(c light velocity) (2) C

Transcription

1 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( NW XPLNTION O DLTION RSULTS O HRGD PRTILS IN HIGHLOITY MOTION IN MGNTI ILD ORRTION O LORNTZ OR Kexin Yao Kexin Yao, Institte of Mechanical ngineering of Shaanxi Province, Room7, Staff ilding, xian Metering Instittion, No., Laodong Soth Road Xian, 768 P. R. hina STRT: It is incorrect to only apply mass change or time change in explanation of the deflection reslt of charged particle in high velocity motion in magnetic field. scientific and correct method is to change mass and time at the same time. However, it is impracticable to necessitate force formla in simltaneos change of mass and time. The paper makes correction of Lorentz orce formla based on analysis method for acting force in electric field, and lanches into a new nderstanding of deflection reslt of charged particles in high velocity motion in magnetic field according to the corrected Lorentz orce formla. KYWORDS:harged particle; Magnetic field; Deflection; Lorentz orce; Mass change; Time change; lectric field force INTRODUTION It is known to all in the field of physics that charged particle moving throgh magnetic field shall ndergo deflection. The general explanation of the phenomenon is that when a charged particle with a charge of Q moves throgh magnetic field at the velocity of along the direction of x, Q shall ndergo Lorentz orce Q ( magnetic indction) along the direction normal to. shall make the charged particle with a mass of M and a charge of Q generate an acceleration a=/m along the direction normal to (direction of Y) to make Q generate migration Y along the direction normal to, namely deflection Y. Sppose the time for Q to move throgh magnetic field is t, then the expression for deflection Y is as follows: Y at t M () Where () is derived nder the condition that the direction of be nchanged; althogh when particle moves throgh magnetic field, directions of velocity and ( is normal to ) are changed to a certain extent, since t is too short, the changes in and are also minor, accordingly, we can consider that there is no change in the directions of and and that the error of Y may be ignored. Where () is practical on condition that velocity be low, bt if is very high, there is obvios deviation between the calclated reslt of () and measred reslt, higher shall bring abot larger deviation, experiment shows that when is very high, deflection distance shall be: t Y (c light velocity) () M ISSN 55655(Print), ISSN 55656X(Online)

2 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( t present, there are several explanations for the experimental reslt indicated by expression (), it is observed that all these explanations are nscientific, the reasons for which are as follows: The most general explanation is that when charged particle is in high velocity motion, according to special relativity, the mass M of the charged particle shall increase to M M expression ()., replace M in expression () with M to obtain the practical nother method is to carry ot analysis based on change of particle momentm. Sppose the migration velocity of particle along direction of Y is and particle mass is M P and particle momentm along direction of Y is M M M and the acting force on particle along direction of Y is dp dt M d dt d dt M It is observed that Y t o dt t o d t dt dt M d dt in the analysis method is constant acceleration a in sbstance, the deflection it determined is still Y at, and that the key to the analysis method is M M, there is no sbstantial difference between this method and the first method. ompared with the first method, it is obvios that this method is lack of its physical significance. There is another method specified in erkeley Physics, the method defines that is particle clock time and that mass is rest mass M. Y is displacement of particle in t along direction of Y, momentm: P M ΔY Δ. It is observed that the time for particle to ndergo displacement along direction of Y is,according to special relativity, there is t, therefore there is P M Y M Y t. Since the displacement velocity of particle along direction of Y is Y P M t, accordingly,,the momentm given in the reslt is identical with that obtained in the previos method. It is natral to come to a conclsion identical with that obtained by expression () according to the dedction steps given in the previos method. It is observed that the first and second methods only apply mass change, althogh they do not mention that they only adopt mass change, in fact, time is nchanged, being a constant; the third method only applies time change, specifying that mass is nrelated to motion, being a constant. However, according to special relativity, the mass of particle in high velocity motion and time are changed simltaneosly, accordingly, it is improper to sppose mass is ISSN 55655(Print), ISSN 55656X(Online)

