Abnormal deflection of electrons crossing the boundary of opposite magnetic fields
1 An experiment imply that electrons rotate around their own axes in magnetic field and Lorentz force is the result of Magnus effect
Changgen Zou , Department of Radio Engineering, Southeast University. Wanshou Jiang, State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University. (August 31, 2019) Abstract:
This paper reports an experiment about abnormal deflection of cathode ray in a specially designed odd-symmetric magnetic field, which is generated by two reverse-connected solenoids. The experiment indicates that during cathode ray passes through an odd-symmetric magnetic field, a deflection opposite to Lorentz force occurs at the boundary of magnetic fields. It can be explained that electrons rotate around their own axes in magnetic field, and Lorentz force is the result of Magnus effect.
Key words:
Lorentz force; electron rotation; moment of inertia; Magnus effect Introduction.
The experiment indicates that during cathode ray passes through an odd-symmetric magnetic field, a deflection opposite to Lorentz force occurs at the boundary of magnetic fields. This result, which contradicts electromagnetics, is due to the moment of inertia of electrons rotating around their own axes.
This experiment is helpful to discover the essence of Lorentz force. Theoretical deflection of cathode ray.
Let’s review the principle of measuring the charge-to-mass ratio of electron using a cathode-ray tube. As shown in Fig-20, an electron with charge of and mass of , its three-dimensional components of initial velocity are respectively and , when the electron enters a constant magnetic field parallel to the X-axis with magnitude of magnetic induction , it does a uniform linear motion in the X-axis direction and a uniform circular motion in the YZ plane, trajectory of the electron is a helical line.
Fig-20
Helical trajectory of an electron
Suppose is the radius of the uniform circular motion of the electron, then Lorentz force can be written as:
From which, we can get the interval required for the electron to circle in the YZ plane and the angular velocity of the electron in uniform circular motion:
1 Corresponding author. Email addresses: [email protected] The direction of the uniform circular motion of the electron in the YZ plane changes while the direction of the changes. When the is a constant, all electrons starting from a same point will arrive at anther point after a period of T, this phenomenon is called magnetic focusing. The projection of the trajectories of electrons on the YZ plane is shown in Fig-21.
Fig-21
Projection of the trajectories of electrons when measuring the charge-to-mass ratio of an electron by a cathode-ray tube, the velocity component of electrons is generated by a constant accelerating voltage , and the velocity component is generated by an alternating voltage , as shown in Fig-22. The alternating voltage causes the change of the magnitude and direction of , but while these electrons reach screen of the cathode-ray tube, they revolve the same angle on the YZ plane and therefore the image on screen is a straight line. Adjusting the magnitude of the magnetic induction, the line image will rotate and be gradually shortened into a point.
Fig-22
Accelerating and alternating voltage of the cathode-ray tube
Assuming that the cathode-ray tube in Fig-22 can be lengthened in the X-axis direction, the line image on screen will rotate with a tiny angle when the distance of electrons motion increases by . Assuming that the direction of the magnetic induction B is still parallel to the X-axis but its magnitude is a function that varies with , then becomes
Fig-23 shows the main device used to measure deflection angle of the line image. The diameter of the screen of the cathode-ray tube is much smaller than distance between the electron gun and the screen. Near the screen of the cathode-ray tube, two identical and reverse-connected solenoids are used as excitation coils, they produce magnetic fields of equal magnitude in opposite directions. These two solenoids are called a coupled-tube, it can be moved left and right, and its axis overlaps with that of the cathode-ray tube. Fig-23
The cathode-ray tube and the coupled-tube
Taking the axis of the cathode-ray tube as the X-axis and the direction of electron motion as the positive direction of the X-axis, assuming that the center position of the coupled-tube is , when the current of constant current source remains unchanged, magnetic induction of the coupled-tube on the X-axis can be shown in Fig-24, where is an odd function.
