Electromagnetic induction: physics, historical breakthroughs, epistemological issues and textbooks Giuseppe Giuliani Formerly, Dipartimento di Fisica, Universit`adegli Studi, via Bassi 6, 27100 Pavia, Italy.
[email protected] 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: ∂A~ = [E~ +(~v B~ )] dl~ ; E~ = ϕ E Il × · −∇ − ∂t 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 = [E~ +(~vc B~ )] dl~ , where ~vc is the velocity E l × · of the charge. It is shown that, this apparentlyH 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.