The Magnetic Moment of Elementary Particles Is Studied by Space Vector and Space Curvature

Total Page:16

File Type:pdf, Size:1020Kb

The Magnetic Moment of Elementary Particles Is Studied by Space Vector and Space Curvature Vol. 14(13), pp. 144-151, September, 2019 DOI: 10.5897/IJPS2019.4838 Article Number: E06CD3461899 ISSN: 1992-1950 Copyright ©2019 International Journal of Physical Author(s) retain the copyright of this article http://www.academicjournals.org/IJPS Sciences Review The magnetic moment of elementary particles is studied by space vector and space curvature Haitao Gao Department of chemical engineering North Minzu University Yinchuan, China Received 1 August, 2019; Accepted 28 August, 2019 This paper reaffirms the basic agreement of the material space theory: (1) Space is a physical existence; (2) "Force" is the action to space, and "force" is equal to the reciprocal value of "time"; in the absence of special description, "force" is the reciprocal of time; (3) There is a steady velocity field in three-dimensional space, whose intensity is the speed of light C; (4) Mass is a property of space produced by force acting on space, there are one-dimensional to four-dimensional masses in the universe, which correspond to velocities, light, electricity and gravitational masses; (5) The "causality principle" of physical changes; (6) The "simplicity principle" of physical changes; (7) The micro world and the macro world follow the same legal system. In this paper, magnetic field and electric field are defined respectively from space vector and space curvature. Studied the properties of magnetic and electric fields. This paper studies the properties of magnetic and electric fields, and in the field of micro electromagnetic interaction are described. Based on the basic principle of the material space theory, this paper proposes a method to calculate the spin magnetic moment of electrons and protons by using the magnetic field strength, and calculates the spin magnetic moment of protons and electrons under specific parameters. The calculated spin magnetic moment of the proton is 4.04035412*10-26J/T, it is close to the reported value of 1.41049964*10-26J/T, the spin magnetic moment of electrons is 6.69044591*10-27 J/T, which is far from the reference value of 9.28674762*10-24J/T, However, if the radius of the electron charge is set as 1.553794368*10-15m, the spin magnetic moment of the electron will be consistent with the reported value in the literature. The research results show that when the magnetic moment of elementary particles is known, the spatial structure of the charge of elementary particles can be calculated by using the method in this paper. This also provides an experimental method to verify the correctness of the proposed method. Key words: Space vector, space curvature, magnetic moment, spin, electron, proton. INTRODUCTION Magnetism is a widespread natural phenomenon, magnetism of matter results from the magnetism of magnetism is widely used in our work and life. We know elementary particles, in scientific research, magnetism is that all substances, have magnetic, we now know that the a physical quantity that can be precisely measured. E-mail: [email protected]. Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Gao 145 Predecessors have made fruitful achievements in the theory of the basic agreement: study of magnetism, and 15 people have won the Nobel Prize in physics for studying the magnetic properties of (1) Space is a physical existence; matter. (2) "Force" is the action to space, and "force" is equal to In the study of magnetism, a magnetic physical quantity the reciprocal value of "time"; in the absence of special that can be directly measured is the magnetic moment, description, "force" is the reciprocal of time; as for the measurement of magnetic moment of (3) There is a steady velocity field in three-dimensional elementary particles (Odom et al., 2006), Otto Stem first space, whose intensity is the speed of light C. used molecular beam method to observe the magnetic (4) Mass is a property of space produced by force acting moment of protons (Taub and Kusch, 1978) and on space, There are one-dimensional to four-dimensional achieved success. Some research results of proton masses in the universe, which correspond to velocities, magnetic moment have been reported in Shirley and light, electricity and gravitational masses. Lederer (1978); Sanders and Turberfield (1963) and (5) The "causality principle" of physical changes. Ulmer et al. (2014), Isidor I. Rabi established a new (6) The "simplicity principle" of physical changes. method for measuring nuclear magnetic moment and (7) The micro world and the macro world follow the same atomic magnetic moment by using the improved legal system. molecular beam - magnetic resonance method (John, 2005; Isidor and Otto, 1944), which laid a foundation for the establishment of more accurate condensed NMR The electromagnetic interaction in the microscopic methods in the future. Building on the work of Willis, field is expressed through the properties of space Kusch and others, Polykarp Kusch and his collaborators vectors used improved