Concept of Scalar-Vector Potential in the Contemporary Electrodynamic, Problem of Homopolar Induction and Its Solution

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1 International Journal of Physis, 04, Vol., No. 6, 0-0 Aailable online at Siene and Eduation Publishing DOI:0.69/ijp--6-4 Conept of Salar-Vetor Potential in the Contemporary Eletrodynami, Problem of Homopolar Indution and Its Solution F.F. Mende * B.I. Verkin Institute for Low Temperature Physis and Engineering NAS, Ukraine, 47 Lenin Ae., Kharko, Ukraine *Corresponding author: mende_fedor@mail.ru Reeied September 6, 04; Reised Otober 0, 04; Aepted Noember 03, 04 Abstrat At present lassial eletrodynamis onsists of two not onneted together parts. From one side this of Maxwell equations, whih determine wae phenomena in the material media, from other side the Lorentz fore, whih determines power interation between the moing harges. Still from the times of Lorenz and Poinare this fore is introdued as experimental postulate. And as yet there is no that united basis, whih onneted together these two odd parts of the eletrodynamis. Present artile soles this problem on the basis of introdution the onept of salar-etor potential, whih assumes the dependene of the salar potential of harge on its relatie speed. In the artile is arried out the analysis of the work of different of the shematis of the unipolar generators, among whih there are diagrams, the priniple of operation of whih, until now, did not yield to explanation. The number of suh diagrams inludes the onstrution of the generator, whose ylindrial magnet, magnetized in the end diretion, reoles together with the onduting disk. Postulate about the Lorentz fore, whom is used for explaining the work of unipolar generators, does not gie the possibility to explain the operating priniple of this generator. It is shown that the onept of salar- etor potential, deeloped by the author, gies the possibility to explain the operating priniple of all existing types of unipolar generators. Physial explanation of Lorentz fore in the onept of salar- etor potential is gien. Keywords: laws of indution, eletri field, salar potential, magneti field, etor potential, Maxwell equation, homopolar indution, unipolar generator Cite This Artile: F.F. Mende, Conept of Salar-Vetor Potential in the Contemporary Eletrodynami, Problem of Homopolar Indution and Its Solution. International Journal of Physis, ol., no. 6 (04): 0-0. doi: 0.69/ijp Introdution Sine Faraday opened the phenomenon of homopolar indution, past almost 00 years, but also up to now not all speial features of this phenomenon found their explanation. 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 gie results. This postulate assumes that on the harge, whih moes in the magneti field, ats the fore FL e = µ 0 H. 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 moes. The osillator iruit, whih realizes the priniple indiated, it is shown in Figure. Faraday also reealed 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 eletromotie fore. This ersion of unipolar generator it is not possible to explain the aid of postulate about the Lorentz fore. Figure. Unipolar generator, with the external magneti field During the rotation in the magneti field of the rotor, made from ondutor, free harges reole together with the body of rotor, and Lorentz fore ats on them, and the eletromotie 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 Figure.

