A Signal Explanation for the Electromagnetic Induction Law

Abstract

We suggest to interpret the electromagnetic as a received electric signal, following a reasoning parallel to that of J. Clerk Maxwell that led to Faraday's law equation. Usually, the solutions of the entire set of equations for electromagnetism are interpreted energet- ically. The law of equation in particular, was interpreted in an energetic sense by Lenz. The interpretation we present is alternative to his one. The reason why we propose it is the con- viction that telecommunications could take advantage of an interpretation of electromagnetism, updated for the technologies now in use. 1. INTRODUCTION M. Faraday calls \magneto electric induction the coupling between a magnet and a piece of metal wire through a vacuum, when detected as transient electric excitation at the terminals of the wire. Before him, among other people, B. Franklin, inventor of the lightning conductor, had anticipated a connection between electricity and magnetism. Already lightning itself can be considered an electric transient that magnetizes metallic objects: cutlery has been said to have been magnetized by lightning. With respect to this experience, the electric excitation observed in the laboratory as an efiect of the movement of a magnet is just a small transient. For us however, Faraday's experiments are more fundamental, because Maxwell was able to connect them to the knowledge his contemporaries had. In the 19th century substantially two interpretations of the speciflc relation between electricity and magnetism gained ground. The flrst, that we might call (A), is more traditional for those days. This describes the magnetic action at a distance in dynamical terms. To discuss action and reaction between magnet and circuit it establishes the equivalence of a magnetized body and a distribution of current by providing a magnetic representation of the electric current. According to Ampµere, the magnetic dipole moment of a circuit with respect to the origin is given by mel = 1 I H r£dl where r is the radius vector from the origin to the point of observation and dl is an element of the electric circuit having an oriented loop. The mechanical action of B on mel is evaluated as a torque t = mel £ B = dD=dt, where D = mr £ v is the angular moment. This formally admits an electric equivalent thanks to the formula mel / IAn, which originates from the representation of the circuits with magnetic shells, of use for calculation of the magnetic potential according to Poisson. Here n is a versor normal to the shell. Hence the magnetic expression for the torque becomes: dmel=dt / mel £ B, or dM=dt / M £ B, where the magnetization M is deflned as a sum over the unit volume of molecular dipole moments mel. H. Lenz suggested that the force due to the magnet may induce within metals, besides the torque, also Faraday's non-mechanical transient ∞ow of electricity. According to the second interpretation of induced current, (B), the magnetic fleld is rather an emanation of the magnet. The electric transient at the terminals of a coil is generated in response to a change of the magnetic ∞ux ' linked with it, that is d' … d(AB), where A is the area enclosed by the coil, and B is the ∞owing magnetic quantity. Whether we conceive of B as a real entity or not, the displacement of the magnet induces in the circuit a current I exactly as would connecting a battery: UK = iLdI=dt, with ' = LI and L the inductance of the wire loop.