Phenomena associated with magnets have been known for many centuries. The fact that a compass needle experiences a torque which aligns it in a particular direction was known to Chinese mariners before 1100, and in Europe about a century later; it was vital to the navigators of the great age of exploration. We now interpret this phenomenon as due to the interaction of the needle with the earth's magnetic field. The torque on the compass needle is similar to that on an electric dipole in an electric field; the needle behaves like a magnetic dipole and the fact that it experiences no net force tells us that it carries no net ‘magnetic charge’.

Until 1819 the connection between magnetism and electricity was unknown, but in that year the Danish physicist Oersted observed that an electric current flowing in a wire deflected a nearby compass needle. Conversely, by Newton's law of action and reaction, the compass needle could be expected to exert forces on the current carrying wire. Oersted's discovery created great excitement in scientific academies throughout Europe and in particular stimulated the more detailed investigations of Biot and Savart, and of Ampère, in Paris. It was Ampère who found that two current carrying wires interacted by magnetic forces.

To account for the experimental phenomena it is natural to introduce a magnetic field B(r), which is determined by the magnets and current flows in the system under consideration, and through which different parts of the system interact.