New Type Contact Potential Difference Electrification of Superconducting Coils and Tori

Transcription

1 AASCIT Journal of Physis 15; 1(): Published online April 3 15 ( New Type Contat Potential Differene Eletrifiation of Superonduting Coils and Tori F. F. Mende B. Verkin Institute for Low Temperature Physis and Engineering NAS Ukraine Lenin Ae. 47 Kharko Ukraine address mende_fedor@mail.ru Keywords Contat Potential Differene Magneti Field Ponder Motie Fore Superondutor Eletrization Salar-Vetor Potential Reeied: April 7 15 Reised: April 3 15 Aepted: April 4 15 Citation F. F. Mende. New Type Contat Potential Differene Eletrifiation of Superonduting Coils and Tori. AASCIT Journal of Physis. Vol. 1 No. 15 pp Abstrat In the artile is examined new physial phenomenon the eletrourent ontat potential differene whose alue depends on the urrent whih flows along the ondutor. Unfortunately the omputed alues of eletrourent ontat a potential differene proed to be onsiderably lower than the potentials obsered in the experiment. The arried out experiments and alulations showed that the disoered eletrization of the superondutie windings and tori finds its explanation in the onept of salar-etor potential deeloped by the author. This onept assumes the dependene of the salar potential of harge on its relatie speed. 1. Eletrourent Contat Potential Differene The ontat potential differene this is the potential differene whih appears between the loated in the eletrial ontat ondutors under the thermodynami equilibrium onditions. As a result this between the ondutors ours the eletron transfer until the Fermi leels in both ondutors are made een. The established ontat potential differene is equal to differene the work funtion of ondutors referred to the eletron harge. But from the attention of researhers slipped off still one type of ontat potential differene whih ours with the flow of the urrent through the superondutors. The amount of the ponder motie fore gradient whih ats on the single square of the surfae of ondutor is determined by the relationship F 1 = µ H where H is magneti field on the surfae of ondutor µ is magneti permeability. This fore is applied to the moing eletrons and attempts to press eletroni flux. In order to balane the fore indiated near the surfae of superondutor is formed the positiely harged layer depleted by eletrons the eletrostati field of this layer it balanes the ponderomotie fore (Fig. 1) If the superondutor along whih flows the urrent to lead into the ontat with the normal metal then the part of the eletrons from this metal will pass to depletion layer and between the superondutor and the normal metal is formed the ontat potential differene whih is proportional to the square of urrent. For forming the layer depleted by eletrons the energy of magneti field is expended and for enumerating the ontat potential differene should be made leel energy of the magneti field R of eletrostati energy of depletion layer. A ontat potential differene omprises for the ase of round ondutor

2 AASCIT Journal of Physis 15; 1(): Fig. 1. Compression of the eletroni flux whih flows along the ondutor. µ I ϕ = (1.1) ( πd) en. Experimental Study of the Eletrization of the Superondutie Windings and Tori For the introdution of urrent into the superondutie winding was used the transformer with the iron ore ooled to helium temperatures using as the seondary winding of transformer the superondutie winding onneted with the external superondutie outline it is possible without the presene of galani ontats to introdue urrent into this outline. For the purpose of the derease of the indutane of outer dut it is exeuted in the form double winding (further nonindutie windings).in the transformer was used ringshaped ore made of transformer steel with a ross setion 9 m. The primary and seondary windings of transformer were wound by niobium-titanium wire with the opper oating and ontained 15 and 1 turns respetiely. Thus transformer has a transformation ratio 15. The wire diameter omposed.5 mm. The seondary winding of transformer is onneted in series with the solenoid with the small indutane whih is wound bifilar and ontains 448 turns of the same wire. The oerall length of oil omposes 91 m. The ends of solenoid and seondary winding of transformer are welded with the aid of the laser welding. Nonindutie windings is wound on the body from teflon resin. Inside and outside diameter of the winding of solenoid 35 and 9 mm respetiely the width of the oil 3 mm. To the midpoint of nonindutie windings is onneted the entral ore of the oaxial whih emerges outside ryostat the same oaxial is onneted also to the sreen whih surrounds nonindutie windings. The onstrution of nonindutie windings and elements of its fastening is shown in Fig.. Fig.. Constrution of that superonduting nonindutie windings with braing struts. By numbers in the figure are designated the following elements: 1- aluminum body - teflon bushing 3 - teflon disk 4- lamp 5 - ounter 6- bolt 7- opper sreen 8 - teflon body. Nonindutie windings are wound on teflon body 8 whih is onluded in aluminum body 1. Outside solenoid is surrounded by opper sreen 7. To body 1 with the aid of bolt 6 and teflon bushing is fastened teflon disk 3 on whih is installed lamp 4.The turns of the seondary winding of transformer oer lamp 4 through whih without onerning it is passed the magneti iruit of transformer. Entire onstrution is attahed to the transformer by means of ounters 5. Transformer together with the nonindutie windings is plaed in the tank of helium ryostat. The diagram of the onnetion of oaxials to nonindutie windings and to sreen to its surrounding is shown in Fig Fig. 3. Diagram of onnetion of nonindutie windings and sreen with the oaxials.

