Maxwell's electromagnetic theory

By about 1860 through the work of Neumann, Weber, Helmholtz and Felici electrodynamics was regarded as the science has finally systematized, with clearly defined boundaries. Basic research is now, it seemed, we had to go on the way of finding and the withdrawal of all the consequences of the established principles and their practical application, which has already begun and ingenious technology.

However, the prospect of a quiet work violated the young Scottish physicist James Clerk Maxwell (1831-1879), pointing to a much wider range of applications of electrodynamics. With good reason Duhem wrote: "There is no logical necessity is not pushed to come up with a new Maxwell electrodynamics; he was guided only by some analogies and the desire to complete the Faraday's work in the same spirit as the works of Coulomb and Poisson were completed Ampere electrodynamics, and perhaps an intuitive sense of the electromagnetic nature of light. "

Perhaps the main motivation that caused Maxwell to do the work, does not require a science of those years, was a delight to the new ideas of Faraday, so original, that the scientists of the time were not able to accept them and learn. Generation of theoretical physicists, brought up on the concepts and mathematical elegance of the works of Laplace, Poisson and Ampere, Faraday thought seemed too vague and experimenters - too tricky and abstract. An odd thing: Faraday, which in its formation was not a mathematician (he began his career as a peddler in a bookshop, and then enrolled in Davie laboratory for position poluassistenta-poluslugi), felt the urgent need for the development of a theoretical method is as effective as and mathematical equations. Maxwell guessed it.

"Getting to the study of labor Faraday - wrote Maxwell in the preface to his famous" Treatise ", - I have determined that this method of understanding the phenomena was also a mathematical, although not represented in the form of conventional mathematical symbols, I also found that this method can be expressed as in the usual mathematical form, and thus, compared with the methods of professional mathematicians.

For example, Faraday saw lines of force that permeate all of space, where mathematicians saw centers of forces, attracting at a distance; Faraday saw a medium where they saw nothing but distance. Faraday supposed sources and causes of phenomena in real actions that take place in an environment that they were satisfied with what they find in the power of action at a distance, attributed to electric fluids.

When I translated what I considered the ideas of Faraday, in mathematical form, I have found that in most cases the results of both methods coincide, so that they explained the same phenomenon, and displayed the same laws of action, but that Faraday's methods resembled those in which we begin with the whole and arrive at the private through the analysis, while the conventional mathematical methods based on the principle of moving from particulars and construction of the whole by synthesis.

I also found that many of the public mathematicians fruitful research methods could be much better expressed in terms of the ideas emanating from the work of Faraday than in their original form. "

As for the mathematical method of Faraday, Maxwell somewhere says that mathematicians who thought Faraday method is devoid of scientific accuracy, do not come up with anything better than to use hypotheses about the interaction of things that do not have a physical reality, as, for example, the current elements " which arise out of nothing, pass the wire section and then again into nothingness. "

To give the ideas of mathematical form Faraday, Maxwell began by saying that he had made electrodynamics dielectrics. Maxwell's theory is directly related to Mossotti theory. While Faraday in his theory of dielectric polarization deliberately left open the question of the nature of electricity, Mossotti, a supporter of Franklin's ideas, imagines electricity as a single fluid, which he calls the ether, and that, in his opinion, there is a certain degree of density in all molecules . When the molecule is under the force induction. Live concentrated at one end of the molecule and diluted on the other: because of this, there is a positive force on the first end and equal to it negative - on the second.

Maxwell entirely accepts this concept in his "Treatise," he writes:

".Elektricheskaya Dielectric polarization is a state of deformation in the body which comes under the influence of electromotive force and which disappear simultaneously with the termination of the force. We can give ourselves it as something that can be called electric displacement produced by the electromotive force. When the electromotive force acts in a conductive medium, it causes a current there, but if the medium is non-conductive or dielectric, the current can not pass through this medium. Electricity, however, it is shifted in the direction of the electromotive force and the magnitude of the shift depends on the magnitude of the electromotive force. If the electromotive force is increased or decreased in the same proportion, respectively, increases or decreases and the electric displacement.

