Elements of electrostatics and potential theory

Abstract

In electrical surveys, resistivity variations distort the current pattern in the earth and so cause anomalies in the potential to be measured. For each current system there exists a uniquely equivalent, physically real system of charge distributions. Since the true sources of static electric field are only charges, this system provides a clear physical basis for using the potential theory in the mathematical formulation of electrical models. An important empirical justification for this is the classical Coulomb law for the field generated by a point charge. In this chapter we shall apply the potential theory in considering the effects generated by the most common source distributions of electrical models. The fundamental bases for this approach are Maxwell's equations, which include Coulomb's law in the form of Gauss's law for the electric field.