3 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( nchanged and time is nchanged, becase it is in violation of special relativity and practical reslt. In accordance with special relativity, the correct method in analyzing the deflection of grain is to se both mass conversion conversion t t M and time M. Take M and t into formla (), and then M M 3 t t Y (3) It is obvios that formla (3) is not in line with the reslt of (). Why? It is certain that formla () is the basic formla of mechanics, and this shall be affirmed; besides, it is withot dobt that qality and time shall be conversed at the same time. Therefore, the only possibility is that formla (3) does not coincide with reality, and it mst be Lorentz orce that fails to show the actal power. Lorentz orce Q is only the experimental conclsion that charged particles of low rnner are stressed in niform magnetic field. It doesn t have necessary theoretical explanation. To analyze Lorentz orce is in line with reality or not, it is necessary to know the reason and change rles of Lorentz orce. Therefore, we have to illstrate the root of Lorentz orce from the theory and then it can analyze and solve the actal problems in formla (3). The original analysis of Lorentz orce It is showed in experiments that electric charge will be inflenced by force in electric field, and the electric field can be considered as the only origin of charge force. Therefore, the electric field force can be considered as the basic point in analyzing Lorentz orce. It can be known from the sperposition principle of static electric field that the distance between two positron and negatron in space, the total electric field of positron and negatron mst be eqal to the vector sm when the positron and negatron exist alone. It can be dedced that any free electron in condctor (hereinafter called negatron) and the proton that is eqal with free electron in electric qantity (hereinafter called positron) has their own electric field. Therefore, when there is crrent in condctor, namely the macroscopic motion of negatron in condctor exists, the electric field of negatron mst move with negatron. nd the macroeconomic effect is that the negative electric field moving arond condctor exists along with the static positive electric field. In terms of magnet, the electron that spins in same direction in magnetic domain is similar to the negatron of macroscopic motion in condctor. Therefore, there are negative electric field of macroscopic motion and static positive electric field in magnetic domain. irst of all, we shall analyze the relationship between magnetic field and electric field. It is showed in iotsavart theorem that, the feeling strength of any crrent element Id l (small lines on the wire that in the same direction of crrent) at the place of r is Idl d r 4 r ISSN 55655(Print), ISSN 55656X(Online) (Unit vector in the direction of r r ) 3

4 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( Since I is actally formed by free electron in the wire in the speed of (in the opposite direction of crrent I). Taking as the linear charge density in the wire, then Idl τ dl dq (the qantity of free electron in dq dl ) and becase, K 4, then K 4 K d dq r r d d. In the pper formla, formla can be written as dq K r r d is the electric field intensity of dq at the place of R. and the (4) (4) The formla shows that the feeling strength at some place is eqal to the vector prodct of kinematic velocity and the electric field intensity. The formla shows that magnetic field is a moving electric field. Pictre Origin analysis of Lorentz orce It is defined that flat consisting of wires with crrent is the crrent srface, in Pictre, and indicates two sections of infinity crrent srface. and crrent srfaces are made p of two common wire with crrent, and the crrent of and is eqal bt in opposite direction. In Pictre, motion in crrent srface; and and shows the electric field intensity that negatron electron in indicate the electric field intensity that prodced by ISSN 55655(Print), ISSN 55656X(Online) 4

5 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( static positive electron that is eqal to negatron in electric qantity. It shall cont ot the feeling strength between two crrent srfaces and. It can be fond ot from formla (4) that, is originated from moving electric field. The motion of and has nothing to do with. nd then we only analyze the electric field of in the speed of and then electric field of is eqal bt in opposite direction, namely and. in the speed of. Obviosly, that moves and. where is the absolte vale of It shall cont ot the feeling strength of from, and from formla (4) Z ( Z is the nit vector in the direction of Z) The feeling strength prodced by is Z The total feeling strength prodced by crrent srface and is Z Pictre, Q is the charge particle with positive electricity in the speed of paralleling two electricity srfaces. The Lorentz orce that is bore by grant with Q charge is Q Y Q ( Y is the nit vector in the direction of Y) (5) When we make analysis of the sorce of Lorentz orce, it will be or natral selection for s to start with the sorce of force Q. There is no dobt that the only sorce of Q force is nder the effect from electric field. There are not only electric field and bt as well between the two crrent srface and ; becase the crrent of and is the same intensive with contrary direction and they has the same relative velocity to any moving Q, and will have a constant force on force Q with contrary directions and their forces will be cancelled ot, namely the effect of force Q. Withot consideration of and possibly. Let s stdy the force on Q from and Q is and and can not be considered on,the force of Q is only sorced from firstly, it is can be known that the relative velocity of from pictre ; ccording to Special Relativity, the electric field with moving on will shrink in the proportion of in the direction of and the filed density is inversely proportional to the distance of power line, therefore the filed density shall be magnified as: ccording to binomial series, ISSN 55655(Print), ISSN 55656X(Online) X can be expanded into 5