magnetic resonance technology to precisely measure the magnetic moment of an electron, Description of electric charge in material space winning the 1955 Nobel Prize in physics. Measurement theory method of electronic magnetic moment is magnetic Material space theory defines three-dimensional mass as resonance method, Polykarp Kusch and his collaborators electric charge, and its space description and mass first completed the accurate measurement of the electron expression are as follows: magnetic moment. The current accurate measurement is: g/2=1.001 159 652 180 73 (28) (Hanneke et al., 2008, In the material space theory, three-dimensional mass is 2009). Because the measured result is different from the defined as electric quantity. In the material space theory, predicted value of quantum mechanics, it is called three-dimensional mass is the space field of cylindrical anomalous magnetic moment. Isidor I. Rabi improved spiral structure, whose field equation structure can be molecular beam - magnetic resonance (NMR) method is described as: used to establish the method of measuring nuclear magnetic moment. In the paper published by Haitao (2019) the forms of electromagnetic interaction in the micro field from different perspectives were discussed. One is to define (1) the magnetic field strength and electric field strength of electric charge under the framework of the material space theory (HaiTao, 2018) through the property of space vector, and obtain the expression of electromagnetic (2) interaction force. The other is based on the principle of differential geometry (Spivak, 1979). By using the The expression of three-dimensional mass is: description of the relationship between curved space and force by general relativity (Carmeli, 1982), the magnetic field strength and electric field strength of charge are (3) defined by the curvature and winding rate of space. The two definitions are consistent in terms of magnetic field Magnetic field with electric charge strength and magnetic field interaction, but differ by one inverse of the time factor in terms of electric field strength Add the space vectors of electric quantity, and we get a and electric field interaction. In this paper, the author will new vector r, which can be expressed as follows: use the above two definitions to discuss the forms of electromagnetic interaction in the microscopic field by comparing the calculated magnetic moment of electrons (4) and protons with the measured results. For the first time to understand the readers convenient reading of the According to the parallelogram rule of vector addition and material space theory, we restate the material space parametric equations of the vector r is a circle equation, 146 Int. J. Phys. Sci. and the sagittal curve represents a circle. According to (8) the relationship between the sagittal curve is drawn in the opposite direction (counterclockwise and clockwise). We define a function φ as a potential function of the When the two space vectors are added, they are electric field E. So what we are talking about here is in multiplied by the velocity vector. The multiplication the microscopic domain, the properties of a three method of the vector is cross product. We get a new dimensional mass entering three dimensional space, and vector: obviously, this property is generated in the form of a vector field, Therefore, it can be considered that after (5) entering three-dimensional space, three-dimensional mass will have intrinsic properties of magnetic field The vector B and C & r conform to the right-handed spiral intensity and electric field intensity, and the properties of relationship, and are in the same direction as the tangent magnetic field intensity and electric field intensity are line of the sagittal curve of the space vector r. We define determined by the spatial structure of three-dimensional vector B as the magnetic vector of a three-dimensional mass and combined forces. mass, and the intensity of the field is the intensity of the magnetic field. The unit of magnetic field intensity is: m2/s. Since the vector r is a variable vector whose Single three-dimensional mass direction extends to the rotation of the circle with radius r, the magnetic field intensity vector is also a variable vector For a single three-dimensional mass, its magnetic field whose direction extends to the tangential rotation of the intensity and electric field intensity are calculated as circle with radius r. follows: We can find that the vector field made up of magnetic field intensity is a vector field with curl. We integrate the Suppose: the spiral radius of the three-dimensional mass circle l of the vector B with radius r, and then ratio it to the is r, and can be obtained from Equation 21: circle area S. When the limit of the circle area is 0, the The magnetic field intensity is: curl of the vector B field can be obtained as: (9) (6) The curl of the magnetic field is: Electric field of electric quantity (10) After entering the three-dimensional space, the three- dimensional mass interacts with the inherent one- The electric field intensity is: dimensional mass field in the three-dimensional space.
