ON THE CAPACITY OF THE CIRCULAR DISC CONDENSER AT SMALL SEPARATION.

Abstract

A pair of identical circular discs, held at equal and opposite potentials, forms a condenser whose capacity C depends on the ratio epsilon of separation against diameter. The determination of an asymptotic expansion for C when epsilon is small poses an axisymmetric boundary value problem for harmonic functions that has engaged the attention of numerous investigators over a long span of time. In the present work an integral equation of the first kind for the distribution of potential off the discs is derived and utilized to obtain an approximation for C when epsilon is small, reproducing the result of Kirchhoff and Hutson. Furthermore, an estimate of the error provides explicit details regarding the next term in the asymptotic expansion of C , which is of the order epsilon(log epsilon)squared.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1968
Accession Number
AD0674518

Entities

People

  • Frank Leppington
  • Harold Levine

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Axisymmetric
  • Boundaries
  • Boundary Value Problems
  • Diameters
  • Differential Equations
  • Equations
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.