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 $\u222el(E\u2192+v\u2192c\xd7B\u2192)\xb7dl\u2192$, where $v\u2192c$ 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 $v\u2192c$ 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.

## References

*t*

_{1},

*t*

_{2}, provided that the distance

*d*between the two points satisfies the equation: $d\u2264c(t2\u2212t1)$. This locality condition is necessary but not sufficient for interpreting an equation causally. For instance, let us consider the law $F\u2192=dp\u2192/dt$. As the momentum varies over time, we are inclined to interpret this equation by saying that the force $F\u2192$ “causes” the momentum variation. However, there are situations where the change in momentum “causes” a force. Consider, for example, a completely absorbing surface

*S*hit perpendicularly by a monochromatic beam of light directed along the negative direction of the

*x*axis. In this case, if

*N*is the number of photons absorbed per unit time, the surface momentum

*P*obeys: $dPx/dt=\u2212Nh\nu /c=Fx$, and we can say that the variation of the photons' momentum has produced a radiative force

_{x}*F*on the surface

_{x}*S*. A similar situation is found in the kinetic theory of gases: the pressure (force per unit area) on the walls is due to the exchange of momentum with the particles.

*causes*an electric field (and symmetrical statements for the equation of the

*curl*of the magnetic field). See, for instance, Ref. 20, where statements of this kind are considered to be conceptual misconceptions that one should avoid in teaching. The equation states only a

*relation*between the fields as the charges produce them: see also Ref. 21. This is well illustrated by the equations that yield the fields produced by a point charge in arbitrary motion. The electric and magnetic fields are given by equations that depend on the charge's velocity and acceleration. These equations are independently deduced one from the other (see, for instance, Ref. 15, pp. 870–879). Only ex-post, do we find that the two fields are

*related*by the equation

*t*to what happens simultaneously on an arbitrary surface having the line as a contour. This habit is widespread in textbooks for high school in Italy but not—for instance—in textbooks published in the United States.

*American Journal of Physics*and

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