A NEW EXPLANATION OF DEFLECTION RESULTS OF CHARGED PARTICLES IN HIGH-VELOCITY MOTION IN MAGNETIC FIELD·CORRECTION OF LORENTZ FORCE

It is incorrect to only apply mass change or time change in explanation of the deflection result of charged particle in high velocity motion in magnetic field. A scientific and correct method is to change mass and time at the same time. However, it is impracticable to necessitate force formula in simultaneous change of mass and time. The paper makes correction of Lorentz Force formula based on analysis method for acting force in electric field, and launches into a new understanding of deflection result of charged particles in high velocity motion in magnetic field according to the corrected Lorentz Force formula.


INTRODUCTION
It is known to all in the field of physics that charged particle moving through magnetic field shall undergo deflection. The general explanation of the phenomenon is that when a charged particle with a charge of Q moves through magnetic field at the velocity of V along the direction of x, Q shall undergo Lorentz Force BQV F  (B-magnetic induction) along the direction normal to V. F shall make the charged particle with a mass of M and a charge of Q generate an acceleration a=F/M along the direction normal to V (direction of Y) to make Q generate migration Y along the direction normal to V, namely deflection Y. Suppose the time for Q to move through magnetic field is t, then the expression for deflection Y is as follows: Where (1) is derived under the condition that the direction of F be unchanged; although when particle moves through magnetic field, directions of velocity V and F (F is normal to V) are changed to a certain extent, since t is too short, the changes in F and V are also minor, accordingly, we can consider that there is no change in the directions of F and V and that the error of Y may be ignored.
Where (1) is practical on condition that velocity V be low, but if V is very high, there is obvious deviation between the calculated result of (1) and measured result, higher V shall bring about larger deviation, experiment shows that when V is very high, deflection distance shall be: , replace M in expression (1) with M  to obtain the practical expression (2).
Another method is to carry out analysis based on change of particle momentum. Suppose the migration velocity of particle along direction of Y is u and particle mass is and particle momentum along direction of Y is and the acting force on particle along direction of Y is dt du It is observed that dt du in the analysis method is constant acceleration a in substance, the deflection it determined is still 2 2 at Y  , and that the key to the analysis method , there is no substantial difference between this method and the first method. Compared with the first method, it is obvious that this method is lack of its physical significance.
There is another method specified in Berkeley 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, momentum: . It is observed that the time for particle to undergo displacement along direction of Y is   ，according to special relativity, there is , therefore there is ,the momentum given in the result is identical with that obtained in the previous method. It is natural to come to a conclusion identical with that obtained by expression (2) according to the deduction steps given in the previous method.
It is observed that the first and second methods only apply mass change, although they do not mention that they only adopt mass change, in fact, time is unchanged, being a constant; the third method only applies time change, specifying that mass is unrelated to motion, being a constant. However, according to special relativity, the mass of particle in high velocity motion and time are changed simultaneously, accordingly, it is improper to suppose mass is 3 ISSN 2055-6551(Print), ISSN 2055-656X(Online) unchanged and time is unchanged, because it is in violation of special relativity and practical result.
In accordance with special relativity, the correct method in analyzing the deflection of grain is to use both mass conversion and time . Take M  and t into formula (1), and then 2 3 It is obvious that formula (3) is not in line with the result of (2). Why? It is certain that formula (1) is the basic formula of mechanics, and this shall be affirmed; besides, it is without doubt that quality and time shall be conversed at the same time. Therefore, the only possibility is that formula (3) does not coincide with reality, and it must be Lorentz ForceF that fails to show the actual power.
Lorentz Force BQV F  is only the experimental conclusion that charged particles of low runner are stressed in uniform magnetic field. It doesn't have necessary theoretical explanation. To analyze Lorentz Force is in line with reality or not, it is necessary to know the reason and change rules of Lorentz Force. Therefore, we have to illustrate the root of Lorentz Force from the theory and then it can analyze and solve the actual problems in formula (3).

The original analysis of Lorentz Force
It is showed in experiments that electric charge will be influenced 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 Force.
It can be known from the superposition principle of static electric field that the distance between two positron and negatron in space, the total electric field of positron and negatron must be equal to the vector sum when the positron and negatron exist alone. It can be deduced that any free electron in conductor (hereinafter called negatron) and the proton that is equal with free electron in electric quantity (hereinafter called positron) has their own electric field. Therefore, when there is current in conductor, namely the macroscopic motion of negatron in conductor exists, the electric field of negatron must move with negatron. And the macroeconomic effect is that the negative electric field moving around conductor 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 conductor. Therefore, there are negative electric field of macroscopic motion and static positive electric field in magnetic domain.
First of all, we shall analyze the relationship between magnetic field and electric field. It is showed in Biot-Savart theorem that, the feeling strength of any current element l Id (small lines on the wire that in the same direction of current) at the place of r is Since I is actually formed by free electron in the wire in the speed of V (in the opposite direction of current I). Taking   as the linear charge density in the wire, then (the quantity of free electron in dQdl ) and because In the upper formula, E d is the electric field intensity of dQ at the place of R. and the formula can be written as (4) The formula shows that the feeling strength at some place is equal to the vector product of kinematic velocity V and the electric field intensity. The formula shows that magnetic field is a moving electric field.

