# capacitance between widely-separated parallel plates

There's a caveat, which is often ignored, to the "easy" equation for parallel plate capacitors C = epsilon * A / d, namely that d must be much smaller than the dimensions of the parallel plate.

Is there an equation that works for large d? I tried finding one and could not. (These two papers talk about fringing fields for disc-shape plates but don't seem to have a valid equation for d -> infinity: http://www.santarosa.edu/~yataiiya/UNDER_GRAD_RESEARCH/Fringe%20Field%20of%20Parallel%20Plate%20Capacitor.pdf and http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.167.3361&rep=rep1&type=pdf)

My hand-waving intuition is that as d -> infinity, C should decrease to a constant value (which is the case for two spheres separated by a very large distance, where C = 4*pi*e0/(1/R1 + 1/R2) ), because at large distances from each plate, the electric field goes as 1/R, so the voltage line integral from one plate to the other will be a fixed constant proportional to charge Q.

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## 1 Answer

There is, of course, a solution for the most simple case of the circular disk parallel plate capacitor. See, for example, the article by G.T. Carlson and B.L. Illman, Am. J. Phys. 62, 1099 (1994).

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any chance you could give a summary? I don't have full-article access. –  Jason S Jul 8 '11 at 18:30
aha, the abstract gave me a couple of search term clues. "Love's equation" in particular. This article is directly available and is pretty useful. jpier.org/PIER/pier97/21.09092503.pdf –  Jason S Jul 8 '11 at 18:32