What is Not Taken into Account and they Did Not Notice Ampere, Faraday, Maxwell, Heaviside and Hertz

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1 AASCIT Journal of Physis 5; (): 8-5 Published online Marh 3, 5 ( What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz F. F. Mende B.I. Verkin Institute for Low Temperature Physis and ngineering NAS Ukraine mail address mende_fedor@mail.ru Keywords Faraday Low, Maxwell quations, letromagneti Indution, Lorentz Fore, Salar-Vetor Potential, Unipolar Generator, Kineti Indutane Reeived: Marh 8, 5 Revised: Marh, 5 Aepted: Marh, 5 Citation F. F. Mende. What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz. AASCIT Journal of Physis. Vol., No., 5, pp Abstrat letrodynamis is developed already more than years, in it still remained suffiiently many problems. For the duration entire of the period in the eletrodynamis indiated primary attention was paid to the eletrial and magneti fields, and this onept as magneti vetor potential remained in the shadow. The arried out analysis showed that the magneti vetor potential is one of the most important onepts of lassial eletrodynamis, and magneti field is only a onsequene of this potential. But physial nature of this potential was not lear. The meaningful result of work is that whih in them within the framework of Galilei onversions is shown that the salar potential of harge depends on its relative speed, and this fat found its experimental onfirmation. The obtained results hange the ideologial basis of lassial eletrodynamis, indiating that the substantial part of the observed in the eletrodynamis dynami phenomena, this by the onsequenes of this dependene. Certainly, the adoption of this onept is ritial step. Indeed the main parameter of harge are those energy harateristis, whih it possesses and how it influenes the surrounding harges not only in the stati position, but also during its motion. the dependene of salar potential on the speed leads to the fat that in its environments are generated the eletri fields, to reverse fields, that aelerate harge itself. Suh dynami properties of harge allow instead of two symmetrial laws of magneto eletri and eletromagneti indution to introdue one law of eletro-eletrial indution, whih is the fundamental law of indution. This method gives the possibility to diretly solve all problems of indution and emission, without resorting to the appliation of suh pour on mediators as vetor potential and magneti field. This approah makes it possible to explain the origin of the fores of interation between the urrent arrying systems. Up to now in the lassial eletrodynamis existed two not onneted with eah other of division. From one side this of Maxwell equation, and from whih follow wave equations for the eletromagneti pour on, while from other side this of the relationships, whih determine power interation of the urrent arrying systems. For explaining this phenomenon the postulate about the Lorentz fore was introdued. Introdution to the dependene of the salar potential of harge on the speed mutually onnets these with those not onneted divisions, and lassial eletrodynamis takes the form of the ordered united siene, whih has united ideologial basis.. Introdution The basis of ontemporary eletrodynamis, were plaed by Ampere [], whih introdued the onept of magneti field. This made possible to obtain the mathematial relationships, whih desribe power interation of the urrent arrying systems. But

2 AASCIT Journal of Physis 5; (): this task was solved only at the phenomenologial level, sine. The physial auses for suh an interation were not found. The following major step in the desription of eletrodynami proesses was onduted by Faraday [], who introdued the law of eletromagneti indution and by Maxwell, whih introdued the onept of bias urrent [ 3]. This made possible to predit and to desribe wave proesses in the material media. The meaningful result of the work of Maxwell was also the introdution of the onept of the vetor potential of magneti field, whih made it possible to write down the generalized salar potential, whih unites the stati and dynami laws of eletrodynamis. eaviside's merit is the fat that he wrote down Maxwell's equations in the terms of vetor analysis. quations reorded by eaviside and it is ustomary to assume Maxwell equations. owever, Maxwell did not introdue the onept of the vetor potential of eletri field, whih makes it possible to symmetrize the equations of eletrodynamis, after writing down them in the plural form. The experimental detetion of eletromagneti waves is the most great merit of ertz [4]. e sueeded in reating the first in the world highfrequeny generator and the antenna, apable of emitting eletromagneti waves. Lorenz is already later and Poinare introdued experimental postulate about the Lorentz fore who up to now is used for enumerating the magneti fores, whih at on the harges, whih move in the magneti field. But no one of higher than enumerated sientists ould explain physial nature of the vetor potential of magneti field and prove that the salar potential of harge and its dependene on the speed is the basis of all stati and dynami laws of eletrodynamis. This was made in the work of the author [5-6]. Introdution to the dependene of the salar potential of harge from the speed not only made it possible to explain nature of the emission of eletromagneti waves, or physis of power interation of the urrent arrying systems, but also ombined two not onneted, until now, parts of the eletrodynamis, whih present wave and power proesses. To the examination of the role of the salar potential of harge and its dependene on the speed to the formulating of the laws of eletrodynamis is dediated this artile. The laws of lassial eletrodynamis they reflet experimental fats they are phenomenologial. Unfortunately, ontemporary lassial eletrodynamis is not deprived of the ontraditions, whih did not up to now obtain their explanation. The fundamental equations of ontemporary lassial eletrodynamis are the Maxwell equation. They are written as follows for the vauum: B rot =, (.) t D rot =, (.) t divd =, (.3) divb =, (.4) where, are tension of eletrial and magneti field, D = ε, B = µ are eletrial and magneti indution, µ, εare magneti and dieletri onstant of vauum. From Maxwell equations follow the wave equations µ ε =, (.5) µ ε =. (.6) These equations show that in the vauum an be extended the plane eletromagneti waves, the veloity of propagation of whih is equal to the speed of light =. (.7) µ ε For the material media the Maxwell equations take the following form: B rot µµ = ɶ =, (.8) D rot nev εε nev = + ɶ = +, (.9) divd = ne, (.) div B =, (.) where µɶ, εɶ are the relative magneti and dieletri onstants of the medium and n, e and v are density, value and harge rate. The equations (. -.) are written in the assigned inertial referene frame (IRF) and in them there are no rules of passage of one IRF to another. These equations assume that the properties of harge do not depend on their speed. In Maxwell equations are not ontained indiation that is the reason for power interation of the urrent-arrying systems, therefore to be introdued the experimental postulate about the fore, whih ats on the moving harge in the magneti field FL = e v µ. (.) This fore is alled the Lorentz fore. owever in this axiomatis is an essential defiieny. If fore ats on the moving harge, then in aordane with third Newton law must our and reating fore. In this ase the magneti field is independent substane, omes out in the role of the

