ELECTROLOGY. — Under this heading is understood the systematic and, as far as possible, logical development of the science of electricity, independently of its major applications which are reserved for electrical engineering. The division and order of such development clearly leave some margin for arbitrariness. Before the discovery of voltaic electric currents, only the phenomena of the production and distribution of electricity under predominantly static conditions, and of the fields produced by such distributions, were to be considered. This is still the task of electrostatics, which is generally introduced before the consideration of the other parts of e., i.e., the study of electric currents and the complex phenomena by which they are produced and which they in turn produce.
It is not without interest to recall that at the end of the 19th century and in the early decades of the present century there was a certain tendency to begin e. directly with the study of electric currents, taken as the principal fundamental phenomenon, and then to treat electrostatics as a particular chapter of II. But, perhaps also as a consequence of some views of modern physics in which the consideration of the atom as pure electricity, i.e., of the electron and its Coulomb field, is fundamental, the aforementioned tendency met with only partial success, e.g., in the widely used treatise by R. W. Pohl.
I. ELECTROSTATICS
This branch of e. is essentially based (v. ELECTROSTATICS): 1) on the experimentally confirmed fact of the existence of two kinds of electricity and of their well-known properties of attraction or repulsion quantitatively governed by Coulomb’s law; 2) on the experimentally confirmed fact of the existence of insulating and conducting bodies; 3) on the hypothesis that in material bodies there are, in general, contained in equal enormous quantities the two aforementioned kinds of electricity, which, though 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 electricity of different kinds and the repulsion of similar charges of electricity of the same kind is the very important phenomenon of electrification by influence or induction, discovered around the middle of the 18th century. Let us consider the simplest case. Any conducting body, supported by a thread or an insulating handle, is electrified by imparting electricity to II. By reason of the repulsion exerted between all its parts, all this electricity moves to the surface of the body itself. Bringing this body near another similarly insulated and neutral conductor, it is observed that a part of its internal electricity of a kind opposite to that of the first body, which we shall call the inductor, moves to the part of its surface nearest to this, while an equal quantity of electricity of the same kind as that of the inductor accumulates on the part of its surface farthest away. It is evident that if this latter part of the electricity is removed (e.g., by dissipating it to earth through our body by touching with a finger the surface where it is located), we shall obtain a quantity of electricity of a kind opposite to that of the inductor, which can be transferred, at least in part, at will to any other insulated conductor; and by repeating the operation, we can evidently accumulate even considerable quantities of such electricity on suitably arranged conductors (on capacitors).
The machines for the production of static electricity all operate on the basis of more or less automatic applications of the principle just explained, together with a few other secondary devices.
In the development of the theory of electric fields, electrostatics introduced and elaborated the very important notion of electric potential, coinciding with that which Volta had generally intuited and called electric tension. An electric charge in an electric field is always subjected to a force of a certain intensity, direction, and sense; therefore an electric charge moving under the action of this force can perform work, while to force it to move in the opposite direction we should perform an analogous amount of work. On the basis of this consideration we shall say that between two points \(P_1\) and \(P_2\) of an electric field there exists the potential difference \(V_1 - V_2\) when a unit positive charge moving from \(P_1\) to \(P_2\) can perform the work \(V_1 - V_2\), or when to move an equal charge from \(P_2\) to \(P_1\) the same amount of work must be supplied; or again when, moving in the same manner a unit negative charge, the aforementioned production or supply of work is reversed. Since experience assures us that the foregoing depends only on the end points \(P_1\) and \(P_2\) and is independent of the path followed by the charges, we can consider \(V_1 - V_2\) as the difference of potential energy between the points \(P_1\) and \(P_2\) of the system constituted by the electric charges determining the field, plus the said unit electric mass.
From the above it follows that potential is a quantity which we cannot define absolutely, but only by difference with respect to another analogous quantity, e.g., the potential \(V_0\) of the earth. We may add that, merely for the purpose of approximate clarification, it is often said that the notion of electric potential stands to that of electricity as the notion of temperature stands to that of heat.
