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Looking for suggestions on how to approach calculating the capacitance of a capacitor where the plates have an arbitrary shape. I've seen derivations of capacitance for a few highly symmetric arrangement (eg coaxial cylinders) but nothing like a general approach to predicting the measurable capacitance of arbitrary arrangements of plates.

Thanks for any suggestions or references.

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the problem comes with the calculation, integrating an arbitrary shape object is difficult to find the charge in capacitor plates... –  Vineet Menon Apr 20 '12 at 6:08
    
If it's arbitrary, it really depends--you can give yourself some differential equations and solve them, I guess. Of course, for any set of parallel plates, it's pretty easy :) –  Manishearth Apr 20 '12 at 6:36
    
... especially if these parallel plates can be taken to be practically infinitive ;) –  Pygmalion Apr 20 '12 at 7:40
    
check if this helps you (i havent read it completely) : docs.google.com/… –  Ashu Apr 20 '12 at 8:33
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1 Answer

up vote 2 down vote accepted

You make a grid, place your shapes on the grid, and solve Laplace's equation with a zero potential at infinity, and some potential on the grid. This will give you an electric field intensity at every point (the gradient of the potential), and you sum up the implied charge. The ratio Q/V is the capacitance.

This is mathematically optimal, and the only improvement is to use non-grid approximations, like expansion in harmonics at large distances, and superior higher-order methods in the interior of the grid. For Laplace's equation on modern computers, there is no issue--- even the worst algorithm will give you an answer to 1% accuracy on an arbitrary shape within a reasonable time.

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