Time-Varying Electromagnetic Fields

Abstract

In this chapter we discuss time-varying or nonsteady state electromagnetic fields by way of the powerful unifying theory of the great Scottish mathematical physicist, James Clerk Maxwell (1831–1879). The reader may want to refer to the original work of Maxwell [32]. In electrostatics and magnetostatics the steady state electric and magnetic fields are treated separately.† Although similar mathematical techniques were used, electric and magnetic phenomena were treated as being independent of each other. The only link is that an electrical current produces a magnetic field. But when we consider time-dependent electric and magnetic fields, Maxwell taught us that these fields are interdependent, being bound together by a unified electromagnetic theory. It is this theory that we consider in detail in this chapter. In particular, we shall investigate Maxwell’s equations and their solutions in a physical setting, as a basis for a discussion of the mathematical properties of these equations vis-à-vis the partial differential equations (PDEs) of wave propagation in an electromagnetic medium. The mathematical theory of these PDEs will be treated in detail in subsequent chapters.