Dynamic potentials and the field of the moving charges

Transcription

1 Dynamic potentials and the field of the moing charges F. F. Mende Abstract Is deeloped the concept of scalar-ector potential, in which within the framework Galiley conersions the scalar potential of charge depends on speed. This made it possible to obtain conersions pour on upon transfer of one inertial system to another and to eplain such phenomena as phase aberration and transerse Doppler effect. 1. Dynamic potentials and the field The method, which is demonstrated in the second chapter, that is concerned the introduction of total deriaties pour on, it is passed in the substantial part still by Hertz [1]. Hertz did not introduce the concept of ector potentials, but he operated only with fields, but this does not diminish its merits. It made mistakes only in the fact that the electrical and magnetic fields were considered the inariants of speed. But already simple eample of long lines is eidence of the inaccuracy of this approach. With the propagation of wae in the long line it is filled up with two forms of energy, which can be determined through the currents and the oltages or through the electrical and magnetic fields in the line. And only after wae will fill with electromagnetic energy all space between the generator and the load on it it will begin to be separated energy. I.e. the time, by which stays this process, generator epended its power to the filling with energy of the section of line between the generator and the load. But if we begin to 1

2 moe away load from incoming line, then a quantity of energy being isolated on it will decrease, since. the part of the energy, epended by source, will leae to the filling with energy of the additional length of line, connected with the motion of load. If load will approach a source, then it will obtain an additional quantity of energy due to the decrease of its length. But if effectie resistance is the load of line, then an increase or the decrease of the power ependable in it can be connected only with a change in the stress on this resistance. Therefore we come to the conclusion that during the motion of the obserer of those of relatiely already eisting in the line pour on must lead to their change. The productiity of this approach with the application of conersions of Galileo will be demonstrated in this chapter. Being located in assigned IMS, us interest those fields, which are created in it by the fied and moing charges, and also by the electromagnetic waes, which are generated by the fied and moing sources of such waes. The fields, which are created in this IMS by moing charges and moing sources of electromagnetic waes, we will call dynamic. Can sere as an eample of dynamic field the magnetic field, which appears around the moing charges. As already mentioned, in the classical electrodynamics be absent the rule of the conersion of electrical and magnetic pour on upon transfer of one inertial system to another. This deficiency remoes STR, basis of which are the coariant of the Lorenz conersions. With the entire mathematical alidity of this approach the physical essence of such conersions up to now remains uneplained [2]. In this diision will made attempt find the precisely physically substantiated ways of obtaining the conersions pour on upon transfer of one IMS to another, and to also eplain what dynamic potentials and fields can generate the moing charges. The first step, demonstrated in the works [3-5], was made in this direction a way of the introduction of the 2

3 symmetrical laws of magnetoelectric and electromagnetic induction. These laws are written as follows: B E dl = ds + B dl t, (1.1) D H dl = ds D dl t or B rote = + rot B t. (1.2) D roth = rot D dt For the constants pour on these relationships they take the form: E = B. (1.3) H = D In relationships ( ), which assume the alidity of the Galilean transformations the primed system and not primed system alues present fields and elements in moing and fied IMS respectiely. It must be noted, that conersions (1.3) earlier could be obtained only from the coariant Lorentz transformations. The relationships ( ), which present the laws of induction, do not gie information about how arose fields in initial fied IMS. They describe only laws goerning the propagation and conersion pour on in the case of motion with respect to the already eisting fields. The relationship (1.3) attest to the fact that in the case of relatie motion of frame of references, between the fields E and H there is a cross coupling, i.e., motion in the fields H leads to the appearance pour on E 3

4 and ice ersa. From these relationships escape the additional consequences, which were for the first time eamined in the work [3]. Electric field beyond the limits of the long charged rod is determined from the relationship speed g E =, where g - charge of the unit length of rod. 2πε r If we in parallel to the ais of rod in the field E begin to moe with the another IMS, then in it will appear the additional magnetic field H = ε E. If we now with respect to already moing IMS begin to moe third frame of reference with the speed motion in the field ( ) 2, then already due to the H will appear additie to the electric field E = µε E. This process can be continued and further, as a result of which can be obtained the number, which gies the alue of the electric field E ( r) in moing IMS with reaching of the speed = n, when 0, and n. In the final analysis in moing IMS the alue of dynamic electric field will proe to be more than in the initial and to be determined by the relationship: gch E ( r, ) c = = Ech. 2πεr c If speech goes about the electric field of the single charge e, then its electric field will be determined by the relationship: ech E ( r, ) c =, 2 4πεr where - normal component of charge rate to the ector, which connects the moing charge and obseration point. 4

5 Epression for the scalar potential, created by the moing charge, for this case will be written down as follows [3,4]: ech (, ) c ϕ r = = ϕ( r) ch, (1.4) 4πε r c where ϕ( r) - scalar potential of fied charge. The potential ϕ ( r, ) can be named scalar- ector since it depends not only on the absolute alue of charge, but also on speed and direction of its motion with respect to the obseration point. Maimum alue this potential has in the direction normal to the motion of charge itself. Moreoer, if charge rate changes, which is connected with its acceleration, then can be calculated the electric fields, induced by the accelerated charge. During the motion in the magnetic field, using the already eamined method, we obtain: H ( ) = Hch. c where - speed normal to the direction of the magnetic field. If we apply the obtained results to the electromagnetic wae and to designate components pour on parallel speeds [ISO] as E and H, and E and H as components normal to it, then conersions pour on they will be written down: 5

