Introduction

Magnetism as a phenomenon has been known since before 600 B.C. (lodestone, magnetite, attracting iron), but it was only put on a systematic scientific footing much later. William Gilbert (1544-1603) was the first to investigate magnetism using the scientific method, and it was Gilbert who also discovered that the Earth itself behaves as a weak magnet. Two centuries later, the Danish physicist Hans Oersted (1777-1851) discovered that an electric current produces a magnetic effect, suggesting for the first time a deep link between electricity and magnetism. James Clerk Maxwell (1831-1879) then showed mathematically that electricity and magnetism are really two aspects of a single underlying force field -- electromagnetism -- unifying what had until then been treated as two separate subjects.

Much of the vocabulary developed for electrostatics carries over directly to magnetism: the relationship between a field and the force it produces on a source placed in it, and the idea of a dipole, both have close magnetic analogues. There is, however, one crucial difference: while an isolated electric charge can certainly exist on its own, an isolated magnetic pole never can -- a magnet is always found as at least a dipole (two poles, N and S) or, more elaborately, a quadrupole. This chapter focuses on the elementary aspects of magnetism (the bar magnet as a source of field, and Gauss' law for magnetism) together with terrestrial magnetism -- the magnetic field of the Earth itself.

Four commonly known facts about magnetism, which every subsequent formula in this chapter must remain consistent with: (i) every magnet, whatever its size or shape, has exactly two poles, called the north pole and the south pole; (ii) if a magnet is broken into two or more pieces, each piece becomes an independent magnet in its own right, with a somewhat weaker field -- isolated magnetic monopoles simply do not appear this way (or in any other way discovered so far; the search for a genuine magnetic monopole continues even today, without success); (iii) like magnetic poles repel each other, while unlike poles attract each other, exactly as with electric charges; and (iv) a bar magnet or magnetic needle, when suspended freely or pivoted so it can turn, always settles into alignment along the geographic North-South direction -- the simple physical fact that makes a magnetic compass work.