3 93 F. F. Mende: New Type Contat Potential Differene Eletrifiation of Superonduting Coils and Tori By the figure are aepted the following designations: 1- nonindutie windings - the sreen of nonindutie windings 34 - oaxials 5 -the ommon sreen whih the helium tank is. Resistane between the grounded elements the sreen of solenoid and solenoid itself omposes not less than ~1 14 Ohm. The elements utilized in the onstrution had the following apaities relatie to the earth:oaxial 3-44 pf oaxial 4-7 pf apaity sreen - the earth it omprises - 34 pf apaity sreen - solenoid ompose - 45 pf as the eletrometer was used by apaitie ibrating reed eletrometer with a input apaitane6 pf and a input resistane ~1 14 Ohm. With the measurements the eletrometer was onneted to the solenoid with the aid of oaxial 3 and sreen with the aid of the oaxial I was grounded. Current into the primary winding of transformer was introdued from the soure of diret urrent indiation of eletrometer in this ase they did not depend on diretion of flow. With the strengths of introdued urrent ~9 A ourred the disharge of the indiations of eletrometer. This means that the urrent in the winding of solenoid reahed its ritial alue and winding onerted to normal state. The experimental dependene of a ontat potential differene is shown in Fig. 4. The alues of a oltage drop aross figure shows with the opposite sign. Fig. 4. Dependene of the gien oltage drop aross solenoid on the urrent in the primary winding of transformer. Experimental data are gien in the table 1. Table 1. Experimental data. I( A ) I ( ) 1 AS A H 1 m U ( U ( mв) U mв I А эф In the first graph of table are gien the alue of the urrent I introdued into the primary winding. In the seond graph are gien the alues of the urrent I 1 in the nonindutie windings alulated on the basis of the alue of the transformation ratio of equal to 15. In this ase it is assumed that in entire range of the introdued urrents the magnetization of ore remains proportional to urrent. In the third graph are gien the alues of magneti pour on the surfae of the superondutie wires of nonindutie windings. In the fourth graph the indiations of eletrometer are indiated. In the fifth graph the indiations of the effetie alues of a potential differene are indiated. These alues orrespond to the alue of potential between the solenoid and the sreen to the onnetion to the sreen of the total apaitane of oaxial and eletrometer. In the U эф sixthgraphthe indiations of the oeffiient k = whih I indiates the deiation of the obtained dependene on the quadrati law. The root-mean-square relatie defletion of the oeffiient of k from its aerage alue equal to 1.93 omposes.13 whih gies relatie root-mean-square error 7%. Thus the obtained dependene between the urrent and the measured alue of potential is ery lose to the quadrati law. It is also eident from the table that with the alues of urrent in the ondutors of solenoid on the order 1 A the field strength on their surfae reahes its ritial alue whih for the utilized superondutor omposes 1.5x15 A/m with whih and is onneted the disharge of the indiations of eletrometer with reahing of these urrents. With this is onneted the disharge of the indiations of the eletrometer whih ours upon transfer of the superondutie winding into the normal state and it leads to damping of the superondutie urrent. The measurement of a potential differene was onduted also aording to the diagram when eletrometer was onneted to the sreen with the aid of oaxial 4 but nonindutie windings anywhere was not onneted. In this ase was obtained the dependene analogous to that whih was depited in Fig. 4 but the amplitude of stress was approximately two times less. It is interesting to note that the dependene indiated remains een when nonindutie windings it is grounded. This it indiates that the eletri fields whih indue potential in the sreen are reated by the harges whih moe into nonindutie windings. These results annot explain the existing laws of eletrodynamis sine. the obtained result indiates that the harge is not the inariant of speed. For the first time ommuniation about the eletrization of the superondutie windings into whih was introdued diret urrent was published in artile [1]. Subsequently similar studies were exeuted by the authors of this artile [ ]. Important irumstane is the fat that with potential measurement of sreen 1 in whih are plaed nonindutie windings ariation gien in Fig. 4 are repeated. Similar results were obtained also in the experiments with the niobium superondutie torus. the diagram of experiment is shown in Fig. 5. Inside the onduting sreen was plaed the