Fig-24
Theoretical curves of magnetic induction and deflection angle
The line image of the cathode ray is used as the reference line while the current of constant current source is 0, assuming that the position of the inner surface of the screen of the cathode-ray tube is , then the deflection angle of the line image is a function as follows:
Because is an odd function, therefore is an even function as shown in Fig-24, is its extreme point. If the cathode-ray tube is moved so that the position of the inner surface of the screen moves from to , it can be found that deflection angle of the line image increases gradually and reaches the maximum at , and then the line image begins to reverse and deflection angle decreases gradually, as shown in Fig-25. Fig-25
Theoretical deflection angle variation Keeping the magnitude of the current of constant current source unchanged and changing the direction of the current, the rotation characteristics of the line image should be exactly the same except direction of rotation. These results can be predicted by existing knowledge of electromagnetics. Actual deflection of cathode ray.
If we increase the measuring accuracy, we will find that the measurement results are different from the predicted value discussed in previous section. And the extreme point of will shift to . When the magnitude of the current of constant current source is unchanged but direction is changed, the distance from the extreme point of to the position of also changes, and the extreme point of deviates more from when the direction of magnetic field which electrons enter first is opposite to the direction of electrons motion, as shown in Fig-26, . Fig-26
Actual curves of magnetic induction and deflection angle
Moving the cathode-ray tube so that the position of the inner surface of the screen moves from to , because the direction of Lorentz force on electrons changes at , the line image should have begun to reverse at . However, the measurement results shown in Fig-26 indicate that the line image continues to rotate for a distance in original direction, indicating that electron is subjected to a force opposite to Lorentz force within this distance, we call this force as "reversed Lorentz force". It is impossible for the line image to rotate for a distance in original direction because of the inertia caused by electrons' circular motion for Lorentz force. If it is caused by this inertia, distance between extreme point of and should be the same in Fig-26, but the fact is . Method for measuring cathode ray deflection.
Although the measurement result is difficult to be explained with the existing knowledge of electromagnetics, it coincides with the result predicted by "Lorentz Force is the result of Magnus effect" presented in annex. In order to verify this prediction, we spent a lot of time in making several special cathode-ray tubes. The shape of the cathode-ray tube that can be used to measure is slender (about 470 mm in length, but the screen is only 20 mm in diameter, smaller than a coin), and the exact value of thickness of the screen must be known, its picture is shown in Fig-27. The reason why the screen diameter of the cathode-ray tube is much smaller than its length ( ) is that the magnetic induction of coupled-tube must have enough attenuation distance to ensure that is an odd function for measurement accuracy. Fig-27
Physical picture of the cathode-ray tube
The deflection of the line image caused by the reversed Lorentz force is very weak, so that it is difficult to be measured. We used a high-pixel industrial camera to take photos of the screen of the cathode-ray tube, and the the deflection angle of the line image can be calculated on the images.
Fig-28
A photo taken during experimental measurement
Fig-28 is an image taken for the measurement, in order to facilitate calculation, the Y-axis is adjusted to a horizontal line, take it as an example to illustrate the method of calculating deflection angle. Because the magnetic field in solenoid is not uniform, the line image is not a straight line but an odd symmetrical curve. The deflection angle of the curve at the midpoint is equal to that of ideal straight line image. Due to various errors, the midpoint of the odd-symmetric curve in Fig-28 cannot be measured directly, but the midpoint of the odd-symmetric curve in Fig-28 is also the inflection point of the curve, the exact value of the inflection point can be calculated. For example, the midpoint of the curve can be roughly calculated first, and then the middle part curve (as shown in Fig-29) is taken for cubic fitting to obtain the curve equation.
Fig-29
Middle part of a photo
The inclination of the tangent of the cubic fitting curve of Fig-28 at each point is shown as Fig-30, the deflection angle corresponding to the extreme point is 27.949539 degrees. For each photo, the deflection angle that meets requirements of measurement accuracy can be calculated. Fig-30
Inclination of the tangent at each point
The main experimental equipment includes: (1) A slender cathode-ray tube with a length of about 470mm and a screen diameter of 20mm. (2) A coupled-tube consists of two hollow coils with inner diameter of 20 mm, thickness of 10.04 mm, line diameter of 0.20 mm and 448 turns. (3) An industrial camera with resolution of 16 megapixels. (4) A laser distance sensor with accuracy of 0.01mm. The main parameters includes: (1) Accelerating voltage on electrons is 2196 V. (2) Current of constant current source is 720 mA. In order to improve measuring accuracy, following 32 measurement combinations were considered, and a total of 672 photos were taken. (1) Four directions of electron motion: in the same direction as geomagnetic field (including geomagnetic declination and geomagnetic dip), in the opposite direction to geomagnetic field, in the same direction as earth rotation and in the opposite direction to earth rotation. (2) Four combinations of connection and direction of coil A and coil B, as shown in Fig-31. (3) Two ways to connect with constant current source.
