ELETTROLOGIA. — This designation refers to the systematic and, insofar as possible, logical development of the science of electricity, independently of its major applications, which belong to electrical engineering. The division and order of this development evidently leave a certain margin for arbitrariness. Before the discovery of voltaic electric currents, it was necessary to consider only the phenomena of the production and distribution of electricity under predominantly static conditions, and of the fields produced by such distributions. This remains the task of electrostatics, which is generally treated before consideration of the other parts of electrology, that is, the study of electric currents and of the complex phenomena by which they are produced and which they subsequently produce.
It is not without interest to recall that at the end of the 19th century and during the first decades of the present century there emerged a certain tendency to begin electrology directly with the study of electric currents, taken as the principal fundamental phenomenon, and then to consider electrostatics as a particular chapter within II. But, perhaps also as a consequence of certain views in modern physics, in which the consideration of the atom of pure electricity—that is, the electron and its Coulomb field—is fundamental, the aforementioned tendency achieved only partial success, for example in the widely circulated treatise by R. W. Pohl.
I. ELECTROSTATICS
This branch of e. is essentially based (v. ELETTRICITÀ): 1) on the fact, confirmed by experience, that two kinds of electricity exist, together with their known properties of attraction or repulsion, quantitatively governed by Coulomb’s law; 2) on the fact, likewise confirmed by experience, that insulating and conducting bodies exist; 3) on the hypothesis that material bodies generally contain, in equal and enormous quantities, the two aforesaid kinds of electricity which, although remaining distinct within them, mutually cancel their external effects, so that the said bodies appear neutral to external observers; 4) on the hypothesis that, in conducting bodies, at least one of these two kinds of electricity moves under the influence of any electric field, however weak.An immediate consequence of the attraction between charges, however distributed, of different kinds of electricity, and of the repulsion between analogous charges of electricity of the same kind, is the highly important phenomenon of electrification by influence or induction, discovered around the middle of the eighteenth century. Let us consider its simplest case. Let any conducting body, supported by an insulating thread or handle, be electrified by bringing electricity onto II. Because of the repulsion exerted among all its parts, all this electricity moves to the surface of the body itself. If this body is brought close to another, similarly insulated conductor in a neutral state, it is found that part of the latter’s internal electricity, of a kind opposite to that of the first body, which we shall call the inducing body, moves onto the part of its surface nearest to it, while an equal quantity of electricity of the same kind as that of the inducing body accumulates on the more distant part of its surface. It is evident that, if this latter portion of electricity is eliminated (e.g., by discharging it to earth through our body, by touching with a finger the surface where it is located), we shall acquire a quantity of electricity of a kind opposite to that of the inducing body, transferable, at least in part, at will to any other insulated conductor; and, by repeating the operation, we can evidently accumulate considerable quantities of this electricity on suitably arranged conductors (on capacitors).
Machines for producing static electricity all operate on the basis of more or less systematic applications of the principle just explained and of a few other secondary devices.
In the development of the theory of electric fields, electrostatics introduced and elaborated the highly important notion of electric potential, coinciding with what Volta had brilliantly intuited and called electric tension. An electric charge in an electric field is always subject to a force of a certain intensity, direction, and sense; hence an electric charge, moving under the action of this force, can perform work, whereas to compel it to move in the opposite direction we would have to perform an analogous amount of work. On the basis of this consideration, we shall say that between two points P₁ and P₂ of an electric field there exists a potential difference V₁ - V₂ when a unit positive electric charge, moving from P₁ to P₂, can perform the work V₁ - V₂, or when, in order to move an equal charge from P₂ to P₃, we must supply it with the same amount of work; or again, when, with a unit negative charge moving in the same manner, the foregoing performances or supplies of work are reversed. Since experience assures us that the foregoing depends only on the terminal points P₁ and P₂ and is independent of the path followed by the charges, we may regard V₁ - V₂ as the difference in potential energy between the points P₁ and P₂ of the system constituted by the electric charges determining the field, together with the aforesaid unit electric mass.
It follows from the foregoing that potential is a quantity which we cannot define absolutely, but only by difference with respect to another analogous quantity, e.g., the potential V₃ of the earth. We may add that, simply for purposes of approximate clarification, it is often said that the notion of electric potential is related to that of electricity as the notion of temperature is related to that of heat.
