Application of Translational Addition Theorems to Electric and Magnetic Field Analysis in Many-Sphere Systems

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Mudun Kotuwage, Sumana Chaminda Kumara
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The purpose of this study is to find analytical solutions to Laplacian field problems rela-tive to arbitrary configurations of spheres based on novel translational addition theorems derived specifically for scalar Laplacian functions. These theorems are used to express in analytic form the fields due to individual spheres in system of coordinates attached to other spheres, thus allowing for the exact boundary conditions to be imposed. In the literature, translational addition theorems are available for scalar cylindrical and spherical wave functions. Such theorems are not directly available for the general solu-tion of the Laplace equation. This thesis presents the derivation of the required translational addition theorems for the general solution of Laplace equation in spherical coordinates and then the application of these theorems to find analytical solutions to some electrostatic and magnetostatic field problems relative to arbitrarily located spheres. Computation results for electric and magnetic spheres have been generated and numerical results are compared with the re-sults obtained by other methods available in the literature for two sphere systems. Such numerical data, of known accuracy, are also useful for validating various approximate numerical methods.
Analytical, Laplace, Spheres