# Calculation of capacitance of conductors

## Main Question or Discussion Point

Hello,

I would like to get a method for calculation of capacitance of conductors. Let say, I have several conductors in space (2D). I know voltage everywhere between and on conductors, and I need to know the value of capacitance between 2 conductors among several. I'm looking for a general method in order to program an algorithm.

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vk6kro

The capacitance is determined by the dimensions of the conductors and the properties of the dielectrics between and around them.

Here is Wikipedias description:

The capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. For example, the capacitance of a parallel-plate capacitor constructed of two parallel plates both of area A separated by a distance d is approximately equal to the following:

C = \epsilon_{r}\epsilon_{0} \frac{A}{d} (in SI units)

where

C is the capacitance in farads, F
A is the area of overlap of the two plates measured in square metres
εr is the relative static permittivity (sometimes called the dielectric constant) of the material between the plates, (vacuum =1)
ε0 is the permittivity of free space where ε0 = 8.854x10-12 F/m
d is the separation between the plates, measured in metres

The equation is a good approximation if d is small compared to the other dimensions of the plates so the field in the capacitor over most of its area is uniform, and the so-called fringing field around the periphery provides a small contribution

End quote.
A technique that is used to analyse radio antennas is to take small segments of each part of the antenna and calculate the effect of all other parts on that part, and vice versa.

So, if you knew the diameter of a wire, you could take a small section of it and work out the area facing each other section of other conductors and estimate the capacitance.
Wire segments along the same wire could have their capacitances added in parallel.

Thanks for reply. I've programmed this formula, resultats lack of accuracy bur anyway it's better that nothing. I've also tried using Gass theorem with calculation of flux for electrical field, results are not better !

vk6kro

Yes, even the Wikipedia article I quoted said this:

The equation is a good approximation if d is small compared to the other dimensions of the plates so the field in the capacitor over most of its area is uniform, and the so-called fringing field around the periphery provides a small contribution.

Meaning that it wasn't a good approximation if d, the separation between the plates, measured in metres, was large. And not if the so-called fringing field around the periphery provides a large contribution.

So, these problems might be contributing to the inaccuracy.