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1. The Electric Current and Its Laws
If we connect two insulated conductors charged with electricity and at different potentials by means of even a very thin metallic wire, a uniform potential is immediately established throughout the system. In this case it is logical to suppose that in the wire there is a flow of positive electricity in one direction or possibly negative in the other, or even both flows simultaneously, i.e., what is briefly called an electric current; but an instantaneous electric current. Even if we apply to the two conductors the electric machines that had previously charged them and brought them to their respective potentials, it is no longer possible to restore them to these potentials and thus maintain a permanent appreciable current in the wire.This, however, is what a battery easily accomplishes, producing potential differences incomparably smaller than the previous ones. As is well known, A. Volta, following long discussions about an electrical phenomenon brought to light by L. Galvani, which the latter interpreted through the potential electrical properties of living matter, succeeded in constructing what he called a chain, i.e., a series of bodies in successive contacts, forming a closed circuit, in which conditions analogous to those of the chains that automatically formed in Galvani’s experiments were created. But whereas Galvani’s chains always included, besides some metallic elements, an element considered essential, consisting of living matter (the posterior part of the body of a frog just killed), Volta’s chains consisted, besides the metallic elements, of an electrolyte (acidulated water) without any recourse to living matter. The closed chain, electrolyte-zinc-copper branch, had the striking characteristic of possessing a permanent potential difference between the copper and the zinc, which consequently implied the existence of an electric current circulating in the chain. Thus the first electric battery was discovered (1799).
In a short time, numerous other types of batteries were devised that allowed for electric currents more intense than those that could be supplied by the primitive voltaic piles, and thus the problem arose of measuring and studying the effects of such currents. However, the most fundamental laws of currents were not discovered until new and surprising effects of them enabled a significant improvement in research methods. In the first three decades of the 19th century, the concepts of specific electrical resistance and electrical resistance of a given conductor, as well as electromotive force, were clarified, leading to the now well-known Ohm’s and Joule’s laws, which are fundamental to currents in any form.
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2. Magnetism
Knowledge of the most evident among the phenomena we now call magnetic dates back to the most remote antiquity; it is also certain that in the Far East, such phenomena were used for orientational purposes on the great magnet constituted by our Earth more than ten centuries before Christ. The first systematic studies in Europe were those of G. Gilbert (1600). Until that time, and for more than two centuries afterward, magnetism was interpreted by the hypothesis of the existence of two magnetic substances or fluids that, in magnetized bodies, accumulated around the so-called poles; in other words, a mechanical hypothesis of acting-at-a-distance substances, which, especially after Coulomb’s discovery of its well-known analogy with that valid for material masses and for electric charges, seemed to be the best that physics could desire.But what is particularly important to recall here is that, at least after Gilbert, albeit in an indeterminate form, repeated attempts were made to foresee relationships between magnetism and electricity to explain certain phenomena, such as the effects of electric machines or lightning strikes, so much so that the Accademia di Bologna had, as early as 1779 (i.e., even before Coulomb’s law was discovered), set a competition for the study of the analogies between electric and magnetic forces. However, ideas on this subject began to clarify only after H. C. Oersted’s discovery that magnetic needles are deflected by electric currents; a discovery that, refined by Biot and Savart and interpreted by Arago and especially by A. M. Ampère, not only marked the beginning of the broadest and most useful chapter of electricity but also raised the first, perhaps the most serious, doubts about the reliability of mechanical hypotheses in physical interpretations, precisely at the time when those hypotheses had reached their widest acceptance and precisely in a chapter that seemed to owe its very existence to them. It was precisely from the adoption of laws incompatible with the mechanical hypothesis that the most interesting developments of modern physics originated.
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3. Electromagnetism
The deflecting force of every electric current on the poles of a magnetic needle, discovered by Oersted and vaguely interpreted by him as a conflict between electric and magnetic tendencies, was immediately formulated quantitatively by Biot and Savart, still in the sense of action-at-a-distance, and interpreted by Arago as due to a magnetic field wrapped around the current; an interpretation that was also confirmed by a well-known and simple experiment. Based on this, various types of devices were constructed (which were, in essence, the first electromagnetic motors), demonstrating that every magnetic pole tends to rotate around a rectilinear current field in a plane normal to it, with direction and sense depending on the nature of the pole and the direction of the current; just as, in accordance with Newton’s third law of dynamics, devices were also constructed in which rectilinear conductors carrying current tended to rotate around magnetic poles.But what was most striking was the fact that the forces acting between a magnetic pole and rectilinear electric currents, contrary to every mechanistic prediction, were not directed along the line connecting the pole and the current but perpendicularly to the plane passing through the current and the pole. This was incomprehensible without assuming a particular intervention of the intervening medium. It was probably to overcome this difficulty, as well as the older one concerning the interpretation of action-at-a-distance, that M. Faraday arrived at the conception of his lines of force in the medium, and then at the admission of an increasingly important role of the medium in the development of electric and magnetic phenomena.