4 AASCIT Journal of Physis 15; 1(): seond onduting sreen in whih the superondutie torus made from niobium was loated and eletrometer was onneted by these sreens. In the experiment as external sreen 1 the yoke of transformer made from transformer steel was used. On the entral rod of yoke was loated primary winding with wound by niobium-titanium wire and whih ontains 186 turns. Torus-shaped metal sreen 3 made from opper was loated on the same rod. Torus 4 made from niobium was loated inside this sreen.the outer diameter of niobium torus was 76 mm and internal 49 mm. Transformer was plaed in the tank of helium ryostat and was ooled to the helium temperature in this ase the yoke of transformer and helium tank were grounded. The urrent was indued during the introdution of diret urrent into the primary winding of transformer in the superondutie torus and eletrometer fixed the appearane between sreen 3 and yoke of transformer a potential differene U. This means that the niobium torus loated inside sreen 3 during the introdution into it of diret urrent eases to be eletrially neutral. The onstant alue urrent in the superondutie torus 186 times exeeds the urrent introdued into the primary winding of transformer. Fig. 5. Diagram of experiment with the superondutie torus. The dependene of a potential differeneu on the urrent I introdued into the primary winding of transformer it is shown in Fig. 6. Fig. 6. Dependene of a potential differene boundary by sreen 3 by the yoke of transformer on the urrent introdued into the primary winding of transformer. The obtained alues of a potential differene in omparison with the ase of the superondutie wire winding proed to be onsiderably smaller this is onneted with the onsiderably smaller surfae of torus in omparison with the surfae of wire winding. This is onneted with the fat that the surfae of torus onsiderably less than the surfae of the wire of solenoid. The form of the dependene of a potential differene on the introdued urrent also strongly differs. Quadrati setion is obsered only in the ery small initial setion up to the alues of urrents ~ A introdued into the primary winding. Further this dependene beomes pratially linear with the small slope angle. The disharge of the indiations of eletrometer it was not obsered. In the ase of nonindutie windings the superondutie urrent is eenly distributed oer the surfae of wire and reahes its ritial alue in all its setions simultaneously. With this is onneted the simultaneous passage of the entire winding of solenoid into the normal state with the reahing in the wire of the ritial alue of urrent. In the ase of torus the proess of establishing the superondutie urrent on its surfae ours differently. That introdued into the diret urrent superonduting torus is ery uneenly distributed oer its surfae. Maximum urrent densities our on the internal surfae of torus and they are onsiderably less on the periphery. With this is onneted the fat that the internal surfaes of torus begin to onert to normal state earlier than external. The proess of passing the torus into the normal state normal phase begins to be moed from the interior of torus to the external regions. Proess lasts until entire torus passes into the normal state. But why in this ase up to the moment of passing the torus into the normal state does not our the disharge of urrent as it takes plae in the ase of wire solenoid? This niobium is onneted with the fat that the superondutor of the seond kind and he has the suffiiently signifiant region of magneti pour on with whih it is in the mixed state. In this ase inside the massie superondutor Abrikoso's orties penetrate. The irumstane that the indiations of eletrometer do not hae a disharge of indiations he indiates the fat that superondutie torus it is in the mixed state. In this ase ortex strutures also present the superondutie urrents and they hae an effet on the eletrization of torus. If we hange diretion of flow in the primary winding then the dependene similar to that depited in Fig. 6 is repeated howeer it is obsered strong hysteresis. This is onneted with the fat that the orties whih penetrated into the depths of the superondutor they are attahed on the staking faults falling into potential wells that also leads to hysteresis. The eletrization of the superondutie windings and tori does not find the explanation of the within the framework existing eletrodynamis these results do not find explanation and within the framework the speial theory of relatiity. Is the thus far only theory whih is apable of explaining the obtained results the onept of salar-etor