Fig-31
Four combinations of connection and direction of coils
There are a total of combinations. In order to facilitate measurement, keep the position of the cathode-ray tube fixed and move the coupled-tube for measurement. Taking the axis of the cathode-ray tube as the X-axis and the direction of electron motion as the positive direction of the X-axis, assuming that the position of the inner surface of the screen of the cathode-ray tube is (object of the reference in experimental measurement is different from object of the reference in previous theoretical analysis, which will lead to the change of positive and negative sign of ). Moving the coupled-tube makes the center of the coupled-tube move step by step from to with a step length of 0.20mm. One photo is taken every step, 21 photos are taken each combination, photos are taken in total. In order to improve reliability of the measurement, differential deflection angle is used for analysis. For each combination, deflection angle at is used as the reference angle, absolute deflection angle minus the reference angle is taken as relative deflection angle for every measurement point. Measurement result.
After processing these photos, the results show that the geomagnetic direction or the earth rotation direction or the connection method of the coupled-tube or AB direction of the coupled-tube has little influence on quantitative analysis, but the current direction of constant current source can influence qualitative analysis. The direction of the current of constant current source can be divided into two categories, one causes that the direction of magnetic field which electrons enter first is the same as direction of electrons motion (as shown in Fig-26 left side), and the other causes that direction of magnetic field which electrons enter first is opposite to the direction of electrons motion (as shown in Fig-26 right side). The results of calculation for 672 photos are divided into two types according to the category of the current of constant current source, and mathematical average is used for each type of data, which can filter out most of noise and reduce error of final measurement results. After cubic fitting the mathematical average, the final measurement results can be obtained, as shown in Tab-1 and Fig-32.
Tab-1
Measurement result table
Measure Point Direction of magnetic field which electrons enter first is opposite to direction of electrons motion Direction of magnetic field which electrons enter first is the same as direction of electrons motion Average of relative deflection angle Fitting value of relative deflection angle Average of relative deflection angle Fitting value of relative deflection angle -10 0.17763 0.17868 0.07829 0.07542 -9 0.32319 0.31644 0.22246 0.22203 -8 0.43593 0.43807 0.35306 0.352 -7 0.54449 0.54368 0.46535 0.46547 -6 0.63006 0.6334 0.55451 0.56256 -5 0.69912 0.70733 0.63561 0.64343 -4 0.75981 0.7656 0.70981 0.70819 -3 0.8129 0.80831 0.75724 0.75698 -2 0.83886 0.83559 0.79627 0.78995 -1 0.85079 0.84755 0.81532 0.80721 0 0.85085 0.84431 0.81403 0.80892 1 0.83359 0.82598 0.79372 0.79519 2 0.78961 0.79267 0.76457 0.76617 3 0.74157 0.74451 0.71917 0.72199 4 0.67564 0.68161 0.66127 0.66279 5 0.6029 0.60409 0.58171 0.58869 6 0.50933 0.51206 0.50132 0.49984 7 0.40471 0.40563 0.39694 0.39637 8 0.2867 0.28493 0.27978 0.27841 9 0.15401 0.15007 0.14682 0.14609
10 0 0.00116 0 -0.00044
Fig-32
Measurement result curves
As shown in Fig-32, the left curve is a relative deflection angle curve when the direction of magnetic field which electrons enter first is opposite to the direction of electrons motion, its cubic fitting equation is , and its extreme point is , that is to say, when the center point of the coupled-tube moves from the position of the inner surface of the screen of the cathode-ray tube to the direction of electron gun, the deflection angle of the line image reaches its maximum value. The middle curve is a relative deflection angle curve when the direction of magnetic field which electrons enter first is the same as direction of electrons motion, its cubic fitting equation is , and its extreme point is , that is to say, when center point of the coupled-tube moves from the position of inner surface of screen of the cathode-ray tube to direction of electron gun, the deflection angle of the line image reaches its maximum value. The dashed line is a reference line symmetric to the right curve. Conclusions.
