Static electric fields in vacuum

This chapter begins using Coulomb’s law to derive Maxwell’s electrostatic equations for a vacuum. In doing this, the integral forms of the electrostatic potential Ф and field E are obtained. These results are then used to determine Ф and E for various charge distributions possessing some symmetry: either via Gauss’s law or by directly integrating a known charge density over a line, surface or volume. Applications which require the use of computer algebra software (Mathematica) are included. A multipole expansion of the potential Ф leads to the various multipolemoments of a static charge distribution. Examples which deal with important properties like origin independence are presented. A range of questions and their solutions, not usually encountered in standard textbooks, appear in this chapter.