2 International Journal of Physis 03 Figure. 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 eletromotie fore appears between the heeks, whih slide along the axis of the onduting disk and its generatrix. The eletromotie fore of the same alue appears and the when onduting disk reoles, and the magnetized disk is fixed. It does not sueed to explain the work of this generator for that reason, that physial nature of ery Lorentz fore is not lear, and up to now it is introdued by axiomati method. Therefore by the first task, whih should be soled in order to explain the work of unipolar generators, the explanation of physial nature of Lorentz fore appears.. The phenomenon of the Lorentz fore and its explanation in the onept of a salar-etor potential.. Introdution Laws of thelassial eletrodynamis they reflet experimental fats they are phenomenologial. Unfortunately, ontemporary lassial eletrodynamis is not depried of the ontraditions, whih did not up to now obtain their explanation. The fundamental equations of ontemporary lassial eletrodynamis are Maksell equations. They are written as follows for the auum [] B rot E = t (..) D rot H = t (..) di D = 0 (..3) di B = 0 (..4) where E and H is tension of eletrial and magneti field, D = ε0e and B = µ 0H is eletrial and magneti indution, µ 0 and ε0 is magneti and dieletri onstant of auum. From these equations follow wae equations for the eletrial and magneti field E E = µε 0 0 (..5) H H = µε 0 0 (..6) These equations show that in the auum an be extended the plane eletromagneti waes, the eloity of propagation of whih is equal to the speed of light = (..7) µε 0 0 For the material media Maxwell equations they take the following form H B rot E = 0 = (..8) E D rot H ne 0 ne = = (..9) di D = ne (..0) di B = 0 (..) where µ and ε is the relatie magneti and dieletri onstants of the medium and of n, e and is density, alue and harge rate. Of equations (....) are written in the assigned inertial referene system (IRS), and in them there are no rules of passage of one IRS to another. Consequently, if are reorded wae equation in one IRS, then it is not known how to write down them in another frame of referene, whih moes relatie to the first system. The gien equations also assume that the properties of harge do not depend on their speed, sine in first term of the right side of equation (..9) as the harge its stati alue is taken. These equations also assume that the urrent an leak both in the eletrially neutral medium and to represent the isolated flow of the harged partiles. These both situations are onsidered equialent. In Maksell 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 moing harge in the magneti field. This postulate assumes that on the harge, whih moes in the magneti field, ats the fore [] FL e = µ 0H (..) Howeer in this axiomatis is an essential defiieny. If fore ats on the moing harge, then must be known the objet, from side of whih ats this fore. In this ase the magneti field is independent substane, omes out in the role of the mediator between the moing harges. Consequently, there is no law of diret ation, whih would gie answer to a question, as interat the harges, whih aomplish relatie motion. Equation (..) auses bewilderment. In the mehanis the fores, whih at on the moing body, are onneted with its aeleration, with the uniform motion there exist fritional fores. The diretion of these fores oinides with the eloity etor. But the fore, determined by Eq. (..), hae ompletely different property. Retilinear motion auses the fore, whih is normal to the diretion motion, what is assumed none of

3 04 International Journal of Physis the existing laws of mehanis. Therefore is possible to assume that this some new law, whih is onerned relatie motion of those only of harged tel. Is ertain, magneti field is one of the important onepts of ontemporary eletrodynamis. Its onept onsists in the fat that around any moing harge appears the magneti field (Ampere law), whose irulation is determined by the equation [] Hdl = I (..3) where I is ondution urrent. If we to the ondution urrent add bias urrent, then we will obtain the seond equation of Maxwell (..9). It should be noted 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, whih with the aid of the speifi mathematial proedures in large quantities of the ases gie the possibility to obtain orret answer with the solution of pratial problems. But there is a number of the physial questions, to whih the onept of magneti field answer does not gie. Using Eqs. (..) 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. Howeer, if we pass into the inertial system, whih moes together with the harges, then there magneti field is absent, and there is no additional attration. This paradox in the eletrodynamis does not hae an explanation. It does not hae an explanation, also, in the speial theory of relatiity (STR). With power interation of ondutors, along whih flows the urrent, fores are applied not only to the moing harges, but to the lattie. But the onept of magneti field also to this question answer does not gie, sine. In Eqs. (..