Electrokinetic Electric Field

Transcription

1 AASCIT Journal of Physics 5; (): Published onli March 3 5 ( Dynaic Scalar Potential and the Electroitic Electric Field F F Mende BI Verin Institute for ow Teperature Physics and Engiering NAS Urai Eail address ende_fedor@ailru Citation F F Mende Dynaic Scalar Potential and the Electroitic Electric Field AASCIT Journal of Physics Vol No 5 pp Keywords Superconductor Scalar Potential Dynaic Scalar Potential Electroitic Electric Field Received: March 8 5 Revised: March 5 Accepted: March 5 Abstract In the article is described the w physical of phenoenon which indicates that in the superconductors the stationary electric field can exist This field exists in the surface layer of superconductor and it is directed noral to its surface Since the field indicated is the consequence of the itic otion of charges in the superconductor it can be naed electroitic electric field The value of this field is sall but it are w previously unnown property of the superconductive state Introduction The electrodynaics of superconductors does not assue the presence in the of stationary electrical fields on since this would lead to an infinite increase in the speed of current carriers In the article is described earlier not the nown physical phenoenon which is assued the presence of stationary electrical fields on in the superconductors These fields are the consequence of the itic otion of charges and therefore they can be naed itic electric fields The value of this field is sall but it are w previously unnown property of the superconductive state Electrodynaics of Plaso-ie Media By plasa edia we will understand such in which the charges can ove without the losses To such edia in the first approxiation can be related the superconductors free electrons or ions in the vacuu In the edia indicated the equation of otion of electron taes the for: dv ee dt = () where is ass electron e is the electron charge E is the tension of electric field v is speed of the otion of charge Using an expression for the current density j = v () fro equation () we obtain the current density of the conductivity j E dt (3) = In relationship () and (3) the value n represents electron density After introducing the designation

2 54 F F Mende: Dynaic Scalar Potential and the Electroitic Electric Field we find = (4) j = E dt (5) In this case the value presents the specific itic inductance of charge carriers [-6] Its existence concted with the fact that charge having a ass possesses irtia properties j = Ecosωt (6) ω For the atheatical description of electrodynaic processes the trigonoetric functions will be here and throughout instead of the coplex quantities used so that would be well visible the phase relationships between the vectors which represent electric fields and current densities Fro relationship (5) and (6) is evident that j presents inductive current since its phase is late with respect to the tension of electric field to the angle π During the presence of sued current it is cessary to consider bias current E j cos ε = ε = εωe ωt t Thus suary current density will copose [7-9] E j = ε E dt t + Maxwell's equations for this case tae the for: rot E = t E rot = ε + E dt t (7) where ε and are dielectric and agtic constant of vacuu Syste of equations (7) describes the properties of superconductors Fro it we obtain rot rot + ε + = (8) t For the case fields on tie-independent equation (8) passes into the ondon's equation where λ rot rot + = = is ondon's depth of petration Fields on wave equation in this case it appears as follows for the electrical: E rot rot E + ε + E = t For constant electrical fields on it is possible to write down rot rot E + E = Consequently dc fields petrate the superconductor in the sae anr as for agtic diinishing expontially owever the density of current in this case grows according to the liar law j = E dt This eans that stationary electric fields in the superconductor it can exist only until current density reaches its critical value for this type of superconductor If around the point in question is soe static configuration of charges then the tension of electric field will be at the particular point deterid by the relationship of where the scalar potential at the assigd point deterid by the assigd configuration of charges If we change the arrangeent of charges then this w configuration will correspond other values of scalar potential and therefore also other values of the tension of electric field In the electrodynaics the fundaental law of induction is Faraday law It is written as follows: ФB B E dl = = ds = ds (9) where B = is agtic induction vector ФB = ds is flow of agtic induction and =ɶ is agtic pereability of ediu It follows fro this law that the circulation integral of the vector of electric field is equal to a change in the flow of agtic induction through the area which this outli covers It is iediately cessary to ephasize the circustance that the law in question presents the processes of utual induction since For obtaining the circulation integral of the vector E we tae the strange agtic field fored by strange source Fro relationship (9) obtain the first Maxwell's equation