According to the annex "Lorentz force is the result of Magnus effect", electrons rotate around their own axes in magnetic field, therefore, the reason why the line image continues to rotate with a tiny angle in the original direction after electrons cross the boundary of opposite magnetic fields can be explained as the result of the MOMENT of INERTIA of electrons rotating around their own axes. In addition, according to the contents of the annex, a stationary electron has microscopic angular momentum components in all directions, but the vector sum of all these microscopic angular momentum components is 0, as shown in Fig-33. It is unclear how microscopic angular momentum changes inside an electron moving and rotating around its axis in magnetic field. Assuming that the angular velocity of an electron crossing in the left figure of Fig-26 is less because of the change of microscopic angular momentum inside an electron, and therefore electrons in left figure of Fig-26 are less affected by Magnus effect, resulting in . Fig-33
Microscopic angular momentum inside an electron
672 photos taken during experiment measurement and related calculation results, as well as the code of Python program for calculation, can be downloaded at https://pan.baidu.com/s/1Eete__RbaZz3pYM3DzYQ_A , the download code is and the URL is case-sensitive. It is suggested that laboratories with good conditions should make more accurate measurements.
References TanWen-Hai et al., "Recent progress in testing Newtonian inverse square law at short range", Acta Physica Sinica,67,160401(2018) DOI:10.7498/aps.67.20180636 Annex: Lorentz force is the result of Magnus effect
Abstract:
Both electric field force and gravitation are differential force, Lorentz force is the result of Magnus effect, and it’s also differential force. Eelectric field and gravitational field and magnetic field are simply different states of physical environment, it's wrong to call them matter.
Key words:
Z-particle; electron; electric field force; strong interaction; gravitation; Lorentz force; magnetic field; Magnus effect Introduction.
Do you really think that electric field and magnetic field are matter? Children asked me why magnets attract each other, can you really explain it? Now I try to explain these problems by basic knowledge of Newtonian mechanics, including why do like charges repel each other while opposite charges attract? why is gravitation always attractive force? what’s magnetic force? is strong interaction force in an atomic nucleus necessary? I need a new kind of particle and I call it Z-particle. Presume of two electrons repulsion. Z.1
A large number of unknown particles collide with an electron and generate pressure on surface of an electron. If there are two electrons E1 and E2, pressure on a certain point on surface of electron E1 is inversely proportional to distance between this point and centerpoint of electron E2. As shown in Fig-1, R is radius of an electron, A is centerpoint of electron E1 and B is centerpoint of electron E2, is distance between A and B.
Fig-1
Analysis of force on an electron
Shadowed surface area is
Pressure on point C is is a scale factor. Horizontal force on electron E1 towards the right is It can be found in integral table that:
So, can be calculated:
The result is similar to the Coulomb’s law. Assuming that Q is electric quantity of an electron, , is permittivity of vacuum, , so Assuming that meter and meter, then pressure on point C is:
Are you surprised? There is still
Pa while the distance between two electrons is 1 million kilometers. Resultant force on entire surface of electron E1 is:
Component force on half surface of electron E1 when is much greater than is:
The component force is about times as resultant force, electric field force is differential force. Field force and presume of Z-particle. Z.2
Z-particle is a kind of tiny particle much smaller than electron. It can move at high speed, and it’s all over any space. State of a Z-particle will change if this Z-particle collides with another Z-particle or an electron or a proton.
Z.3
Z-particles are uniformly distributed in space. A Z-particle is isotropic, it has rotational kinetic energy. Zp-particle and Ze-particle are two kinds of Z-particles. As shown in Fig-2, a Z-particle is a small ball consists of many tiny balls, these tiny balls are rotating and their axes pass through centerpoint of the Z-particle. While we stand at the centerpoint of a Z-particle, if tiny balls rotate clockwise, we call the Z-particle as Ze-particle, if tiny balls rotate anti-clockwise, we call the Z-particle as Zp-particle. Fig-2
Structure of Z-particle
Z.4
A Z-particle has rotational kinetic energy stored inside and translational kinetic energy, the sum of these two kinds of energy is a constant of . Mass and volume of a Z-particle are also constants.