-..3) the presene of lattie is not onsidered. At the same time, with the flow of the urrent through the plasma its ompression (pinh effet), ours, in this ase fores of ompression at not only on the moing eletrons, but also on the positiely 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 whih is the first Maksell equation. Howeer, here are problems. It is onsidered Until now that the unipolar generator is an exeption to the rule of flow. The existing state of affairs and those ontraditions, whih with this are onneted, perhaps, are most are learly formulated in the sixth olume of work []. We read on page 5 we read flow rule, aording to whih eletromotie fore in the outline it is equal to the speed undertaken with the opposite sign, with whih hanges magneti flux through the outline, when flow hanges due to field hange or when outline moes (or when it ours and that and, et). Two of the possibility of - the outline of moes or the field of hanges - are not distinguished of into of tuthe formulation of the rule. Neertheless, for explaining the rule in these two ases we used two ompletely different laws: B B for moing outline and E = for t hanging field. We know in physis not of one suh example, if simple and preise general law required for its present understanding of analysis in the terms of two different phenomena. Usually of so beautiful of the generalization of proes to be of outgoing from of the united of the deep of that being basi of the priniple of. But in this ase of any separately deep priniple it is not eident. All these examples be eidene the fat that the law of the indution of Faraday is inaurate or not omplete and does not reflet all possible ersions of the appearane of eletrial pour on with a hange of the magneti field or during the motion in the Ger. From the aforesaid it is possible to onlude that physial nature of Lorentz fore, whih from the times of Lorenz and Poinare is introdued by axiomati method, is not thus far known to us... Laws of the Indution With onduting of experiments 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 moes relatie to the first outline. Therefore in general form Faraday law is written as follows [3] dφ E dl = B (..) dt This writing of law indiates that with the determination of the irulation of E in the moing oordinate system, near E and dl must stand primes and should be taken total deriatie. But if irulation is determined in the fixed oordinate system, then primes near E and dl be absent, but in this ase to the right in Eq. (..) must stand partiular time deriatie. Complete time deriatie in Eq. (..) indiates the independene of the eentual result of appearane eletromotie fore in the outline from the method of hanging the flow. Flow an hange as beause B it depends on time, so also beause the system, in whih is determined the irulation E dl, it moes in the magneti field, whose alue depends on oordinates. The alue of magneti flux in Eq. (..) is determined from the equation ФB = B ds (..) where the magneti indution B = µ H is determined in the fixed oordinate system, and the element ds is determined in the moing system. Taking into aount Eq. (..), we obtain from Eq..(.) d E dl = B ds dt sine d = grad let us write down [4,5] dt B E dl ds = B dl dibds (..3) In this ase ontour integral is taken on the outline dl, whih oers the area ds. Let us immediately note that

4 International Journal of Physis 05 entire following presentation will be onduted under the assumption the alidity of the Galileo onersions, i.e., dl = dl and ds = ds. During the motion in the magnetostati field is fulfilled the E = B. Let us note that this equation is obtained not by the introdution of postulate about the Lorentz fore. Thus, Lorentz fore is the diret onsequene of the law of magnetoeletri indution. Faraday law indiates that how a hange in the magneti pour on, or motion in these fields, it leads to the appearane of eletrial pour on; therefore it should be alled the law of magnetoeletri indution. Howeer, in the lassial eletrodynamis there is no law of eletromagneti indution, whih would show, how a hange in the eletrial pour on, or motion in them, it leads to the appearane of magneti pour on. The deelopment of lassial eletrodynamis followed along another way. Was first known the Ampere law Hdl= I (..4) where I is urrent, whih rosses the area, inluded by the outline of integration. In the differential form Eq. (..4) takes the form rot H = j σ (..5) where j σ is urrent density of ondutiity. Maxwell supplemented Eq. (..5) with bias urrent D rot H = jσ t (..6) Howeer, must exist the law of eletromagneti indution, whih determines magneti fields in the hanging eletri field