ABSTRACT
This chapter discusses the electrostatic boundary value problems involving Laplacian fields. It begins with the description of Laplacian and Poisson’s fields, Laplacian fields as scalar and vector functions, Laplacian operator, and the scalar electric potential. It describes the uniqueness theorem and the classification of field problems. It deals with one-, two-, and three-dimensional field problems in Cartesian, cylindrical, and spherical coordinates. The 1D problem includes four cases for RCS, three for CCS, and four for SCS. In these, both homogeneous and heterogeneous media are considered and the 1D field is assumed to vary with different coordinates for every case. All the 2D field problems relate to the determination of potential field in a given configuration with specified boundary conditions. For RCS there are five, for CCS four, and for SCS two problems. In some of these the medium is taken to be homogeneous whereas in others as heterogeneous. In three RCS problems the same configuration is used with different boundary conditions. In each problem the field variation is taken to be independent of one of the coordinates. In the 3D case the description is mainly confined to the general solutions of RCS, CCS, and SCS problems.