Z.5 is rotational kinetic energy of one Z-particle and rotational kinetic energy of another Z-particle is , after these two Z-particles collide, each of them will get the rotational kinetic energy as while they are different kinds of Z-particle, and each of them will get the rotational kinetic energy as while they are the same kind of Z-particle.
Z.6
An electron or a proton is isotropic, they have large amount of rotational kinetic energy stored inside. As shown in Fig-3, an electron is a big ball consists of a large number of tiny balls, these tiny balls are high-speed rotating and their axes pass through centerpoint of the electron. While we stand at the centerpoint of an electron, tiny balls rotate clockwise. A proton is similar to an electron, but tiny balls rotate anti-clockwise, and a proton has an additional outer layer, energy of a Z-particle don't get extra change while passes through this layer.
Fig-3
Structure of electric charge
Z.7
An electron swallows up any one Z-particle it collides with, and then spits out a Zp-particle on the collision point, rotational kinetic energy of this Zp-particle is and translational kinetic energy of this Zp-particle is zero. A proton swallows up any one Z-particle colliding with its inside surface, and then spits out a Ze-particle on the collision point, rotational kinetic energy of this Ze-particle is and translational kinetic energy of this Ze-particle is zero. Z.7 is shown in Fig-4. Fig-4
Collision between Z-particle and electric charge
Z.8
After a long time, equilibrium state of Z-particle around a isolated electron is that rotational kinetic energy of a Zp-particle is inversely proportional to distance between this Zp-particle and centerpoint of the electron. After a long time, equilibriumd state of Z-particle around a isolated proton is that rotational kinetic energy of a Ze-particle is inversely proportional to distance between this Ze-particle and centerpoint of the proton. Z.8 is shown in Fig-5.
Fig-5
Attenuation of rotational kinetic energy of Zp-particle
Z.9
All Z-particles in three-dimensional space of arbitrary shape and size, if the sum of their velocity vectors with point A as the reference is zero, point A is called absolute stationary point. Spherical center of a massive celestial body can be approximated as a stationary point. If the celestial body does not rotate, any point on the celestial body can be approximated as a stationary point.
Z.10
A moving electron swallows up any one Z-particle it collides with and then spits out a Zp-particle at the collision point, initial velocity of the Zp-particle is the same as velocity of the collision point on surface of the electron, the sum of translational kinetic energy and rotational kinetic energy of the Zp-particle is . A moving proton swallows up any one Z-particle colliding with its inside surface and then spits out a Ze-particle at the collision point, initial velocity of the Ze-particle is the same as velocity of the collision point on inside surface of the proton, the sum of translational kinetic energy and rotational kinetic energy of the Ze-particle is . Z.11
There are two stationary electrons. Electron A swallows up any one Z-particle it collides with and then spits out a , after a huge amount of collisions between Z-particles, rotational kinetic energy of a is inversely proportional to distance between this and centerpoint of electron A. Electron B swallows up any one Z-particle it collides with and then spits out a with rotational kinetic energy of . After collides with , we call these two collided Z-particles as Z-2nd. The resultant force on electron B because of Z-2nd colliding with it is electric field force, and the resultant force on electron B because of colliding directly with it is gravitation. It is the same while there are two protons or one is electron and another is proton. As shown in Fig-6, electric field force is generated. As shown in Fig-7, gravitation is generated. Fig-6
Electric field force is generated
Fig-7
Gravitation is generated Electric field force and gravitation. Z.12
The reason why two electrons repulse each other is that rotational kinetic energy of Zp-particles between them is more and translational kinetic energy of Z-2nd colliding with electrons is more. The reason why two protons repulse each other is that rotational kinetic energy of Ze-particles between them is more and translational kinetic energy of Z-2nd colliding with protons is more. The reason why an electron and a proton attracts each other is that rotational kinetic energy of Z-particles between them is more and translational kinetic energy of Z-2nd colliding with electron or proton is less.
