11.2 Maxwell’s Equations
When, in 1873, James Clerk Maxwell2 wrote his now famous Treatise on Electricity and Magnetism, he wrote in the preface
to the book that his purpose was essentially that of explaining Faraday’s ideas (published in Experimental Researches in
Electricity in 1839) into a mathematical and, therefore, more universal form. He makes it amply clear that his treatise is a sort
of summary or unification of the knowledge in electrical and magnetic fields as put forward by others, including those who
preceded Faraday (Ampere, Gauss, Coulomb, and others). We might add that the notation we use today to write Maxwell’s
equations was introduced by Oliver Heaviside3 almost 20 years after Maxwell’s theory appeared. If you were to read
Maxwell’s book, you might not recognize the equations written in the previous chapters or in this. What then is Maxwell’s
unique contribution? Why do we normally refer to the electromagnetic field equations as “Maxwell’s equations”? Surely, it
is more than simply because he summarized what others have done.
His main contribution is in proposing the inclusion of displacement currents4 in Ampere’s law. This seemingly minor
change in the field equations as known before his time was, in fact, a fundamental change in the theory of electromagnetics.
Maxwell’s ideas, which were often expressed in mechanical terms, were not immediately accepted since they implied a
number of aspects of the electric and magnetic fields that had no proof at the time. Maxwell himself had no experimental