5 95 F. F. Mende: New Type Contat Potential Differene Eletrifiation of Superonduting Coils and Tori potential whih assumes within the framework the onersions of Galileo the dependene of the salar potential of harge on his speed [47891]. 3. Results of Other Authors and the Consideration of the Obtained Results superondutie windings is arried out in work [1]. In this ase also was used the double winding (nonindutie windings) from the niobium-titanium wire opper-plated. The length of wire is 71 m and the diameter of wire is equal to 18 mm. The shemati of experimental installation is shown in Fig. 7 and its omposition and elements are shown in Fig. 8. The thorough the study of the eletrization of the Fig. 7. The shemati of experimental installation. In the installation besides mehanial keys is loated the thermal key S4 whih makes it possible to onert the part of the superondutie loked outline to normal state. In the hain of outline is a resistane R by whih is shunted nonindutie windings and solenoid L. Solenoid has a small quantity of turns and is used for measuring the urrent into nonindutie windings. Measurement is onduted with the aid of the Hall pikup whih measures the magneti field of solenoid. The resistane of the thermal key R p is seleted in suh a way that would be satisfied the ondition R p R. With satisfation of this ondition after the swithing on of thermal key the urrent of nonindutie windings flows through the resistane R. This gies possibility with the aid of the eletrometer onneted to the outline to obsere the behaior of potential on the outline in the proess of damping urrent into nonindutie windings. Outline and thermal key are loated in the brass sreen. Inside the sreen to teflon ounter are fastened the ontats through whih is introdued the urrent into nonindutie windings. These ontats are fastened to beryllium- Cooper springs to the ontats are onneted the wires of nonindutie windings. Current to the ontats brings with the aid of urrent of rod. When urrent of rod raises upward ontats are opened.

6 AASCIT Journal of Physis 15; 1(): In the proess of onduting the experiments were realized 96 two operating modes. Fig. 8. Composition and the elements of experimental installation. In the first regime urrent was introdued into the outline thermal key and then was inluded. In this regime ourred the exponential damping of urrent into nonindutie windings and the behaior of eletri potential on the outline was obsered with the aid of the eletrometer. The obtained dependenes are represented in Fig. 9. From the represented dependenes is eident that to the great signifianes of urrent orrespond the high absolute alues of potentials whih oinides with the results of the experiments represented in Fig. 4. The amplitude of potential hange omposes ~1 mv. Dependene between the potential and the urrent into nonindutie windings orresponds to quadrati law. The speial interest the results of the experiment when eletrometer was onneted diretly to bras of shields (Faraday Cage) present but outline is not anywhere onneted. This experiment is desribed in the diision B. Variation II.For the realization of this experiment from the