Fig-8
Repulsive force is generated
As shown in Fig-8, Z-1 Z-2 Z-3 Z-4 are Zp-particles around electron A while there is’t any other electric charge nearby, their rotational kinetic energy are respectively. Z-5 and Z-6 are Zp-particles spat out by electron B with rotational kinetic energy . After Z-3 collides with Z-5, Z-2nd will get the rotational kinetic energy as and its translational kinetic energy is . After Z-4 collides with Z-6, Z-2nd will get the rotational kinetic energy as and its translational kinetic energy is , for the reason of , translational kinetic energy of Z-2nd on the left-side of electron B is more than that of right-side and therefore generates greater pressure, so electron B moves to the right.
Fig-9
Attractive force is generated
As shown in Fig-9, Z-1 Z-2 Z-3 Z-4 are Zp-particles around electron A while there is’t any other electric charge nearby, their rotational kinetic energy are respectively. Z-7 and Z-8 are Ze-particles spat out by proton B with rotational kinetic energy . After Z-3 collides with Z-7, Z-2nd will get the rotational kinetic energy as and its translational kinetic energy is . After Z-4 collides with Z-8, Z-2nd will get the rotational kinetic energy as and its translational kinetic energy is , for the reason of , translational kinetic energy of Z-2nd on the left-side of proton B is less than that of right-side and therefore generates smaller pressure, so proton B moves to the left.
Z.13
Electric field force between two stationary electric charges is inversely proportional to square of distance between these two charges, it maybe repulsive force or attractive force. Electric field force is differential force. The environment state of Z-particle, which causes that resultant force of electric field on an electric charge is not zero, is called electric field. Gravitation between two stationary electric charges is inversely proportional to square of distance between these two charges, it is always attractive force. Gravitation is differential force. The environment state of Z-particle, which causes that resultant force of gravitation on an electric charge is not zero, is called gravitational field. As shown in Fig-6, rotational kinetic energy of Zpa around electron A is inversely proportional to distance between the Zpa and centerpoint of electron A:
Assuming that distance between a certain point on surface of elctron B and centerpoint of electron A is , then, rotational kinetic energy of the Z-2nd is:
So, translational kinetic energy of the Z-2nd is: Fig-10
Attenuation curve of translational kinetic energy of Z-2nd
Assuming that distance between a certain point on inside surface of proton B and centerpoint of electron A is , then, rotational kinetic energy of the Z-2nd is:
So, translational kinetic energy of the Z-2nd is:
Fig-11
Enhancement curve of translational kinetic energy of Z-2nd
It’s similar to calculate electric field force between different kinds of electric charges, we calculate electric field force between two electrions following.
Fig-12
Cuboid for calculating pressure As shown in Fig-12, right plane of cuboid is surface of electron B, its area is . Mass of a Z-particale is , velocity component in the X-axis direction of Z-2nd is , there are
Z-2nd collide with electron B per unit volume, so the amount of Z-2nd passed through the left plane and entered surface of electron B in interval of is:
Electron B swallows up any one Z-2nd it collides with and then spits out a Zp-particle with rotational kinetic energy and its momentum is zero, increased momentum of electron B in the X-axis direction is:
It’s equal to force times . Presure on surface of electon B caused by collision of Z-2nd is:
Because Z-2nd is isotropic, assuming that velocity of the Z-2nd is , then
Assuming that translational kinetic energy of the Z-2nd is , then is a scale factor and
According Z.1 and Fig-10, electric field force between two electrons is:
So, electric field force between two stationary electons is inversely proportional to square of distance between these two electons. Electric field force is differential force. Component force on half surface of the electron when is much greater than is: Assuming that meter, while meter: , it’s unimaginable ! When the distance L between two electrons is less than 2R, the two electrons overlap in space as shown in Fig-13, . Fig-13
Force on an electron while L < 2R
According Z.1 and Fig-13, electric field force between these two electrons is:
Assuming that ,then
When , , . According Z.6, a proton is similar to an electron, but tiny balls rotate anti-clockwise, and a proton has an additional outer layer. When two protons in an atomic nuclear is close enough that their distance is just 1.8 times of the radius of an electron, repulsive force between these two protons is zero, so, the strong interaction force between two protons in an atomic nuclear is not necessary. When , assuming that , then Therefore, curve of is shown as Fig-14.