d Φ Hd l = D (..7) dt where Φ D = DdS is the flow of eletrial indution [4,5] D H dl = ds [ D V ] dl VdiDdS t (..8) In ontrast to the magneti pour on, when di B = 0, for the eletrial field on di D = ρ and last term in the right side of Eq. (..8) it gies the ondution urrent of I and from Eq. (..7) the Ampere law immediately follows. During the motion in the DC fields we obtain H = [ D V] (..9) As shown in the work [], from Eq. (..9) follows and Bio-Saart law, if for enumerating the magneti pour on to take the eletri fields of the moing harges. In this ase the last member of the right side of Eq. (..8) an be simply omitted, and the laws of indution aquire the ompletely symmetrial form [4,5,6,7] B E dl ds B = dl (..0) D H dl = ds D dl For the onstants fields on transformation laws they take the following form E = [ B], H = [ D]. (..).3. Dynami Potentials and the Field of the Moing Charges In the lassial eletrodynamis be absent the rule of the onersion of eletrial and magneti fields on upon transfer of one inertial system to another. This defiieny remoes STR. With the entire mathematial alidity of this approah the physial essene of suh onersions up to now remains unexplained. Let us explain, what potentials and fields an generate the moing harges. The first step, demonstrated in the works [4,5,6,7], was made in this diretion a way of the introdution of the symmetrial laws of magnetoeletri and eletromagneti indution Eq. (..0). Equations (..0,..) attest to the fat that in the ase of relatie motion of frame of referenes, between the fields E and H there is a ross oupling, i.e., motion in the fields H leads to the appearane fields E and ie ersa. From these equations esape the additional onsequenes, whih were for the first time examined in the work [4]. The eletri field E = g πε r The eletri field outside along harged rod dereases aording to r. If we in parallel to the axis of rod in the field of begin to moe with the speed another IRS, then in it will appear the additional magneti field. If we now with respet to already moing IRS, begin to moe third frame of referene with the speed, then already due to the motion in the field H will appear additie to the eletri field E = µε E( ). This proess an be ontinued and further, as a result of whih an be obtained the number, whih gies the alue of the eletri field of E ( r) in moing IRS with reahing of the speed of = n, when 0, and n. In the final analysis in moing IRS the alue of dynami eletri field will proe to be more than in the initial and to be determined by the equation gh E ( r, ) = = Eh (.3.) πε r If speeh goes about the eletri field of the single harge, then its eletri field will be determined by the equation

5 06 International Journal of Physis eh E ( r, ) = 4πε r where is normal omponent of harge rate to the etor, whih onnets the moing harge and obseration point. Expression for the salar potential, reated by the moing harge, for this ase will be written down as follows [4,5,6,7] eh ϕ (, r ) = = ϕ() rh (.3.) 4πε r where ϕ () r is salar potential of fixed harge. The potential ϕ (, r ) an be named salar-etor, sine it depends not only on the absolute alue of harge, but also on speed and diretion of its motion with respet to the obseration point. Maximum alue this potential has in the diretion normal to the motion of harge itself. During the motion in the magneti field, using the already examined method, we obtain H ( ) = Hh where is speed normal to the diretion of the magneti field. If we apply the obtained results to the eletromagneti wae and to designate omponents pour on parallel speeds IRSas E, H and E, H as omponents normal to it, then onersions pour on they will be written down E = E, Z0 E E h = H sh, (.3.3) H = H, H = H h E sh, Z 0 µ 0 where Z0 = is impedane of free spae, = ε0 µε 0 0 is speed of light. Conersions fields (.3.3) they were for the first time obtained in the work [4]..4. Power Interation of Parallel Condutors. The onept of magneti field arose to a onsiderable degree beause of the obserations of power interation of the urrent arrying and magnetized systems. Experiene with the iron shaings, 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 sered 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 effetie 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 gie 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 moing harges. Is experimentally known that the fores of interation in the urrent arrying systems are applied to those ondutors, whose moing harges reate magneti field. Howeer, in the existing onept of power interation of the urrent arrying systems, based on the onepts of magneti field and Lorentz fore, the positiely harged lattie, whih is the frame of ondutor and to whih are applied the fores, it does not partiipate in the formation of the fores of interation. Let us examine this question on the basis of the onept of