The displacement is measured by the amount of electricity per unit surface intersecting with increasing displacement from zero to a maximum value. This is, therefore, a measure of the electric polarization. "

If polarized dielectric consists of a plurality of insulating medium in the scattered conductive particles in which electricity is distributed in a certain way, then any change in the polarization state must be accompanied by change in the distribution of electricity in each particle, ie. E. This electric current, although only a limited volume of the conductive particles. In other words, every change of the polarization state is accompanied by the displacement current.

In the same "Treatise" Maxwell says, "Changes in the electrical bias, obviously, cause electric currents. These currents may exist only during a change in bias, and because offset can not exceed a certain value without causing disruptive discharge, these currents can not continue indefinitely in the same direction, like the currents in the conductors. "

After Maxwell introduces the concept of field strength, which is a mathematical interpretation of the concept of Faraday force fields, he writes mathematical relationship for the aforementioned concepts of electric displacement and displacement current. He comes to the conclusion that the so-called charge of the conductor is the surface charge of the surrounding dielectric, the energy stored in the dielectric in the form of a voltage condition that the movement of electricity subject to the same conditions as the motion of an incompressible fluid.

Maxwell himself summarizes his theory as "an electrifying energy is concentrated in a dielectric medium, whether solid, liquid or gas, dense medium, or sparse or completely devoid of ponderable matter, as long as she was able to transmit the electrical action.

Energy is contained in each point of the medium in the form of the deformation state, called the electrical polarization, the value of which depends on the electromotive force acting at this point ...

The dielectric fluids electric polarization is accompanied by tension in the direction of the induction lines and equal to the pressure in all directions perpendicular to the lines of induction; the magnitude of this tension or pressure on the unit area is numerically equal to the energy per unit volume at this point. "

It is difficult to express more clearly the basic idea of ​​this approach is the idea of ​​Faraday: the place in which electrical phenomena occur, is Wednesday. As if to emphasize that this is the most important thing in his treatise, Maxwell finishes it with the following words: "If we accept this medium as a hypothesis, I believe that it should occupy a prominent place in our research and that we should try to construct a rational view all the details of its action, and that was my constant aim in this treatise. "

Grounded theory of dielectrics, Maxwell carries its concepts with the necessary adjustments to create a theory of magnetism and electromagnetic induction. All his theoretical construction, he sums up in a few equations have now become famous: in the six equations of Maxwell.

These equations are very different from the usual equations of mechanics - they define the structure of the electromagnetic field.

While the laws of mechanics are applicable to the fields of space, where there is matter, Maxwell's equations apply to the whole space, regardless of whether there are or are not present there, the body or electrical charges. They determine the changes in the field, while the laws of mechanics determine the change of material particles. In addition, Newtonian mechanics refused action continuity in space and time, whereas Maxwell's equations establish the continuity of the phenomena. They link the events related in time and space: on a given field of "here" and "now" we can deduce the state of the field in close proximity to the times. Such an understanding of the field is absolutely consistent with the idea of ​​Faraday, "but is in insurmountable conflict with the two-century tradition. Therefore there is nothing surprising in the fact that it met resistance.

The objections put forward against Maxwell's theory of electricity, were numerous and were treated as the fundamental concepts laid the foundation of the theory, and perhaps to an even greater extent, to the very free manner, which Maxwell uses in deriving consequences from it.

Maxwell step by step builds his theory using the "finger dexterity," as aptly put Poincare, referring to the theological tension, which sometimes allow themselves to scientists in the formulation of new theories. When in the course of constructing the analytical Maxwell encounters an apparent contradiction, he did not hesitate to overcome it with the help of discouraging liberties.

For example, it costs nothing to exclude any member, to replace the inappropriate expression sign reversed, replace the value of a letter. For those who admired infallible logical construction Ampere electrodynamics, Maxwell's theory was to make a bad impression.

Physicists it could not be brought into harmonious order, t. E. Free from logical errors and inconsistencies. But, on the other hand, they can not abandon the theory, which, as we shall see later, is organically linked with the optics electricity. Therefore, at the end of the last century, the largest physics adhered to the thesis put forward in 1890 by Hertz: time reasoning and calculations by which Maxwell arrived at his theory of electromagnetism, full of mistakes that we can not fix it, take six-Maxwell equations as a starting hypothesis, as a postulate, which will build the whole theory of electromagnetism. "The main thing in Maxwell's theory - it's Maxwell's equations" - says Hertz.

Veselovsky O. Shneiberg A. I "Essays on the History of Electrical Engineering"