Fig-14
Repulsive force changes to attractive force x = L / 2R
It’s similar to calculate gravitation between different kinds of electric charges, we calculate gravitation between two electrons following. As shown in Fig-7, distance between a certain point on surface of electron B and centerpoint of electron A is , then translational kinetic energy of Zpa colliding directly with electron B is:
Fig-15
Enhancement curve of translational kinetic energy of directly colliding Z-particle
There are
Zpa collide directly with electron B per unit volume, velocity of Zpa is , presure on surface of electon B caused by direct collision of Zpa is: is a scale factor and According Z.1 and Fig-15, gravitation between two electrons is:
So, gravitation between two stationary electrons is inversely proportional to square of distance between these two electrons, and gravitation is always attractive force. Gravitation is differential force. Ratio of electric field force to gravitation between two stationary electric charges is:
Because that electric field force is far greater than gravitation between two electrons, so there is very small percentage of Zpa collides directly with electron B in Fig-7. From the production of gravitation, we can correct the misconception that "there must be gravitation between objects with mass", for example, Z-particles have mass, but no matter how large the number of Z-particles is, there is no gravitation between them.
Z.14
Both electric field force and gravitation satisfy superposition principle. It's hard to understand superposition principle of Coulomb force in traditional electromagnetics, if there are N+1 electrons on a line, electron A is on the left end and others N electrons on the right end, no matter how many the N is, repulsive force from electron A to every electron is unchangeable, is electron A green giant? The superposition principle of electric field force is easy to understand by Z-particle model, it's similar to gas pressure. Magnetic field and Lorentz force Z.15
If an electron rotates in an environment that macroscopic velocity of Z-particle is not zero, rotation direction of a proton in this environment is opposite to that of the electron. The environment state of Z-particle, which causes an electric charge to rotate around its axis, is called magnetic field.
Z.16
There are two electrons, A is center of electron 1 and B is center of stationary electron 2. During the process that external force F pushes electron 1 from point A moving to point C, electron 2 will rotate around its axis, the direction of angular momentum of electron 2 rotation is , it is the direction of magnetic induction, and the rotational kinetic energy of electron 2 rotation is the magnetic field energy. If electron 2 is replaced by proton 2, rotation direction of proton 2 is opposite to that of electron 2. Fig-16
A moving electron makes others electron rotating
As shown in Fig-16, when both electron 1 and electron 2 are stationary, resultant force on electron 2 passes through the center of electron 2 along direction of AB. Without considering electron 2, during the movement of electron 1 from point A to point C, Z-particles are symmetrically distributed around the line AC, so the direction of the resultant force on electron 2 is still on plane ABC. However, since the macroscopic right-shift motion of electron 1, translational kinetic energy distribution of Z-particles around electron 1 is no longer spherically symmetrical, so the resultant force on electron 2 no longer passes through its center, which will generate torque in direction of . When voltage is applied to both ends of an inductor, macroscopic translation velocity of electrons accelerates from 0, macroscopic translation of any electron causes other electric charges to rotate around their axes. The energy input from outside is the sum of energy accelerating macroscopic translation of electrons and energy accelerating all electric charges rotation, the sum of rotational kinetic energy of all electric charges rotation in the inductor is magnetic field energy stored in the inductor, because of the energy of magnetic field, energy used to accelerate macroscopic translation of electrons decreases, so acceleration process of macroscopic translation of electrons becomes longer, current increases slowly. When current in the inductor is constant, energy of magnetic field stored in the inductor remains unchanged. When voltage at both ends of the inductor is removed, rotational kinetic energy of electric charges rotation is transformed into translational kinetic energy of electron macroscopic translation, the energy of magnetic field stored in the inductor begins to be released, electrons continue to flow in original direction and current decreases slowly. It is hard to understand energy of magnetic field in traditional electromagnetics. Let's roughly estimate the angular velocity of electrons rotating around their own axes in magnetic field.
