History of the Study of Magnetism
Because magnetic fields were not discovered until recently, the history of how they were discovered is quite interesting, and informative.
1.1 The Detection of Magnetic Fields
We begin by giving an empirical history of the development of electromagnetic theory. As stated, people had long known that magnetic fields existed, but the only known source of these fields were permanent magnets, and no link was made to electricity. In the early 1800's, Hans Christian Oersted began to make the connection between electricity and magnetism. Oersted did most of his work using compass needles, but we will derive the existence of magnetic fields, and their relation to electricity, using more familiar systems-current carrying wires.
Consider two current carrying wires running parallel to one another. A current is simply a collection of moving charges. Traditional electric theory predicts that, since the net charge on each wire is zero, there is no interaction between the two wires.
Experiments in the 1800's, however, showed a surprising result: the wires were actually attracted to each other! The experiment was repeated, with the currents running in opposite directions, with the result that the wires were mutually repelled. Both situations are depicted below.
Figure 1.1: Parallel wires carrying current, in both parallel and antiparallel directions. In each case an attractive or repulsive force is felt by each wire. The large arrows indicate direction of current, while the small arrows indicate the direction of the force felt by each wire.
This experiment established that there was some sort of connection between magnetism and electricity, but a few more distinctions had to be made to generate a coherent definition. Firstly, if a metal sheet (a conductor) were placed between the two wires, it had no effect on the phenomenon. Since conductors shield...