6 E = E, Z0 E = E ch + H sh, c c H = H, 1 H = H ch E sh, c Z c 0 (1.5) where Z µ 0 0 = - impedance of free space, ε 0 c 1 µ ε = - speed of light. Conersions pour on (1.5) they were for the first time obtained in the work [3] Phase aberration and the Doppler transerse effect Of the assistance of relationships (1.5) it is possible to eplain the phenomenon of phase aberration, which did not hae within the framework eisting classical electrodynamics of eplanations. We will consider that there are components of the plane wae H z and E, which is etended in the direction y, and primed system moes in the direction of the ais with the speed. Then components pour on in the primed system in accordance with relationships (16.5) they will be written down: E = E E = y, H zsh c, H = z H zch c. 6

7 Thus, is a heterogeneous wae, which has in the direction of propagation the component E. Let us write down the summary field E in moing IMS: E = ( E ) ( E y ) + = Ech c. (2.1) If the ector H is as before orthogonal the ais y, then the ector E is now inclined toward it to the angle α, determined by the relationship: α sh. (2.2) c c This is phase aberration. Specifically, to this angle to be necessary to incline telescope in the direction of the motion of the Earth around the sun in order to obsere stars, which are located in the zenith. The ector Poynting ector is now also directed no longer along the ais y, but being located in the plane y, it is inclined toward the ais y to the angle, determined by relationships (2.2). Howeer, the relation of the absolute alues of the ectors E in both systems they remained and H identical. Howeer, the absolute alue of the Poynting ector increased. Thus, een transerse motion of inertial system with respect to the direction of propagation of wae increases its energy in the moing system. This phenomenon is understandable from a physical point of iew. It is possible to gie an eample with the rain drops. When they fall ertically, then is energy in them one. But in the inertial system, which is moed normal to the ector of their of speed, to this speed the elocity ector of inertial system is added. In this case the absolute alue of the speed of drops in the inertial system will be equal to square root of the sum of the squares of the 7

8 speeds indicated. The same result gies to us relationship (2.1). The transformations with respect to the ectors E and H is completely symmetrical. Such waes hae in the direction of its propagation additional of the ector of electrical or magnetic field, and in this they are similar to E and H of the waes, which are etended in the waeguides. In this case appears the uncommon wae, whose phase front is inclined toward the Poyntnng ector to the angle, determined by relationship (2.2). In fact obtained wae is the superposition of plane wae with the phase speed 1 c = and µε additional wae of plane wae with the infinite phase speed orthogonal to the direction of propagation. The transerse Doppler effect, who long ago is discussed sufficiently, until now, did not find its confident eperimental confirmation. For obsering the star from moing ISM it is necessary to incline telescope on the motion of motion to the angle, determined by relationship (2.2). But in this case the star, obsered with the aid of the telescope in the zenith, will be in actuality located seeral behind the isible position with respect to the direction of motion. Its angular displacement from the isible position in this case will be determined by relationship (2.2). but this means that this star with respect to the obserer has radial spid, determined by the relationship = sinα. Since for the low alues of the angles sinα frequency shift will compose r 8 α, and α = c, the Doppler 2 ω = d ω0 2 c. (2.3)

9 This result numerically coincides with results STR, but it is principally characterized by rel.un. of results. It is considered in STR that the transerse Doppler effect, determined by relationship (2.3), there is in reality, while in this case this only apparent effect. If we compare the results of conersions pour on (2.5) with conersions STR, then it is not difficult to see that they coincide with an accuracy to the quadratic members of the ratio of the elocity of the motion of charge to the speed of light. The STR conersion although they were based on the postulates, could correctly eplain sufficiently accurately many physical phenomena, which before this eplanation did not hae. With this circumstance is connected this great success of this theory. Conersions (2.4) and (2.5) are obtained on the physical basis without the use of postulates and they with the high accuracy coincided with STR. Difference is the fact that in conersions (2.5) there are no limitations on the speed for the material particles, and also the fact that the charge is not the inariant of speed. The eperimental confirmation of the fact indicated can sere as the confirmation of correctness of the proposed conersions. REFERENCE 1. Мандельштам Л. И. Лекции по оптике, теории относительности и квантовой механике. М: Наука, с. 2. Рашевский П. К. Риманова геометрия и тензорный анализ. М.: Наука, 1967, с. 3. Менде Ф. Ф. Существуют ли ошибки в современной физике. Харьков, Константа, с. 9

10 4. Менде Ф. Ф. Непротиворечивая электродинамика. Харьков, НТМТ, 2008, с. 5. Менде Ф. Ф. Великие заблуждения и ошибки физиков XIX-XX столетий. Революция в современной физике. Харьков, НТМТ, 2010, с. 10