A cylinder with a diameter of 15 mm and a length of 40 mm was made from iron. The density of iron is 7.87 grams per cubic centimeter. Therefore, the mass of the cylinder can be calculated to be 56 grams, which is about 1 mole. With this cylinder as the magnetic core, an inductor is evenly wound using copper enameled wire with a diameter of 0.2mm. When the inductance is L=50 mH, the quality of the enameled wire used is far less than 56 grams. The inductor is connected to a constant current source of 100mA. When the current is constant, the magnetic field energy stored by the inductor is as follows: An iron atom has 26 protons and 26 electrons and 30 neutrons. The 30 neutrons are approximated to 30 protons plus 30 electrons. Therefore, an iron atom contains approximately charges, and the total charge of 1 mole of iron is:
Assuming that an electron is a sphere of uniform mass, with radius R and mass , its moment of inertia is:
Assuming the angular velocity of electrons rotation is ω, then the macroscopic rotational kinetic energy of each charge is:
Because the quality of enameled wire is very small, the magnetic field energy stored in the inductor can be approximated to the rotational kinetic energy of all charges on the magnetic core,
Assuming that meter, then
It shows that electrons rotate at very high speed in magnetic field.
Z.17
Assuming that I is current of an infinitely long straight wire and L is distance from centerpoint of electron A to the wire, electron A will rotate around its axis and angular velocity of electron A would be , is a scale factor. Z.18
Z-particle in space is similar to ideal fluid, is density of Z-particle in space, is the relative macroscopic velocity of motion between Z-particle and electric charge, is the extra pressure on electric charge because of relative macroscopic motion between Z-particle and electric charge, then is a constant.
Fig-17
A stream tube of Z-particle
As shown in Fig-17, which is a stream tube of Z-particle, in interval of , A moved to B and C moved to D. The work that Z-particle did is :
Increased macroscopic translational kinetic energy of Z-particle is: Since, . So
This is special case of Bernoulli equation of ideal fluid, high relative speed leads to low pressure.
Z.19
An electron near a long straight wire passing current will rotate around its own axis, if the rotating electron has a translation velocity opposite to direction of the current, the electron will be pushed toward the wire because of Magnus effect, propulsive force is proportional to translation velocity and rotation angular velocity of the electron, the direction of is perpendicular to translation velocity and angular momentum of the electron, the force is Lorentz force, which is the essence of magnetic force. Place a long straight wire horizontally, under the wire there is an electron A moving horizontally to the right at a speed of V, if the center of electron A is used as a stationary reference, Z-particles close to spherical surface of the electron move to the left at the speed of V, as shown by dashed line in Fig-18. Assuming that current of the long straight wire flows to the left, according to Z.16, electron A will rotate anti-clockwise at an angular velocity of . According to Z.10, after the rotating electron swallows up a Z-particle it collides with, a new Zp-particle which has an initial velocity of is released at the collision point on surface of electron A, is radius of rotation, so, relative macroscopic velocity of motion of Z-particle is different on upper half surface and lower half surface of electron A, relative macroscopic velocity of motion of Z-particle on upper half surface of the electron is , and relative macroscopic velocity of motion of Z-particle on lower half surface of the electron is , and are scale factors. When relative macroscopic velocity of motion of Z-particle is , the pressure on surface of electron A is , when relative macroscopic velocity of motion Z-particle is , the pressure on surface of electron A is , according to Z.18: , is a scale factor. Fig-18
Relative velocity of motion of Z-particle on surface of an electron
In order to facilitate drawing, the direction of angular momentum of electron rotation is drawn upward, as shown in Fig-19. Fig- 19
Magnus effect on an electron
Shadowed surface area is:
Component force perpendicular to paper plane inward is:
The force is Lorentz force in traditional electromagnetics, in fluid mechanics, it is the result of Magnus effect, banana ball shot by football players is the same result. Combine with Z.17, the force on an electron near an infinitely long straight wire is:
According to traditional electromagnetics, Lorentz force on an electron near an infinitely long straight wire is: So , Since and , assuming that meter, then Prophecy
The essence of Lorentz force is Magnus effect which electrons rotate around their axes in Z-particle environment, and the rotating electrons are inertial, this inertia has an effect on the Lorentz deflection of electrons, maybe it is possible to measure this effect by a cathode-ray tube cleverly designed. Some electroneutral particles or objects rotating at high speeds, if their direction of translation velocity is not parallel to direction of angular momentum, they will also deflect in vacuum without magnetic field because of Magnus effect. The Z-particle model is helpful for explaining phenomena that seem to be "abnormal" in physics, such as the Michelson-Morley experiment and the transformation of mass and energy, and maybe it is helpful for calculating the gravitational constant.
References1.