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A.1 Recap: The Four Equations

In a vacuum, Maxwell's four equations of electrodynamics, as expressed in the previous four chapters, are:





A few comments are in order. First, Maxwell did not actually present the four laws in this form in his original discourse. His original work, detailed in a four-part series of papers titled On Physical Lines of Force contained dozens of equations. It remained to others, especially English scientist Oliver Heaviside, to reformulate Maxwell's derivations into four concise equations using modern terminology and symbolism. We owe almost as much a debt to the scientists who took over after Maxwell's untimely death in 1879 as we do to Maxwell himself for these equations.

Second, note that the four equations have been expressed in differential forms. (Recall that the divergence and curl operations, ∇· and ∇× respectively, are defined in terms of derivatives.) There are other forms of Maxwell's equations, including forms for inside matter (as opposed to a vacuum, which is what is considered exclusively in this book), integral forms, so-called "macroscopic" forms, relativistic forms, even forms that assume the existence of magnetic monopoles (likely only of interest to theoretical physicists and science fiction writers). The specific form you might want to use depends on the quantities you know, the boundary conditions of the problem, and what you want to predict. Persons interested in these other forms of Maxwell's equations are urged to consult the technical literature.

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