3 3 F. F. Mende: What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz mediator between the moving harges. Consequently, we do not have law of diret ation, whih would give immediately answer to the presented question, passing the proedure examined. I.e. we annot give answer to the question, where are loated the fores, the ompensating ation of magneti field to the harge. The equation (.) from the physial point sight auses bewilderment. The fores, whih at on the body in the absene of losses, must be onneted either with its aeleration, if it aomplishes forward motion, or with the entrifugal fores, if body aomplishes rotary motion. Finally, stati fores appear when there is the gradient of the salar potential of potential field, in whih is loated the body. But in q. (.) there are no suh fores. Usual retilinear motion auses the fore, whih is normal to the diretion motion. In the lassial mehanis the fores of this type are unknown. Is ertain, magneti field is one of the important onepts of ontemporary eletrodynamis. Its onept onsists in the fat that around any moving harge appears the magneti field (Ampere law), whose irulation is determined by equation dl = I, (.3) where I is ondution urrent. quation (.9) is the onsequene of q. (.3), if we to the ondution urrent add bias urrent. Let us espeially note that the introdution of the onept of magneti field does not be founded upon any physial basis, but it is the statement of the olletion of some experimental fats. Using this onept, it is possible with the aid of the speifi mathematial proedures to obtain orret answer with the solution of pratial problems. But, unfortunately, there is a number of the physial questions, during solution of whih within the framework the onepts of magneti field, are obtained paradoxial results. ere one of them. Using qs. (.) and (.3) not diffiult to show that with the unidiretional parallel motion of two like harges, or flows of harges, between them must appear the additional attration. owever, if we pass into the inertial system, whih moves together with the harges, then there magneti field is absent, and there is no additional attration. This paradox does not have an explanation. Of fore with power interation of material strutures, along whih flows the urrent, are applied not only to the moving harges, but to the lattie, but in the onept of magneti field to this question there is no answer also, sine. In qs. (.-.3) the presene of lattie is not onsidered. At the same time, when urrent flows through the plasma, ours its ompression. This phenomenon is alled pinh effet. In this ase fores of ompression at not only on the moving eletrons, but also on the positively harged ions. And, again, the onept of magneti field annot explain this fat, sine in this onept there are no fores, whih an at on the ions of plasma. As the fundamental law of indution in the eletrodynamis is onsidered Faraday law, onsequene of whom is the Maxwell first equation. owever, here are problems. It is onsidered until now that the unipolar generator is an exeption to the rule of flow, onsequently Faraday law is not omplete. Let us give one additional statement of the monograph [7]: The observations of Faraday led to the disovery of new law about the onnetion of eletrial and magneti field on: in the field, where magneti field hanges in the ourse of time, is generated eletri field. But from this law also there is an exeption. Atually, the magneti fields be absent out of the long solenoid; however, eletri fields are generated with a hange of the urrent in this solenoid around the solenoid. In the lassial eletrodynamis does not find its explanation this well known physial phenomenon, as phase aberration of light. From entire aforesaid it is possible to onlude that in the lassial eletrodynamis there is number of the problems, whih still await their solution.. Laws of the Magnetoeletri Indution The primary task of indution is the presene of laws governing the appearane of eletrial field on, sine only eletri fields exert power influenes on the harge. Faraday law is written as follows: ФB B dl = = µ ds = ds, (.) where B = µ is magneti indution vetor, ФB = µ ds is flow of magneti indution, and µ =ɶ µµ is magneti permeability of medium. It follows from this law that the irulation integral of the vetor of eletri field is equal to a hange in the flow of magneti indution through the area, whih this outline overs. From q.(.) obtain the Maxwell first equation B rot =. (.) t Let us immediately point out to the terminologial error. Faraday law should be alled not the law of eletromagneti, as is ustomary in the existing literature, but by the law of magneto eletri indution, sine. a hange in the magneti field on it leads to the appearane of eletrial field on, but not vie versa. Let us introdue the vetor potential of the magneti field A, whih satisfies the equality µ A dl = ФB, where the outline of the integration oinides with the outline of integration in q. (.), and the vetor of is determined in

4 AASCIT Journal of Physis 5; (): all setions of this outline, then then A = µ. (.3) Between the vetor potential and the eletri field there is a loal onnetion. Vetor potential is onneted with the magneti field with the following equation: rot A =. (.4) During the motion in the three-dimensional hanging field of vetor potential the eletri fields find, using total derivative da = µ. (.5) dt Prime near the vetor means that we determine this field in the moving oordinate system. This means that the vetor potential has not only loal, but also onvetion derivative. In this ase q. (.5) an be rewritten as follows: A = µ µ ( v ) A, wherev is speed of system. If vetor potential on time does not depend, the fore ats on the harge F = µ e v A. v, ( ) This fore depends only on the gradients of vetor potential and harge rate. The harge, whih moves in the field of the vetor potential A with the speed v, possesses potential energy ( ) W = eµ va Therefore must exist one additional fore, whih ats on the harge in the moving oordinate system, namely: F = gradw = eµ grad va. v,. ( ) The value eµ ( va ) plays the same role, as the salar potential of the harge, whose gradient determines the fore, whih ats on the moving harge. Consequently, the omposite fore, whih ats on the harge, whih moves in the field of vetor potential, an have three omponents and will be written down as A F = eµ eµ v A + eµ grad va ( ) ( ). (.6) The first of the omponents of this fore ats on the fixed harge, when vetor potential hanges in the time and has loal time derivative. Seond omponent is onneted with the motion of harge in the three-dimensional hanging field of this potential. ntirely different nature in fore, whih is determined by last term q. (.6). It is onneted with the fat that the harge, whih moves in the field of vetor potential, it possesses potential energy, whose gradient gives fore. From q. (.6) follows A = µ µ ( v ) A + µ grad ( va ). (.7) This is a omplete law of mutual indution. It defines all eletri fields, whih an appear at the assigned point of spae, this point an be both the fixed and that moving. This united law inludes and Faraday law and that part of the Lorentz fore, whih is onneted with the motion of harge in the magneti field, and without any exeptions gives answer to all questions, whih are onerned mutual magnetoeletri indution. It is signifiant, that, if we take rotor from both parts of equality (.7), attempting to obtain the Maxwell first equation, then it will be immediately lost the essential part of the information, sine. rotor from the gradient is identially equal to zero. If we isolate those fores, whih are onneted with the motion of harge in the three-dimensional hanging field of vetor potential, and to onsider that µ grad ( va ) µ ( v ) A = µ v rot A, that from q. (.6) we will obtain F v = eµ v rot A, (.8) and, taking into aount (.4), let us write down or F v = eµ v and it is final A F e e e (.9) v = µ v, (.) = + v = + eµ v. (.) Can seem that q. (.) presents Lorentz fore, however, this not thus. In this equation, in ontrast to the Lorentz fore the field is indution. In order to obtain the total fore, whih ats on the harge, neessary to the right side q. (.) to add the term egrad ϕ F = egrad ϕ + e + eµ v, whereϕ is salar potential at the observation point. In this ase q.(.7) an be rewritten as follows:

5 3 F. F. Mende: What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz A = µ µ ( ) + µ ( ) ϕ v A grad va grad or (.) da = µ + grad ( µ ( va) ϕ dt ). (.3) If both parts of q. (.) are multiplied by the magnitude of the harge, then will ome out the total fore, whih ats on the harge. From Lorentz fore it will differ in terms of A the fore eµ.from q. (.3) it is evident that the value µ va ϕ plays the role of the generalized salar potential. ( ) After taking rotor from both parts of q. (.3) and taking into aount that rotgrad =, we will obtain d rot = µ. dt If we in this equation replae total derivative by the quotient, then we will obtain the Maxwell first equation. After performing this operation, we obtained the Maxwell first equation, but they lost information about power interation of the moving harge with the magneti field. This examination maximally explained the physial piture of mutual indution. We speially looked to this question from another point of view, in order to permit those ontraditory judgments, whih our in the fundamental monograph aording to the theory of eletriity. Previously Lorentz fore was onsidered as the fundamental experimental postulate, not onneted with the law of indution. By alulation to obtain last term of the right side of q. (.) was only within the framework speial relativity (SP), after introduing two postulates of this theory. In this ase all terms of q. (.) are obtained from the law of indution, using the Galileo onversions. Moreover q. (.) this is a omplete law of mutual indution, if it are written down in the terms of vetor potential. And this is the very thing rule, whih gives possibility, knowing fields in one IRF, to alulate fields in another. With onduting of experiments Faraday established that in the outline is indued the urrent, when in the adjaent outline diret urrent is swithed on or is turned off or adjaent outline with the diret urrent moves relative to the first outline. Therefore in general form Faraday law is written as follows: dφ dt B dl =. (.4) This writing of law indiates that with the determination of the irulation in the moving IRF, near and dl must stand primes and should be taken total derivative. But if irulation is determined in the fixed IRF, then primes near and dl be absent, but in this ase to the right in expression (.4) must stand partiular time derivative. Complete time derivative in q. (.4) indiates the independene of the eventual result of appearane e.m.f. in the outline from the method of hanging the flow. Flow an hange both due to the hange of B with time and beause the system, in whih is measured the irulation dl, it moves in the three-dimensional hanging fieldb. The value of magneti flux in q. (.4) is determined from the equation ФB = Bds (.5) where the magneti indution B = µ is determined in the fixed IRF, and the elementds is determined in the moving system. Taking into aount q. (.4), from q. (.5) we obtain d dl = Bds dt. and further, sine d = + vgrad, let us write down dt B dl = ds B v dl vdivbds. (.6) In this ase ontour integral is taken on the outline dl, whih overs the area ds. Let us immediately note that entire following presentation will be onduted under the assumption the validity of the Galileo onversions, i.e., dl = dland ds = ds. From (.6) follows the known result = + v B, (.7) from whih follows that during the motion in the magneti field the additional eletri field, determined by last term of equation appears (.7). Let us note that this equation is obtained not by the introdution of postulate about the Lorentz fore, or from the Lorenz onversions, but diretly from the Faraday law, moreover within the framework the onversions of Galileo. Thus, Lorentz fore is the diret onsequene of the law of magnetoeletri indution. The equation follows from the Ampere law = rot A. Then q. (.6) an be rewritten A = µ + µ v rota, and further A = + ( ) ( ) µ µ v A µ grad va. (.8)

6 AASCIT Journal of Physis 5; (): Again ame out q. (.7), but it is obtained diretly from the Faraday law. True, and this way thus far not shedding light on physial nature of the origin of Lorentz fore, sine the true physial auses for appearane and magneti field and vetor potential to us nevertheless are not thus far lear. With the examination of the fores, whih at on the harge, we limited to the ase, when the time lag, neessary for the passage of signal from the soure, whih generates vetor potential, to the harge itself was onsiderably less than the period of urrent variations in the ondutors. Now let us remove this limitation. The Maxwell seond equationin the terms of vetor potential an be written down as follows: rotrota = j A, (.9) ( ) where j( A ) is ertain funtional from A, depending on the properties of the medium in question. If is arried out Ohm law j = σ, then A j( A) = σµ. (.) For the free spae takes the form: A j( A) = µε. (.) For the free harges the funtional takes the form: of µ j( A) = A, (.) L m wherelk = is kineti indutane of harges [8,9]. In ne this equationm is the mass of harge, e is the magnitude of the harge, nis harge density. quations (. -.) reflet well-known fat about existene of three forms of the eletri urrent: ative and two reative. ah of them has harateristi dependene on the vetor potential. This dependene determines the rules of the propagation of vetor potential in different media. ere one should emphasize that qs. (.-.) assume not only the presene of urrent, but also the presene of those material media, in whih suh urrents an leak. The ondution urrent, determined by qs. (.) and (.), an the leak through the ondutors, in whih there are free urrent arriers. Bias urrent, an the leak through the free spae or the dieletris. For the free spae q. (.9) takes the form: A rot rota = µε. (.3) This wave equation, whih attests to the fat that the k vetor potential an be extended in the free spae in the form of plane waves, and it on its information apability does not be inferior to the wave equations, obtained from Maxwell's equations. This equation on its information apability does not be inferior to wave equations for the eletrial and magneti field on, obtained from Maxwell equations. verything said attests to the fat that in the lassial eletrodynamis the vetor potential has important signifiane. Its use shedding light on many physial phenomena, whih previously were not intelligible. And, if it will be possible to explain physial nature of this potential, then is solved the very important problem both of theoretial and applied nature. 3. Laws of the letromagneti Indution The Faraday law shows, how a hange in the magneti field on it leads to the appearane of eletrial field on. owever, does arise the question about that, it does bring a hange in the eletrial field on to the appearane of magneti field on? In the ase of the absene of ondution urrents the the Maxwell seond equation appears as follows: D rot ε = =, where D = ε is eletrial indution. And further Φ = t dl, (3.) where Φ = Dds is the flow of eletrial indution. owever for the omplete desription of the proesses of the mutual eletrial indution of q. (3.) is insuffiient. As in the ase Faraday law, should be onsidered the irumstane that the flow of eletrial indution an hange not only due to the loal derivative of eletri field on the time, but also beause the outline, along whih is produed the integration, it an move in the three-dimensional hanging eletri field. This means that in q. (3.), as in the ase Faraday law, should be replaed the partial derivative by the omplete. Designating by the primes of field and iruit elements in moving IRF, we will obtain: dφ dt dl =, and further D dl = ds + D v dl + vdivdds. (3.) For the eletrially neutral mediumdiv =, therefore the last member of right side in this expression will be absent. For this ase q. (3.) will take the form:

7 34 F. F. Mende: What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz D dl = ds + D v dl. (3.3) If we in this equation pass from the ontour integration to the integration for the surfae, then we will obtain: D rot = + rot D v. (3.4) If we, based on this equation, write down fields in this inertial system, then prime near and seond member of right side will disappear, and we will obtain the bias urrent, introdued by Maxwell. But Maxwell introdued this parameter, without resorting to the law of eletromagneti indution. If his law of magnetoeletri indution Faraday derived on the basis experiments with the magneti fields, then experiments on the establishment of the validity of q. (3.) annot be at that time onduted was, sine for onduting this experiment sensitivity of existing at that time meters did not be suffiient. On from q.(3.4) we obtain for the ase of onstant eletrial field: v = ε v. (3.5) It is possible to express the eletri field through the rotor of eletrial vetor potential, after assuming = rot A. (3.6) quation (3.4) taking into aount q.(3.6) will be written down: A = ε ε v rot A. Further it is possible to repeat all those proedures, whih has already been onduted with the magneti vetor potential, and to write down the following equations: A = ε + ε ( v ) A ε grad ( va ), A = ε ε v rot A, da ε dt = ε grad va ( ) Is ertain, the study of this problem it would be possible, as in the ase the law of magnetoeletri indution, to begin from the introdution of the vetor A. This proedure was for the first time proposed in artile [5]. The introdution of total derivatives in the laws of indution substantially explains physis of these proesses and gives the possibility to isolate the fore omponents, whih at on the harge. This method gives also the possibility to obtain transformation laws fields on upon. transfer of one IRF to another. 4. Plurality of the Forms of the Writing of the letrodynami Laws In the previous paragraph it is shown that the magneti and eletri fields an be expressed through their vetor potentials = rot A, (4.) = rot A. (4.) Consequently, Maxwell equations an be written down with the aid of these potentials: A rot A = µ (4.3) A rot A = ε. (4.4) For eah of these potentials it is possible to obtain wave equation, in partiular A rotrot A = εµ (4.5) and to onsider that in the spae are extended not the magneti and eletri fields, but the field of eletrial vetor potential. In this ase, as an easily be seen of the qs. ( ), magneti and eletri field they will be determined through this potential by the equations: A = ε. (4.6) = rot A Spae derivativerot A A and loal time derivative are onneted with wave equation (4.5). Thus, the use only of one eletrial vetor potential makes it possible to ompletely solve the task about the propagation of eletrial and magneti field on. Taking into aount (4.6), Pointing vetor an be written down only through the vetor A : P A ε = rot A. Charateristi is the fat that with this method of examination neessary ondition is the presene at the partiular point of spae both the time derivatives, and spae derivative of one and the same potential.

8 AASCIT Journal of Physis 5; (): This task an be solved by another method, after writing down wave equation for the magneti vetor potential: A rotrot A = εµ. (4.7) In this ase magneti and eletri fields will be determined by the equations: = rot A A. = µ Pointing vetor in this ase an be found from the following equation: P = A µ rot A Spae derivativerot A A and loal time derivative of are onneted with wave equation (4.7). But it is possible to enter and differently, after introduing, for example, the eletrial and magneti urrents j = rot, j = rot. The equations also an be reorded for these urrents: j rot j = µ, j rot j = ε. This system in its form and information onluded in it differs in no way from Maxwell equations, and it is possible to onsider that in the spae the magneti or eletri urrents are extended. And the solution of the problem of propagation with the aid of this method will again inlude omplete information about the proesses of propagation. The method of the introdution of new vetor examined field on it is possible to extend into both sides ad infinitum, introduing all new vetorial fields. Naturally in this ase should be introdued additional alibrations. Thus, there is an infinite set of possible writings of eletrodynami laws, but they all are equivalent aording to the information onluded in them. This approah was for the first time demonstrated in the artile [5]. 5. Dynami Potentials and the Field of the Moving Charges The way, whih is onerned the introdution of total. derivatives field on and vetor potential it was begun still in Maxwell, sine it wrote its equations in the total derivatives. ertz also wrote the equations of eletrodynamis in the total derivatives. ertz did not introdue the onept of vetor potentials, but he operated only with fields, but this does not diminish its merits. It made mistakes only in the fat that the eletrial and magneti fields were onsidered the invariants of speed. But already simple example of long lines is evidene of the inauray of this approah. With the propagation of wave in the long line it is filled up with two forms of energy, whih an be determined through the urrents and the voltages or through the eletrial and magneti fields in the line. And only after wave will fill with eletromagneti energy all spae between the generator and the load on it will begin to be separated energy. I.e. the time, by whih stays this proess, generator expended its power to the filling with energy of the setion of line between the generator and the load. But if we begin to move away load from inoming line, then a quantity of energy being isolated on it will derease, sine. the part of the energy, expended by soure, will leave to the filling with energy of the additional length of line, onneted with the motion of load. If load will approah a soure, then it will obtain an additional quantity of energy due to the derease of its length. But if effetive resistane is the load of line, then an inrease or the derease of the power expendable in it an be onneted only with a hange in the stress on this resistane. Being loated in assigned IRF, us interest those fields, whih are reated in it by the fixed and moving harges, and also by the eletromagneti waves, whih are generated by the fixed and moving soures of suh waves. The fields, whih are reated in this IRF by moving harges and moving soures of eletromagneti waves, we will all dynami. Can serve as an example of dynami field the magneti field, whih appears around the moving harges. As already mentioned, in the lassial eletrodynamis be absent the rule of the onversion of eletrial and magneti field on upon transfer of one inertial system to another. This defiieny removes SR, basis of whih are the Lorenz onversions. With the entire mathematial validity of this approah the physial essene of suh onversions up to now remains unexplained. in this division will made attempt find the preisely physially substantiated ways of obtaining the onversions field on upon transfer of one IRF to another, and to also explain what dynami potentials and fields an generate the moving harges. The first step in this diretion was made a way of the introdution of the symmetrial laws of magnetoeletri and eletromagneti indution [5]. These laws are written as follows: B dl = ds + v B dl (5.) D dl = ds v D dl or