salar-etor potential [4,5,6,7]. We will onsider that the salar- etor potential of single harge is determined by Eq. (.3.), and that the eletri fields, reated by this potential, at on all surrounding harges, inluding to the harges positiely harged latties. Let us examine from these positions power interation between two parallel ondutors (Figure 3), along whih flow the urrents. We will onsider that g, g and g, g present positie and negatie linear harges in the upper and lower ondutors. Figure 3. hemati of power interation of the urrent arrying wires of two-wire iruit taking into aount the positiely harged lattie. We will also onsider that both ondutors prior to the start of harges are eletrially neutral, i.e., in the ondutors there are two systems of the mutually inserted opposite harges with the speifi density to, and whih eletrially neutralize eah other. in Figure these systems are moed apart along the axis z. Subsystems with the negatie harge (eletrons) an moe with the speeds and. The fore of interation between the lower and upper ondutors we will searh for as the sum of four fores, whose designation is understandable from the figure. The repulsie fores F and F we will take with the minus sign, while the attrating fore F 3 and 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 g g F =, F = h, πε r πε r (.4.) g g g g F 3 = h, F4 = h. πε r πε r Adding fores, we will obtain the amount of the omposite fore

6 International Journal of Physis 07 gg F h h h Σ = πε r (.4.) In this expression as g and g are undertaken the absolute alues of harges, and the signs of fores are taken into aount in the braketed expression. For the ase << let us take only two first members of expansion in the series h, i.e. we will onsider that h. From Eq. (.4.) we obtain gg II F Σ = πε r = πε r (.4.3) where g and g are undertaken the absolute alues of speifi harges, and and take with its signs. Sine the magneti field of straight wire, along whih flows the urrent I, we determine by the equation H = from Eq. (.4.3) we obtain I π r II HI F Σ = I µ H πε r = ε =, where H is the magneti field, reated by lower ondutor in the loation of upper ondutor. It is analogous FΣ = Iµ H where H is the magneti field, reated by upper ondutor in the region of the arrangement of lower ondutor. The results, obtained in the model of salar- etor potential, ompletely oinide with the results, obtained on the basis of the onept of magneti field. Equation (.4.3) represents the known rule of power interation of the urrent arrying systems, but is obtained it not by the phenomenologial way on the basis of the introdution of phenomenologial magneti field, but on the basis of ompletely intelligible physial proedures, under the assumption that that the salar potential of harge depends on speed. 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 isible 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 h. For the speeds ~ should be taken all terms of expansion. In terms of this the proposed method is differed from the method of alulation of power interations by the basis of the onept of magneti field. If we onsider this irumstane, then the onnetion between the fores of interation and the harge rates proes 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 alues of urrents, but with their different diretions, the attrating fores and repulsion beome unequal. Repulsie fores proe to be greater than attrating fore. This differene is small and is determined by the equation II F =. πε ε But with the speeds of the harge arriers of lose ones to the speed of light it an proe to be ompletely pereptible. Let us remoe the lattie of upper ondutor and after leaing only free eletroni flux. In this ase will disappear the fores F and F 3, and this will indiate interation of lower ondutor with the flow of the free eletrons, whih moe with the speed on the spot of the arrangement of upper ondutor. In this ase the alue of the fore of interation is defined as gg F h h Σ = πε r (.4.4) The Lorentz fore assumes linear dependene between the fore, whih ats on the harge, whih moes in the magneti field, and his speed. Howeer, in the obtained equation the dependene of the amount of fore from the speed of eletroni flux will be nonlinear. From Eq. (.4.4) of it is not diffiult to see that with an inrease in the deiation from the linear law inreases, and in the ase, when >>, the fore of interation are approahed zero. This is ery meaningful result. Speifially, this phenomenon obsered in their known experiments Thompson and Kauffmann, when they noted that with an inrease in the eloity of eletron beam it is more badly slanted by magneti field. They onneted the results of their obserations with an inrease in the mass of eletron. As we see reason here another. Let us note still one interesting result. Taking into aount Eq. (4.3), the fore of interation of eletroni flux with the retilinear ondutor an be determined from the equation gg F Σ =. (.4.5) πε r From Eq. (.4.5) follows that with the unidiretional eletron motion in the ondutor and in the eletroni flux the fore of interation with the fulfillment of onditions of = 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 Eq. (.4.5) an be disregarded. Then, sine g H = πε r will the magneti field, reated by lower ondutor in the plae of the motion of eletroni flux

