Sunday, March 20, 2016

Charged Particle Spinning Creates 

A  Circle-Closed Magnetic Field

Jack Yong Li

Mar 20, 2016

PACS: 03.50.De ,07.55.Db, 11.40.Dw, 41.20.Jb

Abstract

  Charged particle spinning almost not be mentioned in electromagnetic theory of classical physics, I will explain the principle a charged particle's spinning creates a circle-closed magnetic field with novel way, and put forward new law: Charged Particle Spinning Law and new rule: Lorentz Rule, I will use the new concept that a charged particle's spinning creates a circle-closed magnetic field and Charged Particle Spinning Law to calculate the magnetic strength of  infinite long straight current wire, compare with the Biot-Savart Law, also I will use Charged Particle Spinning Law and Lorentz Rule to explain some of electromagnetic phenomena to prove my hypothesis.

1.Introduction

  since 1900's,many physics phenomena can't be explained by classical physics, some physicists tried to use new theory to explain them and got success, those new theories formed quantum mechanics, quantum mechanics got rapidly development in twenty century, many quantum mechanics new concept come from classical physics theory, for instance the electron "spinning down" and "spinning up" about the model of the atomic structure in quantum mechanics, many people was confused by this concept, if we understand the principle for charged particle spinning properly, then we can understand electron "spinning down" and "spinning up" very easily. in the following section, I will explain to you how the charged particle spin.

2. the condition of a charged particle spinning

  object spinning is very common physics phenomenon, when we talk about spinning, many people's first reaction is earth spinning, and also we can give many spinning example, such as football spinning, golf ball spinning, pingpong spinning, the character of this kind of spinning is the spinning axis is not parallel to the moving direction of the object, the angle between the spinning axis and the direction of the moving is non zero. we don't care about this kind of spinning.



  another kind of spinning like a windmill spinning , or a dart spinning, or an arrow spinning, the best example is wind spinner, wind spinner consist of rotors ,spinning axis, and a holder:

  the principle of wind spinner is very similar to windmill, the principle of windmill spinning is very simple, the huge rotor blades on the front of a windmill are the spinning part. as wind passes by, the kinetic energy (air of movement) makes the blades spin around, the blades have a special curved shape so they capture as much energy from the wind as possible. wind spinner almost has the similar principle, the different between windmill and wind spinner is: moving the wind spinner can make the air to push rotor to rotate around spinning axis also, we find if there is a relative movement between air and wind spinner, the wind spinner will spin. this is the wind spinner spinning condition. we call this spinning is a parallel spinning, because the spinning axis parallel to the relative movement direction of the wind spinner.

  now the question is: does a charged particle spin? if it spins, which kind of spinning it belongs to? and what is the condition of a charged particle spinning? to answer these question, we must analyses the component of the charged particle, a charged particle consists of two part, charge and electric field, the electric field more like the rotor of a wind spinner, and charge like the body of the wind spinner, the electric field as a rotor to push the charged particle spinning, air is the media push the rotor of the wind spinner to rotation, but what is the media to push the electric field of the charged particle to rotate, we call this media dark matter, when there is a movement between the charged particle and dark matter, the dark matter will push the electric field of charged particle to rotate, and it force the charged particle spinning.
  so the condition for a charged particle spinning: there is a relative movement between a charged particle and dark matter, we don't discuss dark matter here, we just know the dark matter can push the electric field of the charged particle to rotate is enough.



3.the charged particle spinning direction and the circle-closed magnetic field direction
  we already know the condition of a charged particle spinning, the next important thing we need to know is the direction of the charged particle spinning, what factor can decide the spinning direction? we know the electric field is the rotor parts for charged particle, we can easily figure out the positive and negative charged particle must have different spinning direction. because the electric field for positive and negative charged particle point to the contrary direction.