9 36 F. F. Mende: What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz B rot = + rot v B. (5.) D rot = rot v D dt For the onstants fields on these equations they take the form: = v B. (5.3) = v D In qs. (5.-5.3), whih assume the validity of the Galileo onversions present fields and elements in moving and fixed IRF respetively. It must be noted, that onversions (5.3) earlier ould be obtained only from the Lorenz onversions. quations (5.-5.3), whih present the laws of indution, do not give information about how arose fields in initial fixed IRF. They desribe only laws governing the propagation and onversion fields on in the ase of motion with respet to the already existing fields. quation(5.3) attest to the fat that in the ase of relative motion of frame of referenes, between the fields and there is a ross oupling, i.e., motion in the fields leads to the appearane field on and vie versa. From these equations esape the additional onsequenes. g The eletri field = beyond the limits of the πεr harged long rod, where g is a linear harge, diminishes aording to the law r. If we in parallel to the axis of rod in the field begin to move with the speed v another IRF, then in it will appear the additional magneti field = ε v. If we now with respet to already moving IRF begin to move third frame of referene with the speed v, then already due to the motion in the field will appear additive to the eletri field ( ) = µε v. This proess an be ontinued and further, as a result of whih an be obtained the number, whih gives r in moving IRF with the value of the eletri field ( ) reahing of the speed v = n v, when v, and n.in the final analysis in moving IRF the value of dynami eletri field will prove to be more than in the initial and to be determined by the equation: v gh v ( r, v ). = = h πεr If speeh goes about the eletri field of the single harge e, then its eletri field will be determined by the equation: v eh ( r, v ) =, 4πεr v wherev is normal omponent of harge rate to the vetor, whih onnets the moving harge and observation point. xpression for the salar potential, reated by the moving harge, for this ase will be written down as follows: where ϕ( r) v eh (, ) v ϕ r v = = ϕ( r) h 4πεr (5.4) is salar potential of fixed harge. The potential ϕ ( r, v ) an be named salar-vetor, sine it depends not only on the absolute value of harge, but also on speed and diretion of its motion with respet to the observation point. Maximum value this potential has in the diretion normal to the motion of harge itself. Moreover, if harge rate hanges, whih is onneted with its aeleration, then an be alulated the eletri fields, indued by the aelerated harge. During the motion in the magneti field, using the already examined method, we obtain: v ( v ) = h. wherev isspeed normal to the diretion of the magneti field. If we apply the obtained results to the eletromagneti wave and to designate omponents fields on parallel speeds IRF as,, and, as omponents normal to it, then onversions fields on they will be written down: =, v Z v = h + v sh, v =, v v = h v sh, vz wherez µ = is impedane of free spae, ε (5.5) = is µ ε speed of light. Conversions fields on (5.5) they were for the first time obtained in the artile [5]. 6. Phase Aberration and the Transverse Doppler ffet Using qs. (5.5) it is possible to explain the phenomenon of phase aberration, whih did not have within the framework existing lassial eletrodynamis of explanations. We will onsider that there are omponents of the plane wave z, x, whih is extended in the diretiony, and primed system moves in the diretion of the axisx with the speed x v. Then omponents fields will be written down:

10 AASCIT Journal of Physis 5; (): Thus is a heterogeneous wave, whih has in the diretion of propagation the omponent. v Let us write down the summary field in moving IRF If the vetor =, x x vx y = zsh, vx z = zh. x y x vx = ( ) ( + ) = h. (6.) is as before orthogonal the axis y, then the vetor is now inlined toward it to the angle α, determined by the equation: v v α sh. (6.) Thisis phase aberration. Speifially, to this angle to be neessary to inline telesope in the diretion of the motion of the arth around the sun in order to observe stars, whih are loated in the zenith. The Poynting vetor is now also direted no longer along the axis y, but being loated in the plane xy, it is inlined toward the axisy to the angle, determined by qs. (6.). owever, the relation of the absolute values of the vetors of and in both systems they remained idential. owever, the absolute value of Poynting vetor inreased. Thus, even transverse motion of inertial system with respet to the diretion of propagation of wave inreases its energy in the moving system. This phenomenon is understandable from a physial point of view. It is possible to give an example with the rain drops. When they fall vertially, then is energy in them one. But in the inertial system, whih is moved normal to the vetor of their of speed, to this speed the veloity vetor of inertial system is added. In this ase the absolute value of the speed of drops in the inertial system will be equal to square root of the sum of the squares of the speeds indiated. The same result gives to us q. (6.). Suh waves have in the diretion of its propagation additional of the vetor of eletrial or magneti field, and in this they are similar to and of the waves, whih are extended in the waveguides. In this ase appears the unommon wave, whose phase front is inlined toward the Poynting vetor to the angle, determined by q. (.). In fat obtained wave is the superposition of plane wave with the phase speed = and additional wave of plane wave µε with the infinite phase speed orthogonal to the diretion of propagation. The transverse Doppler effet, who long ago is disussed suffiiently, until now, did not find its onfident experimental onfirmation. For observing the star from moving IRF it is neessary to inline telesope on the motion of motion to the angle, determined by q. (6.). But in this ase the star, observed with the aid of the telesope in the zenith, will be in atuality loated several behind the visible position with respet to the diretion of motion. Its angular displaement from the visible position in this ase will be determined by q. (6.). But this means that this star with respet to the observer has radial speed, determined by the equation v = vsinα. r Sine for the low values of the angles sinα α, and v α =, Doppler frequeny shift will ompose v ω = d ω. (6.3) This result numerially oinides with results SR, but it is prinipally haraterized by of results. It is onsidered SR that the transverse Doppler effet, determined by q. (6.3), there is in reality, while in this ase this only apparent effet. If we ompare the results of onversions fields on (6.5) with onversions SP, then it is not diffiult to see that they oinide with an auray to the quadrati members of the ratio of the veloity of the motion of harge to the speed of light. Conversion SP, although they were based on the postulates, ould orretly explain suffiiently aurately many physial phenomena, whih before this explanation did not have. With this irumstane is onneted this great suess of this theory. Conversions (6.4) and (6.5) are obtained on the physial basis without the use of postulates and they with the high auray oinided with SP. Differene is the fat that in onversions (6.5) there are no limitations on the speed for the material partiles, and also the fat that the harge is not the invariant of speed. The experimental onfirmation of the fat indiated an serve as the onfirmation of orretness of the proposed onversions. 7. The Problem of the Lorentz Fore and Power Interation of the Current-Carrying Systems and Its Solution It was already said, that Maxwell equations do not inlude information about power interation of the urrent arrying systems. In the lassial eletrodynamis for alulating suh an interation it is neessary to alulate magneti field in the assigned region of spae, and then, using a Lorentz fore, to find the fores, whih at on the moving harges. Obsure a question about that remains with this approah, to what are applied the reating fores with respet to those fores, whih at on the moving harges. The onept of magneti field arose to a onsiderable degree beause of the observations of power interation of

11 38 F. F. Mende: What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz the urrent arrying and magnetized systems. xperiene with the iron shavings, whih are ereted near the magnet poles or around the annular turn with the urrent into the lear geometri figures, is espeially signifiant. These figures served as oasion for the introdution of this onept as the lines of fore of magneti field. In aordane with third Newton law with any power interation there is always a equality of effetive fores and opposition, and also always there are those elements of the system, to whih these fores are applied. A large drawbak in the onept of magneti field is the fat that it does not give answer to that, ounterating fores are onretely applied to what, sine. magneti field omes out as the independent substane, with whih ours interation of the moving harges. Is experimentally known that the fores of interation in the urrent arrying systems are applied to those ondutors, whose moving harges reate magneti field.owever, in the existing onept of power interation of suh systems the positively harged lattie, to whih are applied the fores, does not partiipate in the formation of the fores of interation. Let us examine this question on the basis of the onept of salar- vetor potential. We will onsider that the salarvetor potential of single harge is determined by q. (9.4), and that the eletri fields, reated by this potential, at on all surrounding harges, inluding to the harges positively harged latties. Let us examine from these positions power interation between two parallel ondutors (Fig. ), along whih flow the urrents. We will onsider that g +, g + and g, g present the respetively fixed and moving linear harges. searh for as the sum of four fores, whose designation is understandable from the figure. The repulsive fores F, F we will take with the minus sign, while the attrating fore F 3, F 4 we will take with the plus sign. For the single setion of the two-wire iruit of fore, ating between the separate subsystems, will be written down + + g g F =, πεr g g v v F = h, πεr + g g v F3 = + h, πεr + g g v F4 = + h. πεr (7.) Adding all fore omponents, we will obtain the amount of the omposite linearfore gg v v v v FΣ = h h h πε r +. (7.) In this expression as g and g are undertaken the absolute values of the linearharges, and the signs of fores are taken into aount in the braketed expression.for the ase v let us take only two first members of expansion v in the series h, i.e., we will onsider that v v h +.From q. (7.) we obtain gvg v II F = πε r = Σ πε r (7.3) where asg and gare undertaken the absolute values of the linear harges, and v, v take with its signs. Sine the magneti field of straight wire, along whih flows the urrent I, we determine by the equation Fig.. Shemati of power interation of the urrent arrying wires of twowire iruit taking into aount the positively harged lattie. from q. (7.3) we obtain I, = πr The linearharges g +, g + present the positively harged lattie in the lower and upper ondutors. We will also onsider that both ondutors prior to the start of harges are eletrially neutral. This means that in the ondutors are two systems of the mutually inserted opposite harges with the lineardensityg +, g and g +, g, whih neutralize eah other.in Fig. these systems for larger onveniene in the examination of the fores of interation are moved apart along the axis z. Subsystems with the negative harge (eletrons) an move with the speeds v, v. The fore of interation between the lower and upper ondutors we will II I F = I µ πε r = Σ ε =, where is the magneti field, reated by lower ondutor in the loation of upper ondutor. It is analogous F I µ =, Σ where is the magneti field, reated by upper ondutor in the region of the arrangement of lower ondutor. These equations oinide with the results, obtained on the

