Electromagnetic induction: physics, historical breakthroughs, epistemological issues and textbooks

Abstract

The discovery of Electromagnetism by Ørsted (1820) initiated an "extraordinary decennium" ended by the discovery of electromagnetic induction by Faraday (1831). During this decennium, in several experiments, the electromagnetic induction was there, but it was not seen or recognized. In 1873, James Clerk Maxwell, within a Lagrangian description of electric currents, wrote down a 'general law of electromagnetic induction' given by, in modern form and with standard symbols:In Maxwell's derivation, the velocity appearing in this equation, is the velocity of the line element dl. A modern reformulation of Maxwell's general law, starts with the definition of the induced emf as the• dl, where v c is the velocity of the charge. It is shown that, this apparently minor difference, is fundamental. The general law is a local law: it correlates what happens in the line at the instant t to the values of quantities at the points of the line at the same instant t. For rigid circuits, it is Lorentz invariant. If expressed in terms of the magnetic field, it allows -in the approximation of low velocities -the derivation of the "flux rule", for filiform circuits.The "flux rule" is a calculation tool and not a physical law because it not always yields the correct prediction, it does not say where the induced emf is localized, it requires ad hoc choices of the integration paths and -last but not least -because, if physically interpreted, it implies physical interactions with speeds higher than that of light. Maxwell's general law has been rapidly forgotten; instead, the "flux rule" has deeply taken root. The reasons appear to be various. One is plausibly related to the idea that the vector potential does not have physical meaning, a stand clearly assumed by Hertz and Heaviside at the end of the Nineteenth century. An analysis of university textbooks, spanned over one century, assumed to be representative on the basis of the authors and/or on their popularity or diffusion, suggests that other reasons are related to the habit of presenting electromagnetic phenomena following the historical development and to the epistemological stand according to which physical laws must be derived from experiment without the need of recurring, soon or later, to an axiomatic presentation of the matter. On the other hand, the rooting of the "flux rule" has been certainly favored by its calculation utility: this practical feature has overshadowed its predictive and epistemological weakness.