Capacitance of an elliptical disk on a semi-infinite dielectric material

Mimi X. Yang, Fuqian Yang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Using an integral transform, the mixed boundary value problem of a conducting, elliptical disk on a dielectric half-space in an electric field is reduced to the solution of an integral equation. An analytical expression of the electric system capacitance is derived, which is a function of the eccentricity of the elliptical disk. The electric charge and electric stress distribute non-uniformly over the surface of the elliptical disk and display local singularities at the edge of the elliptical disk. The square root singularity of the electric field at the edge of the elliptical disk leads to the divergent of the resultant force on the elliptical disk, which is physically unrealistic. There likely exist geometrical constraint and/or field constraint to limit the presence of the square root singularity of the electric field. For any symmetric conductor in an infinite space that consists of air (vacuum) and a semi-infinite dielectric material with symmetric plane being in the interface between the air and the dielectric material, the electric potential in the space is independent of the dielectric constant of the dielectric material.

Original languageEnglish
Pages (from-to)276-283
Number of pages8
JournalJournal of Electrostatics
Volume87
DOIs
StatePublished - Jun 2017

Keywords

  • Capacitance
  • Elliptical disk
  • Integral transform

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biotechnology
  • Condensed Matter Physics
  • Surfaces, Coatings and Films
  • Electrical and Electronic Engineering

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