. Is there any other way to calculate capacitance or energy? I am looking to calculate the capacitance between a plate and a probe.

Answer 3

[Lalson Vincent]

I am also working on this problem. But i want to calculate for a 3D geometry ? Any suggestions...