12 AASCIT Journal of Physis 5; (): basis of the onept of magneti field and Lorentz fores. quation (7.3) represents the known rule of power interation of the urrent-arrying systems, but it is obtained not on the basis the introdution of phenomenologial magneti field, but on the basis of ompletely intelligible physial proedures. In the formation of the fores of interation in this ase the lattie takes diret part, whih is not in the model of magneti field. In the model examined are well visible the plaes of appliation of fore. The obtained equations oinide with the results, obtained on the basis of the onept of magneti field and by the axiomatially introdued Lorentz fore. In this ase is undertaken only first member of expansion in the series v h.for the speeds v should be taken all terms of expansion. If we onsider this irumstane, then the onnetion between the fores of interation and the harge rates proves to be nonlinear. This, in partiular it leads to the fat that the law of power interation of the urrent-arrying systems is asymmetri. With the idential values of urrents, but with their different diretions, the attrating fores and repulsion beome unequal. Repulsive fores prove to be greater than attrating fore. This differene is small and is determined by the expression v II F = πε ε, but with the speeds of the harge arriers of lose ones to the speed of light it an prove to be ompletely pereptible. Let us remove the lattie of upper ondutor, after leaving only free eletroni flux. In this ase will disappear the fores F, F 3, and this will indiate interation of lower ondutor with the flow of the free eletrons, whih move with the speed v on the spot of the arrangement of upper ondutor. In this ase the value of the fore of interation is defined as: gg v v v FΣ = h h πεr. (7.4) Lorentz fore assumes linear dependene between the fore, whih ats on the harge, whih moves in the magneti field, and his speed. owever, in the obtained equation the dependene of the amount of fore from the speed of eletroni flux will be nonlinear. From q. (7.4) see that with an inrease in v the deviation from the linear law inreases, and in the ase, when v v, the fore of interation are approahed zero. This is meaningful result. Speifially, this phenomenon observed in their known experiments Thompson and Kauffmann, when they noted that with an inrease in the veloity of eletron beam it is more badly slanted by magneti field. They onneted the results of their observations with an inrease in the mass of eletron. As we see reason here another. Let us note still one interesting result. From q. (7.3) the fore of interation of eletroni flux with a straight wire to determine aording to the following dependene: gg vv v FΣ = πεr. (7.5) From q. (7.5) follows that with the unidiretional eletron motion in the ondutor and in the eletroni flux the fore of interation with the fulfillment of onditions v = v is absent. Sine the speed of the eletroni flux usually muh higher than speed of urrent arriers in the ondutor, the seond term in the brakets in q. (7.5) an be disregarded. Then, sine gv = πε r we will obtain the magneti field, reated by lower ondutor in the plae of the motion of eletroni flux: F gg vv πεr g µ v = =. Σ In this ase, the obtained value of fore oinides with the value of Lorentz fore. Taking into aount that F = g = Σ g µ v, it is possible to onsider that on the harge, whih moves in the magneti field, ats the eletri field, direted normal to the diretion of the motion of harge. This result also with v an auray to of the quadrati terms ompletely oinides with the results of the onept of magneti field and is determined Lorentz fore. As was already said, one of the important ontraditions to the onept of magneti field is the fat that two parallel beams of the like harges, whih are moved with the idential speed in one diretion, must be attrated. In this model there is no this ontradition already. If we onsider that the harge rates in the upper and lower wire will be equal, and lattie is absent, i.e., to leave only eletroni fluxes, then will remain only the repulsive fore F. Thus, the moving eletroni flux interats simultaneously both with the moving eletrons in the lower wire and with its lattie, and the sum of these fores of interation it is alled Lorentz fore. Regularly does appear a question, and does reate magneti field most moving eletron stream of in the absene ompensating harges of lattie or positive ions in the plasma? The diagram examined shows that the effet of power interation between the urrent arrying systems requires in the required order of the presene of the positively harged lattie. Therefore most moving eletroni flux annot reate that effet, whih is reated during its motion in the positively harged lattie. Let us demonstrate still one approah to the problem of

13 4 F. F. Mende: What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz power interation of the urrent arrying systems. The statement of fats of the presene of fores between the urrent arrying systems indiates that there is some field of the salar potential, whose gradient ensures the fore indiated. But that this for the field? quation (7.3) gives only the value of fore, but he does not speak about that, the gradient of what salar potential ensures these fores. We will support with onstants the urrents I, I, and let us begin to draw together or to move away ondutors. The work, whih in this ase will be spent, and is that potential, whose gradient gives fore. After integrating q. (7.3) on r, we obtain the value of the energy: W II lnr πε =. This energy, depending on that to move away ondutors from eah other, or to draw together, an be positive or negative. When ondutors move away, then energy is positive, and this means that, supporting urrent in the ondutors with onstant, generator returns energy. This phenomenon is the basis the work of all eletri motors.if ondutors onverge, then work aomplish external fores, on the soure, whih supports in them the onstany of urrents. This phenomenon is the basis the work of the mehanial generators of e.m.f. quation for the energy an be rewritten and thus: where W II lnr πε = = I Az = IAz, A I lnr = πε z is z omponent of vetor potential, reated by lower ondutor in the loation of upper ondutor, and A I lnr = πε z is z omponent of vetor potential, reated by upper ondutor in the loation of lower ondutor. The approah examined demonstrates that large role, whih the vetor potential in questions of power interation of the urrent-arrying systems and onversion of eletrial energy into the mehanial plays. This approah also learly indiates that the Lorentz fore is a onsequene of interation of the urrent-arrying systems with the field of the vetor potential, reated by other urrent-arrying systems. Important irumstane is the fat that the formation of vetor potential is obliged to the dependene of salar potential on the speed. This is lear from a physial point of view. The moving harges, in onnetion with the presene of the dependene of their salar potential on the speed, reate the salar field, whose gradient gives fore. But the reation of any fore field requires expenditures of energy. These expenditures aomplishes generator, reating urrents in the ondutors. In this ase in the surrounding spae is reated the speial field, whih interats with other moving harges aording to the speial vetor rules. In this ase only salar produt of the harge rate and vetor potential gives the potential, whose gradient gives the fore, whih ats on the moving harge. This is the Lorentz fore. In spite of simpliity and the obviousness of this approah, this simple mehanism up to now was not finally realized. For this reason the Lorentz fore, until now, was introdued in the lassial eletrodynamis by axiomati way. 8. Salar-Vetor Potential and omopolar Indution Sine Faraday opened the phenomenon of homopolar indution, past almost years, but also up to now not all speial features of this phenomenon found their explanation [4,5,7]. Up to now unipolar generator is onsidered exeption from the law of the indution of Faraday. The attempts to explain all speial features of homopolar indution with the aid of postulate about the Lorentz fore did not give results. This postulate assumes that on the harge, whih moves in the magneti field, ats the fore FL = e v µ. In order to use this equation, it is neessary to know harge rate and must be assigned the external magneti field, in whih the harge moves. The osillator iruit, whih realizes the priniple indiated, it is shown in Fig..Faraday also revealed that during the rotation of the onduting disk, magnetized in the end diretion, on the brushes, whih slide along the axis of disk and his generatrix, appears the eletromotive fore. This version of unipolar generator it is not possible to explain the aid of postulate about the Lorentz fore. Fig.. Unipolar generator, with the external magneti field. During the rotation in the magneti field of the rotor, made from ondutor, free harges revolve together with the body of rotor, and Lorentz fore ats on them, and the eletromotive fore appears between the axis of rotor and its periphery. The shemati of the unipolar generator, whose work annot be explained with the aid of the postulate about the Lorentz fore, is represented in Fig. 3