7 08 International Journal of Physis gg F g H πε r Σ = = µ. In this ase, the obtained alue of fore exatly oinides with the alue of Lorentz fore. Taking into aount that FΣ = ge = gµ H, it is possible to onsider that on the harge, whih moes in the magneti field, ats the eletri field E, direted normal to the diretion of the motion of harge. This result also with an auray to of the quadrati terms of ompletely oinides with the results of the onept of magneti field and is determined the Lorentz fore, whih ats from the side of magneti field to the flow of the moing eletrons. 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 moed 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 leae only eletroni fluxes, then will remain only the repulsie fore F. Thus, the moing eletroni flux interats simultaneously both with the moing eletrons in the lower wire and with its lattie, and the sum of these fores of interation it is alled Lorentz fore. This fore ats on the moing eletron stream. Regularly does appear a question, and does reate magneti field most moing eletron stream of in the absene ompensating harges? 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 positiely harged lattie. Therefore most moing eletroni flux annot reate that effet, whih is reated during its motion in the positiely harged lattie. 3. Operating Priniple of Different Construtions of the Unipolar Generators In the preious diision 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. r g g - Figure 4. Setion is the ondutor, along whih flows the urrent Let us examine the ase, when there is a single long ondutor, along whih flows the urrent. We will as z before onsider that in the ondutor is a system of the mutually inserted harges of the positie lattie of g and free eletrons of g, whih in the absene urrent neutralize eah other (Figure 4). The eletri field of ondutor, reated by rigid lattie, is determined by the equation g E = (4.) πε r We will onsider that the diretion of the etor of eletri field oinides with the diretion of r. If the harges of eletroni flux moe with the speed, then eletrial field of flow is determined by the equation g g E = h (4.) πε r πε r Adding Eq. (4.) and Eq.(4.), we obtain: g E = 4πε r This means that around the ondutor with the urrent is an eletri field, whih orresponds to the negatie harge of ondutor. Howeer, this field has insignifiant alue, sine in the real ondutors. This field an be disoered only with the urrent densities, whih an be ahieed in the superondutors, whih is experimentally onfirmed in papers [8,9,0]. Let us examine the ase, when ery setion of the ondutor, on whih with the speed flow the eletrons, moes in the opposite diretion with speed (Figure 5. In this ase Eqs. (4.) and (4.) will take the form r E g = πε r g ( ) E = πε r g g - Figure 5. Condutor with the urrent, moing along the axis Z Adding Eqs. (4.3) and (4.4), we obtain g E = πε r (4.3) (4.4) z (4.5) In this equation as the speifi harge is undertaken its absolute alue. Sine the speed of the mehanial motion of ondutor is onsiderably more than the drift eloity of eletrons, the seond term in the brakets an be disregarded

8 International Journal of Physis 09 E g = (4.6) πε r The obtained result means that around the moing ondutor, along whih flows the urrent, is formed eletri field. This is equialent to appearane on the ondutor of the linear positie harge of g g = If we ondutor roll up into the ring and to reole it then so that the linear speed of its parts would be equal, then 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 reoling turn, aquires eletri harge. During the motion of linear ondutor with the urrent the eletri field will be obsered with respet to the fixed obserer, but if obserer will moe together with the ondutor, then suh fields will be absent. But if obserer will moe together with the ondutor, then field will be absent for this obserer. In Figure 6. it is shown, as is obtained a oltage drop aross the fixed ontats, whih slide on the generatrix of the moing metalli plate, whih is loated near the moing ondutor, along whih flows the urrent. Now it is possible wire to roll up into the ring (Figure 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 reoling magnet. In this magnet should be plaed the onduting disk with the opening (Figure 7), that reoles together with the turns of magnet, and with the aid of the fixed ontats, that slides on the generatrix of disk, tax oltage on the oltmeter. 