Chapter One - Coulomb's Law and Stationary Electric Field

Abstract

Publisher Summary This chapter introduces the theory of stationary electric fields—that is, the theory of electric fields that do not vary with time—starting from Coulomb's law of force between electric charges and the principle of superposition. The force of interaction between electric charges is, like the force of gravity, one of the fundamental concepts of physics. The chapter highlights the equations of electric force F(p) at any point p, which can be situated anywhere outside or inside the integration volume V. Using these equations effects of surface, linear, and pint charges could be explained. Like the force field F(p), the electric field E(p) is a vector attached to a point p, defined as the ratio between the electric force and the magnitude of an elementary “test charge” at p. The chapter explains the first equation of the electric field that holds for stationary electric fields along arbitrary paths passing through points at any distance from each other. Since this equation does not contain derivatives, it can be applied at any point of a medium. The chapter also illustrates the second equation for the electric field in integral form. It applies at regular points—where field values are nonsingular, in fact, over any surface where the integral can be defined—and shows that the fluxes of electric field E through all patches of the closed surface S are related in such way that their sum defines the total charge inside. Using these equations, the chapter discusses solutions of Poisson's equation and uniqueness, polarization of a medium, the potential and electric field caused by polarization, and distribution of bound charges.