Picture 1 Origin analysis of Lorentz Force
It is defined that flat consisting of wires with current is the current surface, in Picture 1, A and B indicates two sections of "infinity" current surface. A and B current surfaces are made up of two common wire with current, and the current of A and B is equal but in opposite direction. In Picture, It shall count out the feeling strength between two current surfaces A and B. It can be found out from formula (4) that, B is originated from moving electric field. The motion of It shall count out the feeling strength of A B from -A E , and from formula (4) The total feeling strength produced by current surface A and B is Picture 1, Q is the charge particle with positive electricity in the speed of V paralleling two electricity surfaces. The Lorentz Force that is bore by grant with Q charge is When we make analysis of the source of Lorentz Force, it will be our natural selection for us to start with the source of force Q. There is no doubt that the only source of Q force is under the effect from electric field. There are not only electric field - in the direction of A V and the filed density is inversely proportional to the distance of power line, therefore the filed density shall be magnified as: . Under general condition, V and u is far less than C, therefore  -A E in the above formula can be converted into: Let us turn to -E B , it is can be known that the relative velocity of and it can be got from the explanations mentioned above as: For the moving Q, the total field intensity between the current surface A and B is The force on Q is: It is obvious that the formula is just the Lorentz Force Formula(5) mentioned before. It can be concluded from the above analysis that: when Q is moving in magnetic field at the velocity V, one moving electric field with two current surface  A E and  B E will be formed; for Q, their velocity are V+u and V-u respectively and the electric field of V+u will shrink greater with more intensive filed intensity; when the electric filed of V-u shrinks with less intensive filed intensity, one synthesis electric field will be formed by their differentiated filed intensity, whose force on Q will be just Lorentz Force.

Correction of Lorentz Force
It can be known from the analysis on the derivation formula of above-mentioned Lorentz Force that the derivation process will not hold when the velocity of Q is very large (almost reaching the velocity of light C); there are two reasons, one is that when V is very large, 4 4 C V and 6 6 C V …… can not be neglected, and the above derivation will not hold naturally; the other is that when V is very large, its velocities can not be added or subtracted ; therefore, the above derivation will not hold. Now, let us make further 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. For the condition given in picture 1, 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 V. 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 formula is given as: In the formula, v is the moving velocity of the other inertial system Z  observed from inertial system Z with the motionless of relative subject M; x u is the moving velocity relative to subject N, x V is the relative velocity speed of M and N. For picture 1, we would like to conclude the force on Q (subject M), namely Q is of inertial system of Z and two current surface is of the inertial system of Z  , The velocity of The movement velocity of negative electron is far smaller than C ( electron in magnetic domain is also smaller) in the moving electric field formed in two current surfaces A and B; therefore 2 2 C u is very small, which can be reckoned as 1 1 , and then the above formula can be converted into: The field intensity felt by Q is: , the above formula can be converted into: (11)( The first capitalized E, bold) For the sake of telling the force F, namely Lorentz Force F, exerted by electric field when Q is moving at medium and low speed, the force V F on Q exerted by electric field can be concluded from formula (11): It is shown from former formula (5) that Lorentz Force on Q is when it is moving at medium and low speed, and put it into formula (12): The formula (13) can be used for the correction of the formula of Lorentz Force. It is obvious that formula (13) is also qualified for that at both high and low speed when Q is moving in magnetic field at medium and low speed.

Interpretation of charged particles' deflection with the help of corrected formula for Lorentz Force
The corrected Lorentz Force V F on Q got from above analysis is just the electric field force, which is relatively static to Q; it will move together with Q at the same speed V. For the observer with static relative magnetic field (two current surfaces), force V F is a moving one. I have mentioned in "Set up Invariable Axiom of Force Equilibrium and Solve Problems about Transformation of Force and Gravitational Mass" (References. 3) that the force on moving subject will also change like its length, mass and time. The conversion formula for the force moving at the speed V is： In the formula,  is the included angle between F and V.
F is just the real force exerted on charged particle we would like to discuss, put real  V F into formula (3) instead of F: It is obvious that the deflection distance Y is just as determined in experiment room, namely true deflection distance formula (2).
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 Force in combination with force transformation.

Making analysis of particles' deflection from the inertial system of relative static of charged particles
According 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 surface), it is of course that they will have the same result of the deflection on Q passing through the magnetic field on direction Y.
The former analysis is the conclusion of the observer relatively static to Z  , for this conclusion, the real force  V F is got with the help of corrected Lorentz Force and changed combined power, moreover the analysis result compliance with fact is concluded. Z is moving relatively to Z  at the speed V, it can be reckoned that V F is static relatively to Z (with slight movement of V F on direction Y neglected) there is no need for changing V F any longer…; Whether the change of this kind of conditions will have any influence on our analysis of the corresponding deflection? Let us make detailed analysis for it.
For observer Z, Q is static and one magnetic field (inertial system Z  ) is passing through Q at the speed V  , one downward force V F is be exerted on Q, and moreover distance Y is moved downwards (deflection); because the speed of Q on direction Y is very slow, the mass of Q is still static one, namely no change is occurred to it. Besides the force on Q is also a static one, namely 2 What is the relationship between V t and Z  observed by Z? First of all, we shall make sure that the absolute moving speed V and V  of Z and Z is the same and Z observes t is the time Q passing the magnetic field at the speed V, namely V L t  ; for Z, the magnetic in L wide is moving at the speed of V  ，according to the Relativity Principle given in Special Theory, the width of the magnetic field moving at the speed V  is ; therefore the time used by the magnetic passing through Q from the observation of Z is , put it into formula(15), It is obvious that the relationship formula is also that for real deflection distance (2).
For the above analysis, the deflection results of charged particles moving at high speed got by Z  and Z shall be the same, which is in compliance with Relativity Principle.

Application scope of Lorentz Force
I hereby point out that the force on Q will be the same only in the uniform magnetic field through the analysis with the help of electric magnetic field and Lorentz Force; under normal condition, the two results derived from the two methods will not be the same in non-uniform magnetic field.