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