7 97 F. F. Mende: New Type Contat Potential Differene Eletrifiation of Superonduting Coils and Tori omposition of outline thermal key was exluded. Current into nonindutie windings was introdued with the aid of urrent of rod whih after the introdution of urrent rose upward and urrent soure was disonneted from the outline. At the same moment to bras of shields was onneted the eletrometer. The diagram of this experiment is represented in Fig. 1. by the author in whih the salar potential of harge depends on its speed [47891]. Fig. 9. Dependene of the potential of outline on the urrent in the ger. Fig. 11. Experimental results obtained aording to the diagram Variation II. 4. Dynami Potentials and the Field of the Moing Charges Fig. 1. Isolated outline plaed into Faraday Cage. The experimental results of experiment are represented in Fig. 11. Is eident that a hange of the urrent into nonindutie windings leads to the appearane of potential on the outline whih is loated into Faraday Cage. This result ontradits the existing laws of eletrodynamis sine gies the foundation for assuming that the harge is not the inariant of speed. Similar results were obtained both by ontributor in the experiments with the superondutie windings and by tori desribed in the preious diision. The thus far only theory whih an explain the phenomena indiated is the onept of salar-etor potential deeloped In this diision will made attempt find the preisely physially substantiated ways of obtaining the onersions fields on upon transfer of one IS to another and to also explain what dynami potentials and fields an generate the moing harges. The first step demonstrated in the works [47.8] was made in this diretion a way of the introdution of the symmetrial laws of magnetoeletri and eletromagneti indution. These laws are written as follows: B E dl = t ds + B dl D H dl = ds D dl t (4.1) or B + rot B t D roth = rot D dt rote = (4.)

8 AASCIT Journal of Physis 15; 1(): For the onstants fields on these relationships they take the form: E = B (4.3) H = D In relationships ( ) whih assume the alidity of the Galileo onersions prime and not prime alues present fields and elements in moing and fixed IS respetiely. It must be noted that onersions (4.3) earlier ould be obtained only from Lorenz onersions. The relationships ( ) whih present the laws of indution do not gie information about how arose fields in initial fixed IS. They desribe only laws goerning the propagation and onersion fields on in the ase of motion with respet to the already existing fields. The relationship (4.3) 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 on E and ie ersa. From these relationships esape the additional onsequenes whih were for the first time examined in the work [5]. g The eletri field E = outside the harged longrod πεr with alinear density g dereases as 1 where r is distane r from the entralaxis of the rodto the obseration point. If we in parallel to the axis of rod in the fielde begin to moe with the speed another IS then in it will appear the additional magneti field H = εe. If we now with respet to already moing IS 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 = µεe. This proess an be ontinued and further as a result of whih an be obtained the number whih gies E r in moing IS with the alue of the eletri field ( ) reahing of the speed = n when and n.in the final analysis in moing IS the alue of dynami eletri field will proe to be more than in the initial and to be determined by the relationship: gh E ( r ). = = Eh πεr If speeh goes about the eletri field of the single harge e then its eletri field will be determined by the relationship: eh E ( r ) = 4πεr 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: eh ( ) ϕ r = = ϕ( r) h 4πεr (4.4) 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. Moreoer 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: 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 fields on parallel speeds IS as E H and E H as omponents normal to it then with the onersion fields on omponents parallel to speed will not hange but omponents normal to the diretion of speed are onerted aording to the rule E = Eh + Bsh 1 B = Bh Esh (4.5) where is speed of light. Conersions fields (4.5) they were for the first time obtained in the work [4]. Howeer the iteration tehnique utilized for obtaining the gien relationships it is not possible to onsider strit sine its onergene is not explained Let us gie a striter onlusion in the matrix form een let us show that the form of onersions is wholly determined by the type of the utilized law of addition of eloities - lassial or relatiisti. Let us examine the totality IS of suh that IS K 1 moes with the speed relatie to IS K ISK moes with the same speed relatie to K 1 et. If the module of the speed is small (in omparison with the speed of light ) then for the transerse omponents fields on in ISK 1 K. we hae: E1 = E + B B1 = B E / (4.6) E = E + B B = B E / Upon transfer to eah following IS of field are obtained inreases in E and B

