Calculation of the electric field on dielectric particles in axisymmetrical arrangements

This paper presents an analytical method for calculating the electric field in arrangements of dielectric particles. Unlike the existing methods, our method repetitively inserts monopoles and multipoles until all the boundary conditions are satisfied, which does not require setting up a linear equation system in the calculation. It can be applied to various types of energization such as a uniform field, spherical electrodes, or planar electrodes. The method and the boundary element method, a numerical method, have been utilized to investigate the effects of the particle number and particle permittivity. The results show that the accuracy of the numerical method greatly varies from less than 10^-4% to more than 2%, depending on the condition of the calculation arrangements.