  by this character of the positive and negative charged particle, we can get a law for judging the spinning direction of charged particle, I call this Charged Particle Spinning Law: if charged particle has a relative movement with dark matter, the charged particle will spin and create a circle-closed magnetic field. the spinning direction or the circle-closed magnetic field direction can be judged by left and right hand, left hand for negative charged particle, right hand for the positive charged particle, thumb points to the relative movement direction of charged particle, the direction curled fingers point to is the direction of charged particle spinning or the direction of the circle-closed magnetic field created by the rotation of electric field of the charged particle, the spinning axis is the direction thumb points to. in another word, if we face the relative movement direction of the charged particle, negative charged particle will do the clockwise spinning, the direction of the circle-closed magnetic field created by negative charged particle spinning will be clockwise; positive charged particle will do the counterclockwise spinning, the direction of the circle-closed magnetic field created by positive charged particle spinning will be counterclockwise, because the direction for the rotation of the electric field of the charged particle and the direction for the circle-closed magnetic field created by the charged particle spinning is same, we just need to know the charged particle spinning direction, we will know the direction of circle-closed magnetic field created by the charged particle spinning

 I want to emphasize the relative movement direction of the charged particle, if a charged particle moves, the relative movement direction of the charged particle is the moving direction, if the charged particle doesn't move, but the magnetic field around the charged particle moves, this will lead the dark matter have the same movement direction as the magnetic field movement, then the relative movement direction of the charged particle is contrary to the magnetic field movement direction.

  in this picture, for electron in left side, the relative movement direction is from left to right; for electron in right side, the electron doesn't move, but the magnetic field movement direction is from left to right, dark matter is pushed from left to right by the magnetic field, so the relative movement direction of the electron is from right to left.

4.the direction of the force on a spinning charged particle in a uniform magnetic field
  we already know a moving charged particle will change the moving direction, if the charged particle moving direction is perpendicular to the direction of the magnetic field. but at that time, scientist didn't know the movement charged particle create a circle close magnetic field, so here I will use the principle that a charged particle spinning creates a circle-closed magnetic field to give the rule for judging the direction of the force on a spinning charged particle in a magnetic field, because this force on a moving charged particle in uniform magnetic field was found by Lorentz, in order to commemorate Mr. Lorentz, I call this Lorentz Rule: if a charged particle's relative movement direction is perpendicular to uniform magnetic field, the circle-closed magnetic field created by the relative movement charged particle will interact with the uniform magnetic field and produce a force on the relative movement charged particle, the direction of the force is always from the point where two magnetic field have the same direction to the charged particle and perpendicular to the relative movement direction of the charged particle.


  in this picture, there are 3 points(A ,B,C) where the two magnetic field are the same direction, but only the direction from point A to the charged particle is perpendicular to the relative movement direction of the charged particle, so the direction of the force on the charged particle is from A to the charged particle.

5 proof of the spinning of a charged particle creates a circle close magnetic field
  in this section I will use some physics experiment to prove Charged Particle Spinning Law and Lorentz Rule.

A. the magnetic field around the current wire
  the current wire will create a circle-closed magnetic field, we know the current consists of moving electrons, these moving electrons have the contrary movement direction with the current, all these electrons have the same spinning direction, we can use left hand for Charged Particle Spinning Law, we get the circle-closed magnetic field direction by Charged Particle Spinning Law is the same as the actual experiment.


 
  this proved electrons moving caused the electron spinning to create a circle-closed magnetic field.   

B. a wire moving through the magnetic field
a. if we put part of the closed wire in magnetic field, another part of the closed wire outside the magnetic field, moving the closed wire will create current in closed wire, we can use Charged Particle Spinning Law and Lorentz Rule to explain why there is current in the closed circuit.

  because the wire move from left to right, the freedom electrons inside wire also will move from left to right, use left hand for Charged Particle Spinning Law to those electrons, we get the spinning direction of those freedom electrons and the circle-closed magnetic field direction created by those electrons spinning, we can use the Lorentz Rule for judging the direction of the force on those freedom electrons inside wire and covered by the uniform magnetic field, the direction of the force on these electrons inside wire covered by the uniform magnetic field is from top to bottom, these electrons inside wire covered by the uniform magnetic field will move from up to down, and the movement of these electrons inside wire covered by the uniform magnetic field will force those electrons inside wire not covered in the magnetic field move to the same direction in the closed wire ,current has the contrary direction with the electrons moving direction. this result is the exactly the same as the actual experiment. this also proved the movement electrons will spin and create a circle close magnetic field (Charged Particle Spinning Law) and Lorentz Rule.
b. we put all the closed wire in the uniform magnetic field, no current will be produced, but  there is a voltage difference between top and bottom, we can use Charged Particle Spinning Law and Lorentz's Rule to explain.