9 99 F. F. Mende: New Type Contat Potential Differene Eletrifiation of Superonduting Coils and Tori E = B B = E / (4.7) where of the fielde and B relate to urrent IS. Direting Cartesian axis x along let us rewrite (.7) in the omponents of the etor Ey = Bz E = By By = Ez / (4.8) Relationship (4.8) an be represented in the matrix form 1 Ey 1 Ez U = AU U 1/ = B y 1/ B z If one assumes that the speed of system is summarized for the lassial law of addition of eloities i.e. the speed of final ISK = KN relatie to the initial systemk is = N then we will obtain the matrix system of the differential equations of du( ) = AU( ) (4.9) d with the matrix of the system independent of the speeda. The solution of system is expressed as the matrix exponential ureexp( A ): U U( ) = exp( AU ) U = U() (4.1) here U is matrix olumn fields on in the systemk and U is matrix olumn fields on in the system K. Substituting (4.1) into system (4.9) we are onined that U is atually the solution of system (4.9): [ exp( A) ] du( ) d = U = Aexp( AU ) = AU( ) d d It remains to find this exponential ure by its expansion in the series: where E is unit matrix with the size 4 4. For this it is onenient to write down the matrixa in the unit type form then α 1 A = α. α / = = 1 A A 4 α / = α / A 4 4 α / = 4 4 α / A α / = 3 4 α / 5 4 α / = 5 6 α /.. And the elements of matrix exponential ure take the form 4 exp( ) exp( ) A = A = I ! + 4! [ ] [ ] 3 5 exp( ) exp( ) α... A = A = I ! 5! [ ] [ ] wherei is the unit matrix. It is not diffiult to see that α = α = α = α =... = I therefore we finally obtain Ih / αsh / exp( A) = = ( αsh / ) / Ih / h / sh / h / sh / ( h / ) / h / ( sh / ) / h / Now we return to (4.1) and substituting there exp( A ) we find 1 1 1! 3! 4! exp( a) = E + A + A + A + A +... E y = Eyh / Bzsh / E z = Ezh / + Bysh / B = B h / + E / sh / B = B h / E / sh / ( ) ( ) y y z z z y Or in the etor reord E = Eh + Bsh 1 B = Bh Esh (4.11) This is onersions (4.5) Regular question arises why the onersions examined differ; indeed with the low speeds our idential relationships (4.6) and (4.7). The fat is that aording to the relatiisti law of addition of eloities are added not speeds but rapidities. Aording to definition the rapidity is introdued as θ = arth (4.1)

10 AASCIT Journal of Physis 15; 1(): Preisely if the rapidity of the systems K1and K K and K 1 K 3 and Kthey are distinguished to θ then rapidity the rapidity IS K = KN relatie to K is θ = N θ. With the low speeds θ ; therefore formula (4.7) it is possible to rewrite so E = θ B B = θ E / where θ = θ. System (4.9) taking into aount the additiity of rapidity but not speed it is substituted by the system of equations du( θ) = AU( θ) dθ Thus all omputations will be analogous gien aboe only with the differene that in the expressions instead of the speeds will figure rapidity. In partiular formulas (4.11) take the form or Sine θ θ θ E = Eh + θ Bsh θ 1 θ B = Bh θ Esh θ θ θ E = Eh + Bsh θ 1 θ B = Bh Esh ( θ ) ( θ / ) ( θ ) θ 1 θ th h = sh = 1 th / 1 th / (4.13) that substitution (4.1) in (4.13) leads to the well know onersions fields on 1 E = ( E + B ) 1 /. (4.14) 1 1 B = B E 1 / With the small relatie onersion rates (4.11) and (4.14) differ beginning from the terms of the expansion of the order /. This onept assumes that the salar potential is determined by the relationship (4.4) The eletri field of the moing eletron will be determined by the relationship: eh E ( r ) =. 4πεr If is loated the plane layer of the eletrons whih moe with the speed whose thikness λ then the alue of the eletri field normal to the surfae of layer will omprise: where E = E neλ h = ε neλ is the eletri field of fixed bed n is ε eletron density. In the metal this field is ompensated by the eletri field of lattie. Consequently inrease in the eletri field on the surfae of metalli layer will ompose neλ E = h 1 ε. Deomposing hyperboli osine in a number and leaing only first two terms of expansion we obtain neλ E =. (4.15) ε The alue Q = neλ determines the speifi harge of the layer λ and the alue Q = ε E (4.16) determines the inrease in the