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 reoling turn with the urrent it is possible to take the disk, magnetized in the axial diretion, whih is equialent to turn with the urrent, in this ase the same effet will be obtained. In this ase the same effet will be obtained. Figure 6. Diagram of the formation of the eletromotie fore of homopolar indution We will onsider that r and r 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 moes with the same speed also in the same diretion as the ondutor, along whih flows the urrent. Contats are onneted to the oltmeter, whih is also fixed. Then, it is possible to alulate a potential differene between these ontats, after integrating Eq. (4.6) g r dr g r U = ln = (4.7) πε 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 moes together with the ondutor, a potential differene is absent on it. It seres as the ross onnetion, whih gies the possibility to onert this omposite outline into the soure of the eletromotie strength, whih ats in the iruit of oltmeter. Figure 7. Shemati of unipolar generator with the reoling turn with the urrent and the reoling onduting ring This diagram orresponds to the onstrution of the generator, depited in Figure, when the onduting and magnetized disks reole with the idential speed. The gien diagram explains the work of unipolar generator with the reoling 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 reoling onduting disk desribes the diagram, represented by Figure 8. Figure 8. Equialent the shemati of unipolar generator with the fixed magnet and the reoling onduting disk In this ase the following equations are fulfilled:

9 0 International Journal of Physis The eletri field, generated in the moing plate by the eletrons, whih moe in the fixed ondutor, is determined by the equation g g ( ) E h = = πε r πε r and the eletri field, generated in the moing plate by ions in the fixed ondutor, is determined by the equation E g g = h = πε r πε r The summary tension of eletri field in this ase will omprise g E = πε r The potential differene between the points r and r in the oordinate system, whih moes together with the plate, we will obtain, after integrating this equation with respet to the oordinate g r dr g r U = ln = πε r r πε r It is eident that this equation oinides with Eq. (4.7). In the iruit of oltmeter, fixed with respet to the fixed ondutor, a potential differene is absent; therefore the potential differene indiated will be equal to the eletromotie fore ating in the hain in question. As earlier moing onduting plate an be rolled up into the disk with the opening, and the wire, along whih flows the urrent into the ring with the urrent, whih is the equialent of the magnet, magnetized in the end diretion. Ring an be replaed with solenoid. Thus, the onept of salar-etor potential gies answers to all presented questions. 4. Conlusion In the artile is arried out the analysis of the work of different of the shematis of the unipolar generators, among whih there are diagrams, the priniple of operation of whih, until now, did not yield to explanation. The number of suh diagrams inludes the onstrution of the generator, whose ylindrial magnet, magnetized in the end diretion, reoles together with the onduting disk. Postulate about the Lorentz fore, whom is used for explaining the work of unipolar generators, does not gie the possibility to explain the operating priniple of this generator. It is shown that the onept of salar- etor potential, deeloped by the author, gies the possibility to explain the operating priniple of all existing types of unipolar generators. Physial explanation of Lorentz fore in the onept of salar- etor potential is gien. Referenes [] R. Feynman, R. Leighton, M. Sends, Feynman letures on physis, M:, Mir, Vol. 6, 977. [] V.V.Niolsky, T.I. Niolskaya, Eletrodynamis and propagation of radio waes, Mosow, Nauka, 989. [3] J.Jakson, Classial Eletrodynamis, Mir, Mosow, 965. [4] F.F. Mende, On refinement of equations of eletromagneti indution, Kharko, deposited in VINITI, No B88 Dep., 988. [5] F.F. Mende, On refinement of ertain laws of lassial eletrodynamis, arxi.org/abs/physis/ [6] F. F. Mende, New eletrodynamis. Reolution in the modern physis, Kharko, NTMT, 0. [7] F. F.Mende, New approahes in ontemporary lassial eletrodynamis, Part II, Engineering Physis,, 03. [8] W.F. Edwards, C.S. Kenyon, D.K. Lemon, Continuing inestigation into possible eletri arising from steady ondution urrent, Phys. Re. D 4, 9 (976). [9] F.F. Mende, Experimental orroboration and theoretial interpretation of dependene of harge eloity on DC flow eloity through superondutors, Proeedings International Conferene Physis in Ukraine, Kie -7 June, 993. [0] F. F. Mende, A New Tipe of Contat Potential Differene and Eletrifiation of Superonduting Coils and Tori, Amerian Journal of Eletrial and Eletroni Engineering, Vol., No. 5, (04), 46-5.