6 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( 4 6 X 3 X 8 5 X 6, when x is relative small, it can be neglected inclding 4 X and 6 X etc., it is X X less than, therefore. Under general condition, and is far in the above formla can be converted into: Y Let s trn to, it is can be known that the relative velocity of and it can be got from the explanations mentioned above as: and Q is or the moving Q, the total field intensity between the crrent srface and is The force on Q is: Q Q Y Y Y Y Y Y μ ε Y It is obvios that the formla is jst the Lorentz orce ormla(5) mentioned before. It can be conclded from the above analysis that: when Q is moving in magnetic field at the velocity, one moving electric field with two crrent srface and will be formed; for Q, their velocity are + and respectively and the electric field of + will shrink greater with more intensive filed intensity; when the electric filed of shrinks with less intensive filed intensity, one synthesis electric field will be formed by their differentiated filed intensity, whose force on Q will be jst Lorentz orce. orrection of Lorentz orce It can be known from the analysis on the derivation formla of abovementioned Lorentz orce that the derivation process will not hold when the velocity of Q is very large (almost reaching the velocity of light ); there are two reasons, one is that when is very large, and can not be neglected, and the above derivation will not hold natrally; the other is that when is very large, its velocities can not be added or sbtracted ISSN 55655(Print), ISSN 55656X(Online) 6

7 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( directly, namely and ; therefore, the above derivation will not hold. Now, let s make frther analysis on the force of charged particle in high velocity motion (expressed with electric charge Q) in accordance with the synthesis velocity method given in Special Relativity. The synthesis velocity mentioned in Special Relativity refers to that in the direction of X, Y and Z. or the condition given in pictre, the velocity on direction Z does not exist and migration velocity on direction Y is very slow, that s to say they can be neglected owing to the comparison with. Therefore, it can be considered that there is also no velocity component on direction Y and we only need to make analysis of the synthesis velocity on direction X whose formla is given as: x x (6) x In the formla, v is the moving velocity of the other inertial system Z observed from inertial system Z with the motionless of relative sbject M; is the moving velocity relative to sbject N, x is the relative velocity speed of M and N. or pictre, we wold like to conclde the force on Q (sbject M), namely Q is of inertial system of Z and two crrent srface is of the inertial system of Z, The velocity of Z (two crrent srface) observed from Z is, namely, and the motion velocity of (sbject N) observed from Z (two crrent srface) is, namely x ; The velocity speed of Q (sbject M) relative to (sbject N) is in accordance with formla (6) (7) However, the motion velocity of observed from Z (two crrent srface) is namely x ; The velocity speed of Q (sbject M) relative to accordance with formla (6) (8) moving at the speed of Ā will shrink for Q, it shall be magnified as: x, (sbject N) is in Pt conclded from (7)in the following formla: Ā 4 ISSN 55655(Print), ISSN 55656X(Online) 7

8 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( 8 ISSN 55655(Print), ISSN 55656X(Online) 4 The movement velocity of negative electron is far smaller than ( electron in magnetic domain is also smaller) in the moving electric field formed in two crrent srfaces and ; therefore is very small, which can be reckoned as, and then the above formla can be converted into: Ā (9) or, moving at the speed of shall be shrank and magnified as: Pt the got in formla(8)into the following formla: 4 4 () The field intensity felt by Q is: Owing to, the above formla can be converted into:

9 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( ( Y ) ()( The first capitalized, bold) or the sake of telling the force, namely Lorentz orce, exerted by electric field when Q is moving at medim and low speed, the force on Q exerted by electric field can be conclded from formla (): Q Q Y () It is shown from former formla (5) that Lorentz orce on Q is Q Y when it is moving at medim and low speed, and pt it into formla (): Q (3) The formla (3) can be sed for the correction of the formla of Lorentz orce. It is obvios that formla (3) is also qalified for that at both high and low speed when Q is moving in magnetic field at medim and low speed. Interpretation of charged particles deflection with the help of corrected formla for Lorentz orce The corrected Lorentz orce on Q got from above analysis is jst the electric field force, which is relatively static to Q; it will move together with Q at the same speed. or the observer with static relative magnetic field (two crrent srfaces), force is a moving one. I have mentioned in Set p Invariable xiom of orce qilibrim and Solve Problems abot Transformation of orce and Gravitational Mass (References. 3) that the force on moving sbject will also change like its length, mass and time. The conversion formla for the force moving at the speed is: cos (4) In the formla, is the inclded angle between and. or analyzed in pictre, the inclded angle between cos, therefore the force (4): Pt formla (3) into this formla (3) and is 9 and can be converted into in accordance with the formla ISSN 55655(Print), ISSN 55656X(Online) 9

10 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( is jst the real force exerted on charged particle we wold like to discss, pt real into formla (3) instead of : 3 t t Y M M It is obvios that the deflection distance Y is jst as determined in experiment room, namely tre deflection distance formla (). It is shown from the above analysis that the problem in connection with the deflection of charged particle moving at high speed can be solved reasonably provided that its mass and time are changed at the same time with the help of corrected Lorentz orce in combination with force transformation. Making analysis of particles deflection from the inertial system of relative static of charged particles ccording to the relativity principle given in Special Relativity, for the observers of inertial system Z (inertial system Z moving at the same speed of Q ) and inertial system Z (relative magnetic field or static srface), it is of corse that they will have the same reslt of the deflection on Q passing throgh the magnetic field on direction Y. The former analysis is the conclsion of the observer relatively static to Z, for this conclsion, the real force is got with the help of corrected Lorentz orce and changed combined power, moreover the analysis reslt compliance with fact is conclded. Z is moving relatively to Z at the speed, it can be reckoned that is static relatively to Z (with slight movement of on direction Y neglected) there is no need for changing any longer ; Whether the change of this kind of conditions will have any inflence on or analysis of the corresponding deflection? Let s make detailed analysis for it. or observer Z, Q is static and one magnetic field (inertial system Z ) is passing throgh Q at the speed, one downward force is be exerted on Q, and moreover distance Y is moved downwards (deflection); becase the speed of Q on direction Y is very slow, the mass of Q is still static one, namely no change is occrred to it. esides the force on Q is also a static one, namely (corrected Lorentz orce), of corse will not change. The accelerated speed of Q on direct Y is a m. Provided the time Q passing throgh the magnetic field is t observed by Z, the deflection distance of Q on direction Y is: ISSN 55655(Print), ISSN 55656X(Online)

11 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( Y t at (5) m What is the relationship between t and Z observed by Z? irst of all, we shall make sre that the absolte moving speed and of Z and Z is the same and Z observes t is the time Q passing the magnetic field at the speed, namely t L ; for Z, the magnetic in L wide is moving at the speed of,according to the Relativity Principle given in Special Theory, the width of the magnetic field moving at the speed is L L ; therefore the time sed by the magnetic passing throgh Q from the observation of Z is t L L t, pt it into formla(5), Y m t t m It is obvios that the relationship formla is also that for real deflection distance (). or the above analysis, the deflection reslts of charged particles moving at high speed got by Z and Z shall be the same, which is in compliance with Relativity Principle. pplication scope of Lorentz orce I hereby point ot that the force on Q will be the same only in the niform magnetic field throgh the analysis with the help of electric magnetic field and Lorentz orce; nder normal condition, the two reslts derived from the two methods will not be the same in nonniform magnetic field. Pictre nalysis on interaction between moving electric charge and crrent component Pictre, electric charge dq is moving towards Idl at speed, the capacity of negative electron moving in Idl is dq and velocity speed of dq is (contrary direction with I), the capacity of positive electron in Idl with the same capacity of that in dq is dq irst, the interaction force between dq and Idl is sbject to analysis based on ISSN 55655(Print), ISSN 55656X(Online)