speifi harge of surfae layer aused by eletron motion. Comparing relationships (4.15) and (4.16) we obtain inrease in the speifi harge neλ Q = (4.17) In the superondutor the depth of penetration of urrent is equal to the London depth of penetration λ therefore this relationship applies to superondutors if we onsider that the speed of eletron motion in the surfae layer is equal. The speed of eletron motion in the surfae layer of superondutor is onneted with the magneti field with the relationship H = (4.18) neλ Substituting relationship (3.18) in relationship (4.17) we obtain: H Q = (4.19) neλ The magneti field on its surfae of superondutor equal to speifi urrent an be determined from the relationship H = I. (4.) If along the round superondutor whose diameter is equal d flows the urrenti and its depth of penetration is equal λ

11 11 F. F. Mende: New Type Contat Potential Differene Eletrifiation of Superonduting Coils and Tori then speifi urrent is determined from the relationship I I = (4.1) πd Taking into aount relationships (4.) and (4.1) from relationship (4.19) we obtain: I Q = ( πd) neλ In order to obtain total inrease in the harge of the surfae in question should be this relationship multiplied by the surfae area. Sine the surfae area of round ondutor is onneted with its length L and diameter with the relationship π dl finally we obtain: LI Q = πdneλ If we with the aid of this harge load apaitor with the apaity C then a oltage drop aross the terminals of apaitor will be equal LI U = Cπdneλ (4.) Is obtained quadrati dependene between the urrent whih flows through the superondutie wire and the potential that also is obsered in the experiments examined. Into this relationship enter known tabular alues parameters of hain and urrent whih flows through the superondutie winding. If this outline was plaed into the metal sreen then the eletri fields of winding will diret on this sreen potential. Relationship (4.) explains quadrati dependene between the potential and the urrent introdued into nonindutie windings by urrent. Howeer absolute alues of potentials alulated with the aid of this relationship proe to be seeral times greater than obsered in the experiment. Suh diergenes are onneted with the fat that with alulations we they onsidered that the eletri fields form the harges of the flat surfae of unonfined in the sizes. This means that suh fields are uniform along the plane and their alue does not depend from the distane to the surfae. In atuality the annular ondutors of different diameters form eletri fields; therefore their eletri fields strongly depend on distane from these rings with this are onneted the existing diergenes. 5. Conlusion In the artile is examined new physial phenomenon the eletrotourent ontat potential differene whose alue depends on the urrent whih flows along the ondutor. Unfortunately the omputed alues of eletrotourent ontat a potential differene proed to be onsiderably lower than the potentials obsered in the experiment. The arried out experiments and alulations showed that the disoered eletrization of the superondutie windings and tori finds its explanation in the onept of salar- etor potential deeloped by the author. This onept assumes the dependene of the salar potential of harge on its relatie speed. Referenes [1] W.F. Edwards C.S. Kenyon D.K. Lemon. Continuing inestigation into possible eletri arisingfrom steady ondution urrent Phys. Re. D [] W.G.V. Roser. Seond-Order Eletri Field due to a Conduting Curent. Amerian Journal of Physis [3] Don A. Baker. Seond-Order Eletri Field due to a Conduting Curent. Amerian Journal of Physis [4] F.F. Mende. On refinement of equations of eletromagneti indution Kharko deposited in VINITI No 774 B88 Dep [5] F.F. Mende. On seondary eletri fields exited at diret urrents flowing through superondutors. Kharko deposited in VINITI No.318 B9. Dep.199. [6] 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 June1993. [7] F. F. Mende. Are the reerrors in modern physis.kharkoconstant3. [8] F.F. Mende On refinement of ertain laws of lassial eletrodynamisarxi.org/abs/physis/484. [9] F. F.Mende. Coneption of the salar-etor potential in ontemporary eletrodynamis arxi.org/abs/physis/5683. [1] F. F.Mende. New approahes in ontemporary lassial eletrodynamis. Part II Engineering Physis 13.