3 AASCIT Journal of Physics 5; (): B rot E = () t et us iediately point out to the terinological error Faraday law should be called not the law of electroagtic as is custoary in the existing literature but by the law of agtoelectric induction since a change in the agtic fields on it leads to the appearance of electrical fields on but not vice versa et us assue that in the region of the arrangeent of the outli of integration there is a certain local vector A which satisfies the equality A dl = ФB where the outli of the integration coincides with the outli of integration in relationship (9) and the vector of is deterid in all sections of this outli then A E = () Introduced thus vector A deteris the local conction between it and by electric field It is not difficult to show that introduced thus vector A is concted with the agtic field with the following relationship: rot A = () At those points of the space where rot A = agtic field is absent Thus we will consider that the vector exists by a consequence of the presence of the vectora but not vice versa If there is a straight conductor with the current then around it also there is a field of vector potential the truth in this case rot A in the environts of this conductor is therefore located also the agtic field which changes with a change of the current in the conductor The section of wire by the length dl over which flows the current I gerates in the distant zo (it is thought that the distancer considerably ore than the length of section) the vector potential Idl da( r) = 4πr Until now resolution of a question about the appearance of electrical fields on in different irtial oving systes (IS) it was possible to achieve in two ways The first - consisted in the calculation of the orentz force which acts on the oving charges the alternate path consisted in the easureent of a change in the agtic flux through the outli being investigated Both ethods gave identical result and this was incoprehensible [] In conction with the incoprehension of physical nature of this state of affairs they began to consider that the unipolar gerator is an exception to the rule of flow [] et us exai this situation in ore detail In order to answer the presented question should be soewhat changed relationship (3) after replacing in it partial derivative by the coplete: da E = (3) dt Prie ar the vectore eans that this field is deterid in the oving coordinate syste while the vectora it is deterid in the fixed syste This eans that the vector potential can have not only local but also convection derivative ie it can change both due to the change in the tie and due to the otion in the three-diensional changing field of this potential In this case relationship (6) can be rewritten as follows: A E = ( v ) A wherev is speed of the prie syste If vector potential on tie does not depend we obtain F = e v A v This force depends only on the gradients of vector potential and charge rate The charge which oves in the field of the vector potential A with the speedv possesses potential ergy [] W = e va Therefore ust exist o additional force which acts on the charge in the oving coordinate syste naely: F = gradw = e grad va v ( ) Consequently the value e ( va ) plays the sae role as the scalar potentialϕ whose gradient gives the force which acts on the charge Consequently the coposite force which acts on the charge which oves in the field of vector potential can have three coponts and will be written down as A = + ( ) F e e v A e grad va (4) The first of the coponts of this force acts on the fixed charge when vector potential changes in the tie and has local tie derivative Second copont is concted with