  the freedom electrons movement direction is the same as the wire movement direction, so freedom electrons in left part and right part has the same spinning direction and produce the same direction of circle close magnetic field, we use Charged Particle Spinning Law and Lorentz Rule, we will find the force on these electrons in both left and right part have the same strength and direction, all those electrons in both left and right part will move to the bottom and will be stuck at the bottom, after all these freedom electrons reach to the bottom, there aren't moving electrons in the closed wire, so there isn't current inside the closed wire, but all the freedom electrons arrive at the bottom, there is a voltage difference between top and bottom. this result is the exactly same with the actual experiment. this also prove the movement electron will spin and create a circle-closed magnetic field(Charged Particle Spinning Law) and Lorentz Rule.

C. moving magnet and coil wire
  when we move the magnet toward the closed coil wire, it will produce a current, the current direction depend on the magnetic pole and the movement direction of the magnet, I will use Charged Particle Spinning Law and Lorentz Rule to judge the current direction. 
  
  in above picture, we assume that the closed coil wire is a round and symmetry, we just choose two symmetric point to research, one point close to us and another point away from us, the magnet move from right to left, when the magnet move, the magnetic field of the magnet force the dark matter moving from right to left, and dark matter moving will force the freedom electrons to spin, the electrons relative movement direction is from left to right, so use the Charged Particle Spinning Law to judge the spinning direction of the electron, we get the direction of circle-closed magnetic field at those two point, we find both of the circle-closed magnetic field have the same direction.
   but when we use Lorentz Rule to judge the direction of the force on the electron, we find the direction of the force on the electron at the point close to us is from bottom to top, the direction of the force on the electron at the point away from us is from top to bottom, you will find the force direction on every freedom electron in coiled wire will follow the force direction of the electron in front of itself, all the freedom electrons in coiled wire will move in circular circuit, obviously this will produce current.
  when we move magnet away again, the relative movement of these electron changed to the contrary direction and all the force direction on these electrons changed to contrary direction and the current also changed to the contrary direction. this result is the same as the experiment, this prove the relative movement electron will spin and create circle close magnetic field(Charged Particle Spinning Law) and Lorentz Rule.
  in this example, we think the magnetic field of the magnet as one uniform magnetic field, perhaps this is very easy confused.  

D. the waveform phase difference between primary and secondary coil for transformer  
  In a transformer circuit, if we put the alternative current in primary coil, the current induced in secondary coil will be alternative also, but there will be a phase difference between the current waveform in primary coil and the current waveform in secondary coil, I will use Charged Particle Spinning Law and Lorentz Rule to explain why.
  From example C we know, we just need analyze the movement direction of the electron at one point, we can judge the direction of the current in coil wire circuit. in this example if no specific instruction, "the electron" always mean the electron at the dedicated point we chose, for convenience, we divide the period T into four equal time parts, by analyzing every single time part, we can get the waveform of the input and output current in the whole period T and find out the phase difference of the current waveform.


