The Capacitance of a Circular Annulus

Abstract

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.

Scale analysis and accurate correlations for some Dirichlet problems involving annular disc

“…Table 1 compares the results computed by Eq. (15) to those given by Smythe [1] and Cooke [2]. The results are in excellent agreement.…”

“…Cooke [2] has developed an analytical study from integral method. The author has solved the obtained integral solution by numerical way and has shown that his results are in excellent agreement with those computed by Smythe [1]. Collins [3] has studied the potential problem for a circular annulus.…”

“…Smythe [1] has performed an analysis based on the superposition technique to determine the flow through an annular disc. Cooke [2] gives some numerical data evaluated by the numerical solving of the governing integral equations.…”

“…Many authors have investigated this problem since 1950s. Smythe [1] has performed an ingenious analysis based on the superposition technique to determine the capacitance of a circular annulus. Cooke [2] has developed an analytical study from integral method.…”

Scanning Electrochemical Microscopy Approach Curves for Ring Microelectrodes in Pure Negative and Positive Feedback Mode

“…19,20 However, they often rely on purely analytical approaches that have limited validity ranges, considering infinite R g situations and present restricted predictive ability. 15 To develop the analytical approximations from numerical results, the dependence of both R g and a/b on I Tϱ is considered.…”