Another surprising fact was that in the Biot-Savart expression for the force with which a pole is acted upon in the aforementioned direction, depending on its intensity, the intensity of the current, and their distance, the proportionality factor, introduced a priori for the necessary homogeneity of the equation, had the dimensions and thus the nature of a velocity; and that by employing any consistent system of units for the two quantities and performing an experiment, that velocity could be determined and turned out to be equal to the speed of light expressed in the same system. This was the first, at the time very mysterious, connection between an optical quantity and electric and magnetic quantities.
As a brief complement to these fundamental remarks, it should be recalled that Ampère immediately intuited that analogous actions must occur between circuits carrying currents, and thus discovered electromagnetic phenomena; that Faraday, aided by his lines of force, intuited the analogous existence of electromagnetic induction phenomena, for which, by varying the current in a circuit and thus the number of lines of force linked with it, important responses must occur in other circuits (mutual induction) and even in the inducing circuit itself (self-induction). These are the phenomena that, on a large scale, are now employed for the production of all direct and alternating currents, for all their transformations, and in all electric motors; the phenomena that, on a smaller scale, led to the theoretical prediction and production of electromagnetic waves and to their ever more numerous and surprising applications.
V. ELECTROMAGNETIC WAVES
In accordance with Faraday’s ideas about the participation of the media in which material bodies are immersed—bodies that until then had been the sole seat of electromagnetic phenomena—in developing his theory, J. C. Maxwell set out to construct the general expression of the elementary law governing the development of these phenomena in any spatial element, whether in conductive or insulating matter, or even in a vacuum, at any instant of time. This was the broadest scientific synthesis ever attempted. Maxwell, in addition to some earlier publications, expressed it in 1870 in the first edition of his famous Treatise. Although the deductive procedures followed were not always rigorously consistent, and although they appeared more as brilliant leaps than as logical deductions—surprising even the minds of those most scrupulous about scientific exactitude—the Maxwellian theory imposed itself within a few years.It is not possible to briefly explain how one passes from the system of generic differential equations to the concrete solutions of individual problems. But to immediately grasp the extraordinary power of Maxwell’s theory and recognize its imperishable merit, it suffices to recall the particular case that led to the prediction of electromagnetic waves and their identification with light.
The condition that Maxwell’s equations correspond to electromagnetic phenomena, understood in their entirety, implied that in addition to the quantities to be determined—namely, the distribution and surface density of electricity on conductors, and the intensities of the electric and magnetic fields E and H as unknown functions—there should also intervene coefficients expressing certain fundamental properties, such as the conductivity of conductors, the dielectric power, and the magnetic permeability of the media. It was also evident that the coefficient which had mysteriously insinuated itself into the Biot-Savart expression of the electromagnetic law—and was later found to be identifiable with the velocity of light—must likewise be included.
Maxwell, considering the special case of the absence of conductors and hence of zero electric density distributions, observed that the perturbations of the electric and magnetic field intensities E and H, which everywhere remained contained within one another, propagated transversely (i.e., perpendicularly to the plane of those perturbations) with the velocity in question, namely the velocity of light. He therefore concluded that the propagation of the transverse light waves—which until then had been thought to occur in a certain constructed medium endowed with highly mysterious properties (cf. ETHER)—must instead take place in the far simpler ether that he posited as the foundation of his theory.
Everyone knows that the electromagnetic waves thus foreseen were realized by H. Hertz eighteen years later (1888) and what role they play in our daily lives today; that the electromagnetic theory of light advantageously replaced Fresnel’s earlier theory; and that in our customary macroscopic physics it remains fully valid.
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