As documented by textbooks, the teaching of electromagnetic induction in university and high school courses is primarily based on what Feynman labeled as the “flux rule,” downgrading it from the status of physical law. However, Maxwell derived a “general law of electromagnetic induction” in which the vector potential plays a fundamental role. A modern reformulation of Maxwell's law can be easily obtained by defining the induced electromotive force as l(E+vc×B)·dl, where vc is the velocity of the positive charges which, by convention, are the current carriers. Maxwell did not possess a model for the electric current. Therefore, in his law, he took vc to be the velocity of the circuit element containing the charges. This paper aims to show that the modern reformulation of Maxwell's law governs electromagnetic induction, and the “flux rule” is not a physical law but only a calculation shortcut that does not always yield the correct predictions. This paper also tries to understand why Maxwell's law has been ignored, and how the “flux rule” has taken root. Finally, a section is dedicated to teaching this modern reformulation of Maxwell's law in high schools and elementary physics courses.

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The name “electromotive force” is misleading, because, as we know, the electromotive force is not a force: it has the dimensions of an electric potential, and it is measured in volts. Since a more suitable name has not been invented, we shall keep on using the same name. It is worth noting that, today's use of some historical names appears to have no justification. For instance, we find that the magnetic field B, recovering a nineteenth century's denotation, is called “magnetic induction vector”; and the field H, whose sources are the current densities J, is called “magnetic field.” Then one has to stress that what appears in the expression of the Lorentz force is the magnetic induction vector and not the magnetic field. Let us also mention the conceptual confusion created by the habit of recalling the contributions of different researchers in the name of a formula, a habit that often badly distorts history. For instance, as for the “flux rule,” we have encountered the denomination “Faraday–Neumann–Lenz law,” or variants at will. The presence of Lenz is justified by the sign (−) that appears in the formula, but Faraday and Neumann have nothing to do with the “flux rule.”
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The above discussion reminds us of another question. Let us consider Maxwell's equation:
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The applicability of this proposal to high schools depends on the mathematical background of the students. It is likely applicable in Italy's scientific Lyceums, where mathematical knowledge is sufficient to treat electromagnetic induction as here suggested.
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