The Field Equations

This chapter postulates Maxwell's equations at the outset and proceeds to deduce the structure and properties of the field together with its relation to the source. The source of an electromagnetic field is a distribution of electric charge and current. Throughout the early history of electromagnetic theory the absolute electromagnetic system of units was employed for all scientific investigations. The integration of Maxwell's equations may be reduced to the determination of a vector and a scalar potential, which in homogeneous media satisfy one and the same differential equation. The chapter estimates the gradient, divergence, curl, and Laplacian in an orthogonal system of curvilinear coordinates, and deals with the simpler aspects of tensor calculus. To ensure the invariance of the field equations under a Lorentz transformation it is only necessary to assume that the four-current and the four-potential do indeed transform like vectors, and that the transform like field tensors.