II. THE ELECTRIC CURRENT AND ITS LAWS
If we connect two insulated conductors charged with electricity and at different potentials by means of even the thinnest metal wire, a uniform potential is immediately established throughout the system. In this case it is logical to suppose that a flow of positive electricity in one direction, or possibly of negative electricity in the other, or even both flows simultaneously, has taken place in the wire—that is, what is briefly called an electric current; but an instantaneous electric current. Even if we apply to the two conductors the electrical machines that had previously electrified them and brought them to their respective potentials, it is no longer possible to restore those potentials and thus maintain a permanent appreciable current in the wire.This, on the other hand, is accomplished with the greatest ease by a voltaic cell, which establishes a difference of potential incomparably smaller than the preceding ones. As is well known, A. Volta, following lengthy discussions concerning a phenomenon of an electrical nature brought to light by L. Galvani, who interpreted it through hypothetical electrical properties of living matter, succeeded in constructing what was called a chain, that is, a series of bodies in successive contact, forming a closed circuit, in which conditions analogous to those of the chains that were formed automatically in Galvani’s experiments occurred. But whereas Galvani’s chains always consisted, in addition to certain metallic elements, of an element considered essential and constituted by living matter (the hind part of the body of a recently killed frog), Volta’s chains consisted, in addition to metallic elements, of an electrolyte (acidulated water), without any recourse to living matter. The closed chain, copper–electrolyte–zinc–copper, displayed the striking characteristic of possessing a permanent difference of potential between the copper and the zinc, which consequently implied the existence of an electric current circulating through the chain. Thus the first electric cell was discovered (1790).
In a short time, numerous other types of cells were devised, enabling the production of electric currents more intense than those supplied by the primitive voltaic cells; thus the problem arose of measuring these currents and studying their effects. The most fundamental laws of currents, however, were not reached until new and surprising discoveries concerning their effects made it possible to improve the means of investigation considerably. During the first three decades of the nineteenth century, the concepts of specific electrical resistance and of the electrical resistance of a given conductor, as well as that of electromotive force, were clarified; the well-known laws of Ohm and Joule were then established, fundamental for currents in whatever form they may occur.
III. MAGNETISM
Knowledge of the existence of the most evident among the phenomena that we call magnetic goes back to the remotest antiquity; it is also certain that, in the Far East, uses of these phenomena for purposes of orientation were in practice, based on the great magnet constituted by our earth, more than ten centuries B.C. The first systematic studies in Europe were those of G. Gilbert (1600). Until that time, and for more than two centuries thereafter, magnetism was interpreted by the hypothesis of the existence of two magnetic substances or fluids which, in magnetized bodies, accumulated around the so-called poles; that is, by a mechanistic hypothesis of substances acting at a distance, which, especially after Coulomb’s discovery of its well-known analogy with the law applicable to material masses and to electric charges, seemed to be the best that physics could desire.Here, however, it is particularly important to recall that, at least after Gilbert, although in an indeterminate form, relations between magnetism and electricity were repeatedly anticipated in order to interpret certain phenomena occurring in discharges from electrical machines and in certain lightning strikes, so much so that the Bavarian Academy had, as early as 1774 (that is, even before the discovery of Coulomb’s law), offered a prize for the study of the analogies between electrical forces and magnetic forces. But ideas on the subject began to become clear only after H. C. Oersted’s discovery that magnetic needles are deflected by electric currents; this discovery, clarified by Biot and Savart and interpreted by Arago and, above all, by A. M. Ampère, not only marked the beginning of the broadest and most useful chapter of electrology, but also raised the first, and perhaps the most serious, doubts concerning the reliability of mechanistic hypotheses in physical interpretations—precisely at the time when those hypotheses had attained their widest acceptance, and precisely in a chapter that seemed to owe its existence to them. Yet it was precisely from the adoption of laws incompatible with the mechanistic hypothesis that the most interesting developments of modern physics arose.
IV. ELECTROMAGNETISM
The deflecting force exerted by every electric current on the poles of a magnetic needle, discovered by Oersted and obscurely interpreted by him as a conflict between electrical and magnetic tendencies, was soon quantitatively formulated by Biot and Savart, still in terms of action at a distance, and interpreted by Arago as being due to a magnetic field wrapped around the current—an interpretation that was likewise confirmed by means of a very well-known and simple experiment. On this basis various types of apparatus were constructed (which were, in essence, the first electromagnetic motors), demonstrating that every magnetic pole tends to rotate around every straight current in a plane normal to it, in a direction and sense dependent on the nature of the pole and the direction of the current; likewise, in accordance with the third principle of Newtonian dynamics, apparatus were constructed in which straight conductors carrying a current tended to rotate around magnetic poles.But what most impressed observers was the fact that the forces acting between a magnetic pole and straight electric currents, contrary to every mechanistic expectation, were not directed along the line joining the pole and the current, but perpendicular to the plane passing through the current and the pole. This was incomprehensible without assuming a particular intervention by the intervening medium. And it was probably in order to overcome this difficulty, in addition to the older difficulty of interpreting action at a distance, that H. Faraday arrived at the conception of his lines of force in the medium, and subsequently at the admission of an ever more important intervention by that medium in the course of electrical and magnetic phenomena.
