Dipolar response of an ellipsoidal particle with an anisotropic coating

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In this paper we study the response of an ellipsoidal particle with a dielectrically anisotropic coating (the coating dielectric function being different parallel and perpendicular to the coating normal) placed in a constant external electric field. For the coating region we find that potential can be written in terms of solutions to a one-dimensional Heun's equation which is derived from the three-dimensional Gauss equation for the potential in ellipsoidal coordinates. We give solutions to Heun's equation in three forms: for the general case we obtain solutions in terms of a series expansion. For the case of spheroidal particles we write the solutions using hypergeometric functions. For large coating anisotropy we derive a simple form of the solution for the potential. The inside of the ellipsoid and the surroundings are assumed dielectrically isotropic and the potential is therefore given by standard results. By matching the solutions across the boundaries we obtain the ellipsoidal particle polarizability, which is written in terms of the standard depolarization factors and logarithmic derivatives of the Heun's equation solutions. The results above also allow us to obtain the magnetic polarizability of a coated ellipsoid in a constant external magnetic field.


External organisations
  • Chalmers University of Technology
  • University of Gothenburg
  • Indian Institute of Technology, Bombay
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Other Physics Topics
Original languageEnglish
Pages (from-to)10651-10665
JournalJournal of Physics A: Mathematical and General
Issue number42
Publication statusPublished - 2003 Oct 24
Publication categoryResearch
Externally publishedYes