Current Flow in Cylinders
- 1 January 1953
- journal article
- research article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 24 (1) , 70-73
- https://doi.org/10.1063/1.1721136
Abstract
The mixed boundary value problem arising from the flow of current into a right circular cylinder of radius a through a perfectly conducting coaxial disk electrode at one end is solved approximately. The boundary conditions are met rigorously except that the electrode is not quite plane. A solution valid for all values of the disk radius is given for which in the worst case the deviation from flatness is nearly 0.01a. More exact solutions are worked out for disk radii ¼a, ½a, and ¾a and the first forty coefficients in the Bessel function series for the potential in the cylinder are tabulated. A cylinder whose diameter is eight times its length is also treated for disk radii ¼a and ½a and the first forty coefficients in the potential series are tabulated. The probable errors in the resistance formulas derived from these solutions are given.This publication has 1 reference indexed in Scilit:
- A new table of the zeros of the Bessel functions 𝐽₀(𝑥) and 𝐽₁(𝑥) with corresponding values of 𝐽₁(𝑥) and 𝐽₀(𝑥)Bulletin of the American Mathematical Society, 1927