The existence of a magnetic force was known for centuries before William Gilbert pointed out in 1600 that the Earth itself behaved like a huge magnet. Gradually maps were made of the geomagnetic elements. Systematic investigation of magnetic behavior was undertaken in the late eighteenth and early nineteenth centuries. The French scientist Charles Augustin de Coulomb showed experimentally that forces of attraction and repulsion exist between the ends of long thin magnetized rods, and that they obey rules similar to those determining the interaction of electrical charges. A freely suspended magnet was observed to align approximately north–south; the north-seeking end became known as its north pole, the opposite end as its south pole. The origin of magnetic force was attributed to magnetic charges, which, through association, became known as magnetic poles. Subsequently, it was shown that individual magnetic poles, or monopoles, do not exist. All magnetic fields originate in electric currents. This is true even at atomic dimensions; circulating (and spinning) electrical charges impart magnetic properties to atoms. However, the concept of multiple pole combinations (e.g., the dipole, quadrupole, and octupole) proved to be very useful for describing the geometries of magnetic fields.

The dipole magnetic field and potential

The most important field geometry is that of a magnetic dipole. This was originally imagined to consist of two equal and opposite magnetic poles that lie infinitesimally close to each other (Appendix A2).