Two formulas are derived for the capacitance of a flat circular annulus. The first has an accuracy of 1 part in 1000 or better when the ratio of the external to the internal radius lies between 1.1 and ∞ and is exact at ∞. The second, C=34.96R/ln(32R/c) μμf, has an accuracy of 1 part in 1000 when the ratio lies between 1.000 and 1.1 and is exact at 1.000. In this formula c is the difference of the radii and R their mean value in meters. An approximate expression for the charge density is given in the first case.
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W. R. Smythe (1951) studied this question.
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