Уравновешенные концентраторы потока и их применение для снижения электромагнитных сил в магнитных системах

Magnetic flux concentrators, viz., bodies with radial cuts introduced into the field of a magnet, substantially affect the magnitude and distribution of electromagnetic forces in magnetic systems. The fields of magnetic systems with flux concentrators are calculated in the perfect conduction approximation, which is valid in the case of a clearly pronounced skin effect. The possibility of complete or partial compensation of forces acting on the concentrator is demonstrated for some model problems. At the same time, it is shown that the placement of the concentrator near the winding of the magnet can reduce the forces acting on the winding. Therefore, the concentrator unloads the winding, remaining balanced completely or partly. As a result, the requirements of devices ensuring the durability of the magnetic system are substantially reduced.

The transmission of electric waves around the Earth's surface

The value of the magnetic force at a point on the earth's surface, due to a simple oscillator placed on the surface with its axis normal to the surface, has been recently calculated by Love for a wave-length of 5 kilom. at certain distances from the oscillator. His results for the case of perfect conduction are the same as the corresponding series when the surface of the earth is supposed to be imperfectly conducting, The object of the present communication is to obtain the general formula for the case of imperfect conduction. Let r, θ, ϕ be the polar co-ordinates of a point, where r is its distance from the centre of the earth, θ its angular distance from the oscillator, E r , E θ , E ϕ the components of the electric force, and α, β, γ , the corresponding components of the magnetic force. Then, Since there is symmetry round the axis of the oscillator, α =0, β =0, γ =0; and throughout space outside the surface

The transmission of electric waves over the surface of the Earth

An analytical solution of the general equation of electrodynamics is obtained for the case of waves generated by a vibrating doublet in presence of a conducting sphere, and is adapted to obtain the known solution for perfect conduction, and the correction for moderate resistance, such as that of sea-water. The known solution is expressed by the sum of a series involving zonal harmonics, and the correction by a similar series. Different results have been obtained by different writers who have investigated the numerical value of the former sum. In the paper a new method of summing the series is explained, and worked out in detail for the wave-length 5 km. In the case of perfect conduction the result confirms that found by H. M. Macdonald. The effect of resistance is found to be a slight increase of the strength of the signals at considerable distances, counteracting to some small extent the enfeebling effect of the curvature of the surface. A comparison is instituted between the results of the theory and those of recorded experiments. From these it had previously been inferred that the diffraction theory fails to account for the facts; but, after a discussion of the experimental evidence, it appears that the observations may admit of a different interpretation, according to which the results of the diffraction theory would be in good agreement with those of daylight observations at great distances.

IV. The transmission of electric waves over the surface of the Earth

1. Ever since the time, about 1902, when Marconi first succeeded in sending wireless signals across the Atlantic the question of explaining the mechanism of such transmission has attracted attention among mathematicians. The question may be put in the following form:—The electric waves generated by the sending apparatus differ from waves of light only by having a longer wave-length, which is, nevertheless small compared with the radius of the earth; and the curved surface of the earth may therefore be expected to form a sort of shadow, effectively screening the receiving apparatus at a distance. How, then, does it happen that in practice the waves penetrate into the region of the shadow ? Unfortunately, the question has been investigated by different methods without adequate co-ordination, and the results that have been obtained are somewhat discordant. In these circumstances it appears to be desirable to undertake a critical survey of the question. The various theoretical investigations may be classified as developments of three suggestions: (l) The imperfectly conducting quality, or resistance, of the material, generally sea-water, over which the transmission takes place, may cause the effect observable at a distance to be greater than it would be if the material were perfectly conducting. (2) Owing to the numerical relations connecting the actual wave-lengths used in practice, the size of the earth, and the distances involved, the amount of diffraction, even in the case of perfect conduction, may be greater than would, at first sight, be expected. (3) Transmission through the atmosphere may be notably different from transmission through a homogeneous dielectric. We may refer to these suggestions briefly as the “resistance theory,” the “diffraction theory,” and the “atmospheric theory.” It may be said at once that the atmospheric theory has arisen from the alleged failure of the other two, and that it has not yet been formulated in such a way as to admit of being tested in the same precise analytical fashion as they can. It is still rather speculative and indefinite. In what follows I propose to attend chiefly to the first two suggestions, and to investigate the result that can be obtained by combining them.

Experimental researches in electricity: Twelfth series

The object of the present series of researches is to examine how far the principal general facts in electricity are explicable on the theory adopted by the author, and detailed in his last memoir, re­lative to the nature of inductive action. The operation of a body charged with electricity, of either the positive or negative kind, on other bodies in its vicinity, as long as it retains the whole of its charge, may be regarded as simple induction , in contradistinction to the effects which follow the destruction of this statical equilibrium, and imply a transit of the electrical forces from the charged body to those at a distance, and which comprehend the phenomena of the electric discharge . Having considered, in the preceding paper, the process by which the former condition is established, and which consists in the successive polarization of series of contiguous particles of the interposed insulating dielectric; the author here proceeds to trace the process, which, taking place consequently on simple induction, terminates in that sudden, and often violent interchange of electric forces constituting disruption , or the electric discharge. He investigates, by the application of his theory, the gradual steps of transition which may be traced between perfect insulation on the one hand, and perfect conduction on the other, derived from the varied degrees of specific electric relations subsisting among the particular substances interposed in the circuit: and from this train of reasoning he deduces the conclusion that induction and conduction not only depend essentially on the same principles, but that they may be regarded as being of the same nature, and as differing merely in degree. The fact ascertained by Professor Wheatstone, that electric conduction, even in the most perfect conductors, as the metals, requires for its completion a certain appreciable time, is adduced in corrobo­ration of these views; for any retardation, however small, in the transmission of electric forces can result only from induction; the degree of retardation, and, of course, the time employed, being proportional to the capacity of the particles of the conducting body for retaining a given intensity of inductive charge. The more perfect insulators, as lac, glass and sulphur, are capable of retaining electri­city of high intensity; while, on the contrary, the metals and other excellent conductors, possess no power of retention when the in­tensity of the charge exceeds the lowest degrees. It would appear, however, that gases possess a power of perfect insulation, and that the effects generally referred to their capacity of conduction, are only the results of the carrying power of the charged particles either of the gas, or of minute particles of dust which may be present in them: and they perhaps owe their character of perfect insulators to their peculiar physical state, and to the condition of separation under which their particles are placed. The changes produced by heat on the conducting power of different bodies is not uniform; for in some, as sulphuret of silver and fluoride of lead, it is increased; while in others, as in the metals and the gases, it is diminished by an augmentation of temperature.