14 AASCIT Journal of Physis 5; (): g v g v = h = πεr πεr +. (8.) Adding q. (8.) and q.(8.), we obtain: g v = 4πε r Fig. 3. Unipolar generator with two disks. On the ommon axis are loated two disks, one of whih is magnetized, but no another. When both disks aomplish joint rotation, the eletromotive fore appears between the heeks, whih slide along the axis of the onduting disk and its generatrix. The eletromotive fore of the same value appears and the when onduting disk revolves, and the magnetized disk is fixed. It does not sueed to explain the work of this generator for that reason, that physial nature of very Lorentz fore is not lear, and up to now it is introdued by axiomati method. Therefore by the first task, whih should be solved in order to explain the work of unipolar generators, the explanation of physial nature of Lorentz fore appears. In the previous division it was shown that the Lorentz fore is the result of the dependene of the salar potential of harge on the speed. Consequently, and the speial feature of the work of different onstrutions of unipolar generators one should also searh for by this method. Let us examine the ase, when there is a single long ondutor, along whih flows the urrent. We will as before onsider that in the ondutor is a system of the mutually inserted harges of the positive lattie of g + and free eletrons of g, whih in the absene urrent neutralize eah other (Fig. 4). The eletri field of ondutor, reated by rigid lattie, is determined by the equation + g + = (8.) πεr This means that around the ondutor with the urrent is an eletri field, whih orresponds to the negative harge of ondutor. owever, this field has insignifiant value, sine in the real ondutors v. This field an be disovered only with the urrent densities, whih an be ahieved in the superondutors. Let us examine the ase, when very setion of the ondutor, on whih with the speedv flow the eletrons, moves in the opposite diretion with speedv (Fig. 5. In this ase qs.(8.) and (8.) will take the form + + g v = πεr + g ( v v) = + πεr Fig. 5. Condutor with the urrent, moving along the axis z. Adding qs. (8.3) and (8.4), we obtain g vv v + = πεr (8.3) (8.4) (8.5) In this equation as the speifi harge is undertaken its absolute value. Sine the speed of the mehanial motion of ondutor is onsiderably more than the drift veloity of eletrons, the seond term in the brakets an be disregarded gvv + = (8.6) πε r Fig. 4. Setion is the ondutor, along whih flows the urrent. We will onsider that the diretion of the vetor of eletri field oinides with the diretion r. If the harges of eletroni flux move with the speedv, then eletrial field of flow is determined by the equation The obtained result means that around the moving ondutor, along whih flows the urrent, is formed eletri field. This is equivalent to appearane on the ondutor of the linear positive harge g + = gvv If we ondutor roll up into the ring and to revolve it then so that the linear speed of its parts would be equal v, then

15 4 F. F. Mende: What is Not Taken into Aount and they Did Not Notie Ampere, Faraday, Maxwell, eaviside and ertz around this ring will appear the eletri field, whih orresponds to the presene on the ring of the speifi harge indiated. But this means that the revolving turn, aquires eletri harge. During the motion of linear ondutor with the urrent the eletri field will be observed with respet to the fixed observer, but if observer will move together with the ondutor, then suh fields will be absent. But if observer will move together with the ondutor, then field will be absent for this observer. In Fig. 6.it is shown, as is obtained a voltage drop aross the fixed ontats, whih slide on the generatrix of the moving metalli plate, whih is loated near the moving ondutor, along whih flows the urrent. together with the turns of magnet, and with the aid of the fixed ontats, that slides on the generatrix of disk, tax voltage on the voltmeter. As the limiting ase it is possible to take ontinuous metalli disk and to onnet sliding ontats to the generatrix of disk and its axis. Instead of the revolving turn with the urrent it is possible to take the disk, magnetized in the axial diretion, whih is equivalent to turn with the urrent, in this ase the same effet will be obtained.in this ase the same effet will be obtained. Fig. 7. Shemati of unipolar generator with the revolving turn with the urrent and the revolving onduting ring. Fig. 6. Diagram of the formation of the eletromotive fore of homopolar indution. We will onsider that r andr of the oordinate of the points of ontat of the tangeny of the fixed ontats, whih slide on the generatrix of metalli plate. Plate itself moves with the same speed also in the same diretion as the ondutor, along whih flows the urrent. Contats are onneted to the voltmeter, whih is also fixed. Then, it is possible to alulate a potential differene between these ontats, after integrating q. (4.6) This diagram orresponds to the onstrution of the generator, depited in Fig. 3, when the onduting and magnetized disks revolve with the idential speed. The given diagram explains the work of unipolar generator with the revolving magnetized disk, sine the onduting and magnetized disk it is possible to ombine in one onduting magnetized disk. The work of generator with the fixed magnetized disk and by the revolving onduting disk desribes the diagram, represented by Fig. 8. gvv dr gvv r U = πε = (8.7) r ln r r πε r In order to apply to the ontats this potential differene, it is neessary sliding ontats to lok by the ross onnetion, on whih a potential differene is absent. But sine metalli plate moves together with the ondutor, a potential differene is absent on it. It serves as the ross onnetion, whih gives the possibility to onvert this omposite outline into the soure of the eletromotive strength, whih ats in the iruit of voltmeter. Now it is possible wire to roll up into the ring (Fig. 7) and to feed it from the soure of diret urrent. Instead of the single turn it is possible to use a solenoid. Contats should be onneted to the olletor ring, loated on the rotational axis, and to the olletor joined feeder brushes. Thus, obtain the revolving magnet. In this magnet should be plaed the onduting disk with the opening (Fig. 5), that revolves Fig. 8. quivalent the shemati of unipolar generator with the fixed magnet and the revolving onduting disk. In this ase the following equations are fulfilled: The eletri field, generated in the moving plate by the