(1) During 0 ~ T/4, the current in primary coil increase from zero to maximum, the magnetic field will increase from zero to maximum, so we can think the magnetic field produced by the primary coil will move from right to left, we know the magnetic field moving will force the dark matter move from right to left, so the freedom electrons in secondary coil will spin, the relative movement direction of these electrons in secondary coil is from left to right. in secondary coil, using Charged Particle Spinning Law to the electron at the point we chose, we get the electron spinning direction and the direction of the circle-closed magnetic field produced by the electron spinning, then we use Lorentz Rule to the electron at the point we chose, we can get the force direction on the electron is from bottom to top, the electron will move from bottom to top, the current direction will be from top to bottom, so the direction of the current is the same as the direction of the current in primary coil, both of the direction of the current are positive during 0~T/4, we already confirm the direction of the current in secondary coil, we need to confirm the current initial value is maximum or zero in secondary coil, we can assume that the current initial value in secondary coil is zero, the current in secondary coil will change from zero to maximum during 0~T/4, by the continuous character of the waveform, the direction of the current in secondary coil must be positive during T/4~T/2, but if we use Charged Particle Spinning Law and Lorentz Rule, we find the direction of the current in secondary coil will be negative during T/4~T/2,it conflict with the assumption, so the waveform of the current in secondary coil must be from positive maximum to zero during the first time part.
(2)During T/4~T/2,the current in primary coil decrease from positive maximum to zero, the magnetic field will decrease from maximum to zero, so we can think these magnetic field produced by the primary coil move from left to right, we know the magnetic field move will force the dark matter move from left to right, so the freedom electrons in secondary coil will spin, the relative movement direction of the electron is from right to left, we use Charged Particle Spinning Law to the electron at the point we chose, we get the electron spinning direction and the direction of the circle-closed magnetic field produced by the electron spinning, then we use Lorentz Rule to the electron at the point we chose, we can get the force direction on the electron is from top to bottom, the electron will move from top to bottom, so the current direction will be from bottom to top. we noticed during this time part, the direction of the force on the electron changed, that is why the current direction changed in second time part, by the continuous character of the waveform, the waveform of the current in secondary coil will change from zero to negative maximum.
(3)During T/2~3T/4,the direction of current in primary coil changes from positive to negative, but the current value increases from zero to negative maximum, so the magnetic field direction produced by the primary coil wire changes to the contrary, when we use Charged Particle Spinning Law and Lorentz Rule, we find the direction of the force on electron in secondary circuit keep the same as the direction during the second time part, but the current value will decrease from negative maximum to zero.
(4)During 3T/4~T,the current in primary coil keep the same direction, but the current value will decrease from negative maximum to zero, when we use Charged Particle Spinning Law and Lorentz Rule, we find the direction of the force on electron in secondary coil change to the contrary, so the current will be positive and the waveform of the current in secondary coil will change from zero to positive maximum .
  we find the phase difference of the waveform of the current between primary coil and secondary coil is л/2,this result is the same as the actual experiment, so we proved Charged Particle Spinning Law and Lorentz Rule again.        
 
E. The magnetic field of the current coil wire
  if two electrons have the same spinning direction at one point, the strength of the magnetic field created by two electron can be add up. for example, the strength of the magnetic field at the central of the multiple coiled wire would be the sum of the strength of the magnetic field produced by the single coiled wire, this means the strength of the magnetic field at one point is the sum of the strength of the magnetic field produced by all the freedom movement electrons spinning in coiled wire, that is why more coil numbers more strong of the magnetic field.

  we can give more example, for example, the force on a straight current wire in uniform magnetic field, and we can explain why two parallel current wire appeal each other..., all the phenomena about relationship between electric field and magnetic field should be explained by Charged Particle Spinning Law and Lorentz Rule, I don't want waste to much time to the explanation of these one by one, you can use Charged Particle Spinning Law and Lorentz Rule to explain them very easily.

F. the force on a moving charged particle in uniform magnetic field
  All of the five examples above, charged particles are contained in certain object, in this example, I will prove the charged particle even in free space do the same spinning, we know if a moving charged particle pass through a uniform magnetic field, if the direction of the movement charged particle is perpendicular to the uniform magnetic field, the charged particle will change the moving direction and do a circle movement.


  we can use left hand for negative charged particle and right had for positive charged particle to the Charged Particle Spinning Law to judge the charged particle spinning direction(circle-closed magnetic field direction),and then we use Lorentz Rule to judge the force direction on the charged particle,we get the force direction on positive and negative charged particle is contrary and the result is the same as the experiment. this proved a free charged particle in free space do the same spinning as the free charged particles inside certain object.
  from this example, we can confirm electron's spinning axis always parallel to the relative movement direction of the electron in any situation,this is very important,it will be very useful for researching the atomic structure.  

