Chapter 1

Scalar and Vector Fields

Masud Mansuripur

Abstract

The concepts of scalar and vector fields, which are central to the theory of electrodynamics, are introduced. These fields are generally defined in 3-dimensional Euclidean space as complex-valued functions of the space-time coordinates (x, y, z, t). Integration and differentiation in time and space, leading to such operations as gradient, divergence, and curl, and subsequently to theorems of Gauss and Stokes, are developed. The intuitive approach taken here avoids mathematical formalism in favor of physical understanding. Throughout the chapter, examples based on complex-valued scalar and vector plane-waves help to illustrate the various mathematical operations. The end-of-chapter problems should help refresh the reader’s memory of elementary mathematical tools needed in this as well as in subsequent chapters.

Total Pages: 3-22 (20)

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