Field Theories

The discovery of a connection between electricity and magnetism is usually attributed to Hans Christian Ørsted (1777–1851), who in the winter of 1819 found that a wire carrying a current deflects a magnet. Subsequent experiments determined the dependence of the effect on the relative distance and orientation between the wire and the magnet. Ørsted had pursued his investigations because of his commitment to Naturphilosophie and his belief that "the same forces manifest themselves in magnetism as in electricity" and that the fundamental forces of nature were polar. Ørsted's discovery motivated numerous further investigations, by Francois Arago (1786–1853), Jean-Baptiste Biot (1774–1862), Felix Savart (1791–1841), among others, and particularly by André-Marie Ampère (1775–1836) who formulated the force law describing the interaction between two current-carrying wires. Ampère's guiding assumption was that all electrodynamic phenomena could be understood in terms of the interactions among electric charges and the currents they produce when in motion; a magnet being composed of an aggregate of electric currents.

Michael Faraday (1791–1867), prompted by analysis of Ørsted's and Ampère's investigations and of their theoretical assumptions, carried out a series of perceptive experiments. In 1821 Faraday corroborated that the force on a magnet near a current-carrying wire did not act along the line between the centers of two bodies. Following Sir Isaac Newton's (1642–1727) law of action and reaction, Faraday expected that for every effect of electricity on magnetism there should correspond an effect of magnetism on electricity. Displeased with theories of instantaneous action-at-a-distance, he sought the causes of electric and magnetic effects not only within conductors and magnets, but in the medium around them. He assumed that such effects would take time to propagate through space as "lines of force" that could interact with matter. He came to believe in the reality of these lines of force. In 1831 he found that only a changing current in a wire will induce a current in a nearby second wire. He came to believe that the phenomenon of the induction of a current in a wire near another that carried a time-varying current was due to its "cutting" lines of force. He also discovered that as light passes through glass near a magnet, the polarization of light rotates. Having found such connections among electricity, magnetism, and light, Faraday continued to investigate the properties of the field around ponderable bodies. His conceptualization of lines of force and of fields continued to evolve from the early 1830s through the late 1840s. Constant in this evolution was the belief that the forces between two or more electrically charged bodies were mediated by some influence—the field—that was created by each body separately, propagated in space and acted upon the other charged bodies. It is difficult to summarize Faraday's notions because contemporary language uses some of the same words as he used but with different meanings. And since Faraday did not use mathematics to describe his theoretical models, we cannot rely on that technical language to clarify his works, as in the case of later researchers. What is clear is that Faraday's notion of a field was entwined with his visualization of it in terms of lines of force.

In the 1840s, William Thomson (1824–1907) began to mathematically analyze Faraday's findings in terms of the deformations of a hypothetical material substance, an "ether." Drawing analogies to hydrodynamics and heat conduction, he applied the Laplace/Poisson equation to electrostatics. He showed how to represent work as spread throughout space, and described the ponderomotive force as the tendency of the field to distribute work. He represented magnetic lines of force by vortices and sought a vortex theory of ether and matter.

James Clerk Maxwell (1831–1879) developed extensively this line of research. Following Faraday, Maxwell showed that the lines of electric current and the magnetic lines were linked in a "mutual embrace." He formulated a theory with differential equations that conveyed the reciprocal embrace of constant field lines, and in 1863, for fields varying in time. The latter resulted in transverse waves in the medium, which Maxwell identified as propagating light waves. Like Thomson, Maxwell sought a mechanical account of the ether. He devised a model consisting of cellular vortices and idle wheels that transmit the motion amongst cells and represent electricity.

In Maxwell's theory, the field, which stored and conveyed energy, was fundamental and its displacements constituted charges and currents. Maxwell's theory showed a close causal connection between the separately existing electric and magnetic fields. Heinrich Rudolph Hertz (1857–1894) experimentally demonstrated the existence of invisible electromagnetic waves. Meanwhile, theorists such as Hendrik Antoon Lorentz (1853–1928) interpreted the source terms in Maxwell's equations as densities of charged particles, called electrons. Lorentz developed a theory in which ether and electrons were fundamental entities. He showed that even inside ponderable bodies, electric and magnetic effects are not merely states of matter, but of the fields within.