  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
$\oint_l (\vec E +\vec v_c\times \vec B)\cdot\vec{dl}$, where $\vec v_c$ 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 $\vec v_c$ 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 that the ``flux rule''
is not a physical law but only a calculation shortcut that does not always
yield the correct predictions. The 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.