6.The calculating of magnetic strength of circle-closed magnetic field
  in this section, I will use the concept of charged particle spinning creates a circle-closed magnetic field to build a mathematic model and then to calculate the circle-closed magnetic field around the unlimited straight current wire, and compare with Biot_Sarvat Law.


  if a electron moves speed at V, we can define the strength of the magnetic field created by the electron spinning at the point P is
θ is the angle between the moving direction of the electron and the direction of the electric field of point P,Ex is the projection of E to the electron moving direction, Ey is the projection of E to the plane which is perpendicular to the moving direction of electron, we use j represent the circle-closed magnetic field, so the magnetic field consists of two vector,one vector is circle-closed magnetic field and another vector is parallel to the movement direction, the strength of the electric field of a point charged particle is
so the strength of the magnetic field produced by the movement electron 
  we have the definition of the circle-closed magnetic field created by the movement charged particle now,we can calculate the magnet
-ic field strength of an unlimited straight wire, we know the current consist of moving electrons,moving electrons will spin and produce a circle-closed magnetic field,because all electrons have the same moving direction,if we want to calculate the magnetic strength at one dedicated point around the wire, we can add up all the moving electron's circle-closed magnetic field at the dedicated point together by integral calculus.

  assume that cross sectional area of wire is s, and electron density isρ,q is unit electrical charge quantity, the distance from the point we will calculate the magnetic field strength to the current wire is a ,so the electrical charge quantity of the electrons in a small piece of length dx is qsdx, we can think qsdx as one electron, because it can be add up, the magnetic field strength at point P produced by this small piece of wire dx is B=ExV+jEyV=EVcosθ+jEVsinθ,V is the speed of the electron moving in wire, θ  is the angle between the moving direction of the electron and the direction of the electric field of point P,the electrical strength of the point P is 

 we have

   we get the circle-closed magnetic field is:


because the current I=ρsqv,so finally we get
but biot-Savart law's calculation
  we find the result almost the same, if we use some constant to     modify my result,we get the same result,this also can prove the circle-closed magnetic field created by electron spinning.

7.conclusion
   from the above proof, we know if there is a relative movement between a charged particle and  dark matter, dark matter will push the electric field of a charged particle to rotate, the electric field rotation lead the charged particle to spin and create a circle-closed magnetic field, and the charged particle's spinning axis is always parallel to the relative movement direction of the charged particle, positive and negative charged particle moving at the same direction have different spinning different direction and create different direction circle-closed magnetic field.if we face the relative movement direction of a charged particle, the negative charged particle will do a clockwise spinning(the circle-closed magnetic field direction is clockwise), the positive charged particle will do a counter-clockwise spinning(the circle-closed magnetic field direction is counter-clockwise).



Saturday, February 8, 2014

the condition for Fourier series convergence





the condition for Fourier series convergence
 Jack Yong Li    Feb 08,2014
    I just finished the learning of Fourier series, in many book it says if the Fourier series meet one of the conditions, (1) Direchlet-Jordan (2) Dini-Lipschitz conditions. the Fourier series will convergence, I think even it doesn't  satisfy these 2 conditions, it can convergence. these 2 conditions is not necessary for Fourier series convergence,even both of f(x+) and f(x-) are infinite, but the sum of the f(x+) and f(x-) exist, the Foruier series should convergence.
  So the condition for the Fourier series convergence should be:
   f(x) is a Riemann integrable or absolute integrable function on [-+] and if f(x+)+f(x-) exist on [-+],the f(x)'s Forier Series convergence to (f(x+)+f(x-))
Proof
   f(x) is a Riemann integrable or absolute integrable function on [-+],the partial sum of Fourier series should be
from Euler-Fourier formula
   
     =
     =
we have the equation
                 (θ≠0)
assume that tx, the partial Sum should be 
(let t-x=u)
(the definite integral of periodic function has the same value in any period length )
=
=(let t=-u)+
 =
0  is  the Singularityassume that ε>0,εcan go to very close to 0but not equal to 0we can change the partial sum of Fourier series to:
=
from Riemann lemma ,we know when M goes to +∞,0So the Sum equation can be write into:
=0................(1)
from Reimman lemma ,we can build this equation
=0,and then times f(x-)+f(x+)to this equation,
=
so the equation (1) can be changed into
=
               ................(2)
letε→0so the integrable length of
goes to 0, also u0,and f(x+u)=f(x+),f(x-u)=f(x-)
the equation can be changed to:
=
=
=
=
finally =
 f(x) is a Riemann integrable or absolute integrable function on [-+] and if f(x+)+f(x-) exist on [-+],the f(x)'s Forier Series convergence to (f(x+)+f(x-))it is not necessary to meet the Direchlet-Jordan  and  Dini-Lipschitz  conditions