Solving Maxwell’s Equations in Space-time: The Wave Equation

Abstract

The problem addressed in the present chapter is the same problem as discussed in the preceding one, namely, the determination of fields for given distributions of charge, current, polarization and magnetization. Here, however, we will derive expressions for the scalar and vector potentials as functions of space and time coordinates for the given source distributions, which are also specified in space-time. Once the potentials are obtained, the electromagnetic fields will be calculated by straightforward differentiation. The integrals will look very different from those encountered in Chapter 4, but the final results will be exactly the same.

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