Maxwell's equations for electromagnetism are the fundamental understanding of how electric fields, magnetic fields, and even light behave. There are various versions, depending on whether there is vacuum, a charge present, matter present, or the system is relativistic or quantum, or is written in terms of differential or integral calculus. Here, we will discuss a little bit of historical development as a prelude to the introduction of the laws themselves.
One of the pinnacles of classical science was the development of an understanding of electricity and magnetism, which saw its culmination in the announcement of a set of mathematical relationships by James Clerk Maxwell in the early 1860s. The impact of these relationships would be difficult to minimize if one were to try. They provided a theoretical description of light as an electromagnetic wave, implying a wave medium (the ether). This description inspired Michelson and Morley, whose failure inspired Einstein, who was also inspired by Planck and who (among others) ushered in quantum mechanics as a replacement for classical mechanics. Again, it's difficult to minimize the impact of these equations, which in modern form are known as Maxwell's equations.
In this chapter, we will discuss the history of electricity and magnetism, going through early 19th-century discoveries that led to Maxwell's work. This historical review will set the stage for the actual presentation of Maxwell's equations.