A numerical verification of the Clausius-Mossotti relation

Author

Steffan, J. ; Richter, K.R.

Author_Institution

Inst. for Fundamentals & Theor. in Electr. Eng., Graz Univ. of Technol., Austria

Volume

26

Issue

2

fYear

1990

fDate

3/1/1990 12:00:00 AM

Firstpage

528

Lastpage

531

Abstract

The results of the approximation formula deduced by Clausius and Mossotti to calculate the effective permittivity of an arrangement of a large number of spheres with a permittivity ξ_s filling a medium with a permittivity ξ_s are compared with a highly accurate three-dimensional finite-element method solution. This formula gives the effective permittivity as a function of ξ_s and σ_m as well as the ratio of the two volumes. The influence of different structures with the same volume ratios is investigated. It is shown that there is only an insignificant difference between the Clausius-Mossotti approximation formula and the highly accurate finite-element solution for different lattice structures. The differences between the two solutions become more pronounced for higher values of the volume ratio and of the conductivity ratio of the two materials

Keywords

dielectric properties of solids; finite element analysis; numerical methods; permittivity; Clausius-Mossotti approximation formula; Clausius-Mossotti relation; conductivity ratio; effective permittivity; lattice structures; numerical verification; three-dimensional finite-element method; Conductivity; Equations; Finite element methods; Lattices; Permittivity;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/20.106370

Filename

106370