The postulate In 1864, James Clerk Maxwell proposed one of the most successful theories in the history of science. In a famous memoir to the Royal Society [125] he presented nine equations summarizing all known laws on electricity and magnetism. This was more than a mere cataloging of the laws of nature. By postulating the need for an additional term to make the set of equations self-consistent, Maxwell was able to put forth what is still considered a complete theory of macroscopic electromagnetism. The beauty of Maxwell’s equations led Boltzmann to ask, “Was it a god who wrote these lines | Chapter 2 Maxwell s theory of electromagnetism The postulate In 1864 James Clerk Maxwell proposed one of the most successful theories in the history of science. In a famous memoir to the Royal Society 125 he presented nine equations summarizing all known laws on electricity and magnetism. This was more than a mere cataloging of the laws of nature. By postulating the need for an additional term to make the set of equations self-consistent Maxwell was able to put forth what is still considered a complete theory of macroscopic electromagnetism. The beauty of Maxwell s equations led Boltzmann to ask Was it a god who wrote these lines . 185 . Since that time authors have struggled to find the best way to present Maxwell s theory. Although it is possible to study electromagnetics from an empirical-inductive viewpoint roughly following the historical order of development beginning with static fields it is only by postulating the complete theory that we can do justice to Maxwell s vision. His concept of the existence of an electromagnetic field as introduced by Faraday is fundamental to this theory and has become one of the most significant principles of modern science. We find controversy even over the best way to present Maxwell s equations. Maxwell worked at a time before vector notation was completely in place and thus chose to use scalar variables and equations to represent the fields. Certainly the true beauty of Maxwell s equations emerges when they are written in vector form and the use of tensors reduces the equations to their underlying physical simplicity. We shall use vector notation in this book because of its wide acceptance by engineers but we still must decide whether it is more appropriate to present the vector equations in integral or point form. On one side of this debate the brilliant mathematician David Hilbert felt that the fundamental natural laws should be posited as axioms each best described in terms of integral equations 154 . This idea has .