12 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( electric field. Since the relative velocity between negative charges or negative charge and positive charge in any relative motion is identical in magnitde and contrary in direction, The shrinkage condition observed each other is completely similar; therefore the force on each other is the same as that when they are relatively static. It is certain that they are the same in force and contrary in direction. We can know from this that both the interaction between dq and dq and that between dq and positive electron dq are eqal in force and contrary in direction; namely, the interforce is natrally eqal with contrary direction. It is obvios that the analysis reslt for electric field is in compliance with reaction law. It is observed from analysis of interaction between dq and IdL based on Lorentz orce that only dq in motion in crrent element generates magnetic field; since dq is in no motion, accordingly, it generates no magnetic field. The electric field strength generated by dq in dq is d, d is also referred to as d,the following X, Y and Z are nit rectors, the motion velocity of d is,, according to the previos formla(4), the magnetic indction is referred to as Y strength generated by d d d Z d X in dq is as follows: Y d X The motion velocity of dq is, Lorentz orce on dq is as follows: d dq is also referred to as X d dq d Z dq Y d dqy d X, accordingly, With regard to Lorentz orce on dq, the electric field strength generated by dq in dq is d X, the magnetic indction strength generated by d X in dq is as follows: d X d X Since positive charge dq in no motion,therefore dq is not sbject to Lorentz orce, the Lorentz orce on crrent element IdL is the Lorentz orce on dq, the Lorentz orce on dq is as follows: d dq Y d d It is observed from comparison between action d and reaction d that they are ISSN 55655(Print), ISSN 55656X(Online)

13 ropean Jornal of Mechanical ngineering Research ol., No., pp.3, Jne 5 Pblished by ropean entre for Research Training and Development UK ( different in magnitde and identical in direction; that is to say that adopting Lorentz orce to analyze interaction force between charge in motion and crrent element reslts in action and reaction are different in magnitde and not contrary in direction; namely, the reslt is contrary to law of reaction. It is observed from frther analysis that in addition to in parallel with as motion velocity of, it is observed from analysis of Lorentz orce along any direction of that the interaction and reaction between dq and Idl are different in magnitde and not contrary in direction, namely the reslts are contrary to the law of reaction. It is stated that there is no isolated crrent element in the niverse and it is impractical to adopt crrent element for analysis. It is also known that scientific theory necessitates both tenable macroanalysis and microanalysis. In fact, many theories are based from microanalysis to macroanalysis. If microanalysis fails to be tenable, there shall be an example showing that macroanalysis fails to be tenable. The microcrrent element given in fig. extends along the dotted line shown in the fig, becoming the macrocrrent carrying coil. nalysis of the interaction force between crrent carrying coil and dq shown in dotted line in fig., the inevitable analysis conclsion is that the interaction and reaction between charge in motion dq and crrent carrying coil are not contrary in direction and different in magnitde. Reference docment details the analysis reslt. ccording to the above mentioned analysis, it is conclded that Lorentz orce is only applicable to niform magnetic field and not applicable to nonniform magnetic field. In order to analyze the force on charge in motion in nonniform magnetic field, the only way is to adopt acting force in electric field for analysis. RRNS. Yao Kexin Inferring the act that Static Magnetic ield xists long with lectrostatic ield and ondcting xperimental erification in ccordance with the Theory of Relativity. pplied Physics Research ol.4.no.. ebrary.. Yao Kexin Qestion on Some Principles of lectromagnetism. pplied Physics Research.4.No.3gst 3. Yao Kexin Set p Invariable xiom of orce qilibrim and Solve Problems abot Transformation of orce and Gravitational Mass. pplied Physics Research..5.No. ebrary 3 4. Yao Kexin xplanation of lectromagnetics by Motion of lectric ield LP LMRT cademic Pblishing(3) 5..M. Prcell [U.S.] erkeley Physics orse, pblished by Science and technology of hina press (979) 6. ndamental of Relativity Theory, compiled by W Shobo, pblished by Shaanxi Science & Technology Press (987) ISSN 55655(Print), ISSN 55656X(Online) 3