Teaching Electromagnetism in elementary physics or upper high school courses

Traditionally, Electromagnetism is taught following the chronological development of the matter. The final product of this path is a presentation of Electromagnetism realized by adding one layer over another with the risk of transferring concepts and formulae from Electrostatics to Electrodynamics. In this paper, we suggest a new approach based on the idea that the matter should be presented within the conceptual framework of Maxwell-Lorentz-Einstein Electromagnetism. This approach is founded on the concept of a field as a primary theoretical entity and on the statement that a point charge produces, in general, an electric and a magnetic field and that the force exerted by these fields on a point charge is the Lorentz's force. Developing this idea, one finds that macroscopic laws corroborated by experiments have a microscopic origin. It also follows that the electromotive force induced in a closed conducting circuit must be defined as the line integral of Lorentz's force on a unit positive charge. This definition leads to a local law of electromagnetic induction, Lorentz's invariant for rigid and filiform circuits. This law contrasts with what Feynman labeled as the "flux rule" - generally taught in textbooks and teaching practices - downgrading it from the status of physical law. Particular attention is given to the teaching dilemma of Maxwell's equations: ignore them, write them in integral form, or speak of them, focusing on their conceptual and physical meaning.