  The discovery of Electromagnetism by Oersted (1820) started 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. Faraday built up a
local theory of electromagnetic induction based on the idea that there is an
induced current when there is an intersection between lines of magnetic force
and a conductor in relative motion. In 1873, Maxwell, within a Lagrangian
description of electric currents, wrote down a 'general law of electromagnetic
induction' in which a fundamental role is played by the vector potential. A
modern reformulation of Maxwell's general law is based on the definition of the
induced emf as the line integral of the Lorentz force on a unit positive charge
and the use of the equation that relates the electric field to the potentials.
Maxwell's general law has been rapidly forgotten; instead, the "flux rule" has
deeply taken root. The "flux rule" 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. It is not a physical law but only a calculation tool. To
understand why Maxwell's `general law' has been forgotten, also a sample of
representative textbooks, distributed over about a century, has been analyzed.
In this framework, a part of the paper deals with the idea of rotating lines of
magnetic force, falsified by Faraday, but common in the first decades of the
Twentieth century and astonishingly resumed recently. It is shown that this
hypothesis is incompatible with Maxwell - Lorentz - Einstein electromagnetism
and that it is falsified also by recent experiments. Finally, the
electromagnetic induction in some recent research papers is briefly discussed.