4 56 F F Mende: Dynaic Scalar Potential and the Electroitic Electric Field the otion of charge in the three-diensional changing field of this potential Entirely different nature in force which is deterid by last ter of relationship (4) It is concted with the fact that the charge which oves in the field of vector potential it possesses potential ergy whose gradient gives force Fro relationship (4) follows A E = ( v ) A + grad ( va ) (5) This is a coplete law of utual induction It defis all electric fields which can appear at the assigd point of space this point can be both the fixed and that oving This united law includes and Faraday law and that part of the orentz force which is concted with the otion of charge in the agtic field and without any exceptions gives answer to all questions which are concerd utual agtoelectric induction It is significant that if we tae rotor fro both parts of equality (5) attepting to obtain the first Maxwell's equation then it will be iediately lost the essential part of the inforation since rotor fro the gradient is identically equal to zero If we isolate those forces which are concted with the otion of charge in the three-diensional changing field of vector potential and to consider that grad ( va ) ( v ) A = v rot A that fro (4) we will obtain F v = e v rot A (6) and taing into account () let us write down of F v = e v (7) or and it is final E v = v (8) A F = ee + eev = e + e v (9) Can see that relationship (9) presents orentz force however this not thus In this relationship the field E and the field E v are induction The first equation is concted with a change of the vector potential with tie the second is obliged to the otion of charge in the three-diensional changing field of this potential In order to obtain the total force which acts on the charge cessary to the right side of relationship (9) to add the ter e grad ϕ F = e grad ϕ + ee + e v whereϕ is scalar potential at the observation point In this case relationship (5) can be rewritten as follows: A E = ( v ) A + grad ( va ) grad ϕ () or after writing down the first two ebers of the right side of relationship () as the derivative of vector potential on the tie and also after introducing under the sign of gradient two last ters we will obtain da E = + grad ( ( va) ϕ ) () dt If both parts of relationship () are ultiplied by the agnitude of the charge then will coe out the total force which acts on the charge Fro orentz force it will differ in A ters of the force e Fro relationship () it is va ϕ plays the role of the evident that the value geralized scalar potential The Maxwell's second equation in the ters of vector potential can be written down as follows: rot rota = j A ( ) () where j( A ) is the current density which presents functional fro the vector potential In the superconductor the current density is deterid by the relationship j( A) = A (3) where = is itic inductance of charges The dependence of current density on the coordinate in the superconductor is deterid by relationship [] z j( z) = j e λ ( 4) where z is coordinate directed into the depths of the superconductor j is current density on the surface of superconductor Using relationship () we obtain the dependence of the electron velocity in the superconductor on the coordinate z v( z) = v e λ (5) Using relationships (3-5) fro relationship () we obtain the value of itic electric field with the presence of the steady currents E = grad va = λ v e λ (6) z

5 AASCIT Journal of Physics 5; (): Consequently when in the surface layer the superconductor of steady currents is present in this layer exists the electric field noral to the surface dependence which fro coordinate is deterid by relationship (6) This field can be naed electroitic since it is gerated by the itic electron otion The agtic field on its surface of superconductor equal to specific current can be deterid fro the relationship = vλ Then relationship (9) can be rewritten E z λ = e (7) λ et us produce the estiate of the agnitude of this field 8 3 for niobiu assuing n = 54 / With the zero of teperatures the critical agtic field of niobiu is equal 5 5 A/ Substituting these values in relationship (7) we obtain the value of electroitic field ar the surface E 3 V/ when currents in superconductive niobiu are close to the critical 3 Conclusion In the article is described the w physical of phenoenon which indicates that in the superconductors the stationary electric field can exist This field exists in the surface layer of superconductor and it is directed noral to its surface Since the field indicated is the consequence of the itic otion of charges in the superconductor it can be naed electroitic electric field References [] F F Mende A I Spitsyn Surface ipedance in superconductors Kiev Nauova Dua 985 [] F F Mende On refient of equations of electroagtic induction Kharov deposited in VINITI No 774 B88 Dep 988 [3] F F Mende Are there errors in odern physics Kharov Constant3 [4] F F Mende On refient of certain laws of classical electrodynaics arxivorg/abs/physics/484 [5] F F Mende Role and place of the itic inductance of charges in classical electrodynaics Engiering Physics [6] F F Mende Kitic Indutance Charges and its Role in Classical Electrodynaics Global Journal of Researches in Engiering (4) Volue 4 Issue 5: 5-54 [7] F F Mende Are there errors in odern physics Kharov Constant 3 [8] F F Mende Greatis conceptions and errors physicists XIX- XX centuries Revolutionin odern physics Kharоv NTMT [9] F F Mende New electrodynaics Revolution in the odern physics Kharov [] R Feynan R eighton M Sends Feynan lectures on physics M: Mir Vol 6 977