Another surprising fact was that, in Biot and Savart’s expression for the force by which a pole is acted upon in the aforementioned direction, as a function of its intensity, the intensity of the current, and their distance, the proportionality factor, introduced a priori, proves, by the necessary homogeneity of the equation, to have the dimensions—and therefore the nature—of a velocity; and that, when any coherent system of units of measurement for these quantities is employed and an experiment is carried out, that velocity can be determined and proves equal to the velocity of light, expressed naturally in that same system. This was the first, at that time highly mysterious, association of an optical quantity with electrical and magnetic quantities.
As a brief complement to these fundamental indications, it should be recalled that Ampère immediately intuited that analogous actions to those described above must also occur between circuits carrying currents, and thus discovered electrodynamic phenomena; and that Faraday, aided by his lines of force, intuited the analogous existence of electromagnetic induction phenomena. In these phenomena, by varying the current in a circuit and hence the quantity of lines of force linked with it, various important effects were to be produced on other circuits (mutual induction) and also on the inducing circuit itself (self-induction). These are the phenomena that, on an enormous scale, are employed today in the production of all direct and alternating currents, in all their transformations, and in all electric motors; they are the phenomena that, on a more modest scale, led to the theoretical prediction and production of electromagnetic waves and to their increasingly numerous and remarkable applications.
V. ONDE ELETTROMAGNETICHE
Confirming Faraday’s ideas concerning the participation, in the unfolding of electromagnetic phenomena, of the media in which the material bodies that until then had been their sole locus are immersed, J. C. Maxwell set out to construct the general expression of the elementary law governing the development of those phenomena in any spatial element occupied by conducting or insulating matter, or even vacant, at any element of time. This was the broadest scientific synthesis ever attempted. Maxwell, in addition to some earlier publications, expounded it in 1870 in the first edition of his celebrated Treatise. Although the deductive procedures followed were not always rigorously consistent, and although here and there what appeared were rather flashes of genius than logical deductions, thereby surprising and even scandalizing certain practitioners of extreme scientific exactitude, Maxwell’s theory established itself within a few years.It is not possible to say briefly how one passes from the system of general differential equations to the concrete solutions of individual problems. But to become immediately convinced of the extraordinary power of Maxwellian theory, and to recognize its imperishable merit, it will suffice to recall the particular case that led to the prediction of electromagnetic waves and to the electromagnetic theory of light.
The condition that Maxwell’s equations should correspond to electromagnetic phenomena, understood in their entirety, implied the intervention in them, besides the quantities to be determined—namely, the distribution of electricity at surface density on conductors ρ, and the intensities of the electric and magnetic fields E and H as unknown functions—also of coefficients expressing certain fundamental properties, such as the conductivity σ of conductors, the dielectric constant ε, and the magnetic permeability μ of media. There also evidently had to enter that coefficient which had been seen to insinuate itself mysteriously into Biot and Savart’s expression of the electromagnetic law and which subsequently proved identifiable with the speed of light. Now Maxwell, considering the particular case of the absence of conductors, and therefore of null distributions of electric density, observed that the perturbations of the intensities of the electric and magnetic fields E and H, which were everywhere interconnected, propagated transversely (that is, perpendicularly to the plane of those perturbations) with the speed f_{eff} = ε, coinciding, that is, with the speed of light. He therefore thought that the propagation of the transverse waves of light, which until then had been considered to take place in an ether devised ad hoc and necessarily endowed with very mysterious properties (v. ETERE), ought instead to take place in the much simpler ether that was to serve as the basis of his theory. Everyone knows that the electromagnetic waves thus predicted were produced by H. Hertz eighteen years later (1888), and what role they play today in our everyday life; that the electromagnetic theory of light replaced Fresnel’s earlier theory to considerable advantage; and that in our customary macroscopic physics it is still fully valid.
#### ELETTROSHOCK : V. SHOCK.