Recommended publications
  • Basic Magnetic Measurement Methods
    Basic magnetic measurement methods Magnetic measurements in nanoelectronics 1. Vibrating sample magnetometry and related methods 2. Magnetooptical methods 3. Other methods Introduction Magnetization is a quantity of interest in many measurements involving spintronic materials ● Biot-Savart law (1820) (Jean-Baptiste Biot (1774-1862), Félix Savart (1791-1841)) Magnetic field (the proper name is magnetic flux density [1]*) of a current carrying piece of conductor is given by: μ 0 I dl̂ ×⃗r − − ⃗ 7 1 - vacuum permeability d B= μ 0=4 π10 Hm 4 π ∣⃗r∣3 ● The unit of the magnetic flux density, Tesla (1 T=1 Wb/m2), as a derive unit of Si must be based on some measurement (force, magnetic resonance) *the alternative name is magnetic induction Introduction Magnetization is a quantity of interest in many measurements involving spintronic materials ● Biot-Savart law (1820) (Jean-Baptiste Biot (1774-1862), Félix Savart (1791-1841)) Magnetic field (the proper name is magnetic flux density [1]*) of a current carrying piece of conductor is given by: μ 0 I dl̂ ×⃗r − − ⃗ 7 1 - vacuum permeability d B= μ 0=4 π10 Hm 4 π ∣⃗r∣3 ● The Physikalisch-Technische Bundesanstalt (German national metrology institute) maintains a unit Tesla in form of coils with coil constant k (ratio of the magnetic flux density to the coil current) determined based on NMR measurements graphics from: http://www.ptb.de/cms/fileadmin/internet/fachabteilungen/abteilung_2/2.5_halbleiterphysik_und_magnetismus/2.51/realization.pdf *the alternative name is magnetic induction Introduction It
    [Show full text]
  • The Magnetic Moment of a Bar Magnet and the Horizontal Component of the Earth’S Magnetic Field
    260 16-1 EXPERIMENT 16 THE MAGNETIC MOMENT OF A BAR MAGNET AND THE HORIZONTAL COMPONENT OF THE EARTH’S MAGNETIC FIELD I. THEORY The purpose of this experiment is to measure the magnetic moment μ of a bar magnet and the horizontal component BE of the earth's magnetic field. Since there are two unknown quantities, μ and BE, we need two independent equations containing the two unknowns. We will carry out two separate procedures: The first procedure will yield the ratio of the two unknowns; the second will yield the product. We will then solve the two equations simultaneously. The pole strength of a bar magnet may be determined by measuring the force F exerted on one pole of the magnet by an external magnetic field B0. The pole strength is then defined by p = F/B0 Note the similarity between this equation and q = F/E for electric charges. In Experiment 3 we learned that the magnitude of the magnetic field, B, due to a single magnetic pole varies as the inverse square of the distance from the pole. k′ p B = r 2 in which k' is defined to be 10-7 N/A2. Consider a bar magnet with poles a distance 2x apart. Consider also a point P, located a distance r from the center of the magnet, along a straight line which passes from the center of the magnet through the North pole. Assume that r is much larger than x. The resultant magnetic field Bm at P due to the magnet is the vector sum of a field BN directed away from the North pole, and a field BS directed toward the South pole.
    [Show full text]
  • PH585: Magnetic Dipoles and So Forth
    PH585: Magnetic dipoles and so forth 1 Magnetic Moments Magnetic moments ~µ are analogous to dipole moments ~p in electrostatics. There are two sorts of magnetic dipoles we will consider: a dipole consisting of two magnetic charges p separated by a distance d (a true dipole), and a current loop of area A (an approximate dipole). N p d -p I S Figure 1: (left) A magnetic dipole, consisting of two magnetic charges p separated by a distance d. The dipole moment is |~µ| = pd. (right) An approximate magnetic dipole, consisting of a loop with current I and area A. The dipole moment is |~µ| = IA. In the case of two separated magnetic charges, the dipole moment is trivially calculated by comparison with an electric dipole – substitute ~µ for ~p and p for q.i In the case of the current loop, a bit more work is required to find the moment. We will come to this shortly, for now we just quote the result ~µ=IA nˆ, where nˆ is a unit vector normal to the surface of the loop. 2 An Electrostatics Refresher In order to appreciate the magnetic dipole, we should remind ourselves first how one arrives at the field for an electric dipole. Recall Maxwell’s first equation (in the absence of polarization density): ρ ∇~ · E~ = (1) r0 If we assume that the fields are static, we can also write: ∂B~ ∇~ × E~ = − (2) ∂t This means, as you discovered in your last homework, that E~ can be written as the gradient of a scalar function ϕ, the electric potential: E~ = −∇~ ϕ (3) This lets us rewrite Eq.
    [Show full text]
  • Ph501 Electrodynamics Problem Set 8 Kirk T
    Princeton University Ph501 Electrodynamics Problem Set 8 Kirk T. McDonald (2001) [email protected] http://physics.princeton.edu/~mcdonald/examples/ Princeton University 2001 Ph501 Set 8, Problem 1 1 1. Wire with a Linearly Rising Current A neutral wire along the z-axis carries current I that varies with time t according to ⎧ ⎪ ⎨ 0(t ≤ 0), I t ( )=⎪ (1) ⎩ αt (t>0),αis a constant. Deduce the time-dependence of the electric and magnetic fields, E and B,observedat apoint(r, θ =0,z = 0) in a cylindrical coordinate system about the wire. Use your expressions to discuss the fields in the two limiting cases that ct r and ct = r + , where c is the speed of light and r. The related, but more intricate case of a solenoid with a linearly rising current is considered in http://physics.princeton.edu/~mcdonald/examples/solenoid.pdf Princeton University 2001 Ph501 Set 8, Problem 2 2 2. Harmonic Multipole Expansion A common alternative to the multipole expansion of electromagnetic radiation given in the Notes assumes from the beginning that the motion of the charges is oscillatory with angular frequency ω. However, we still use the essence of the Hertz method wherein the current density is related to the time derivative of a polarization:1 J = p˙ . (2) The radiation fields will be deduced from the retarded vector potential, 1 [J] d 1 [p˙ ] d , A = c r Vol = c r Vol (3) which is a solution of the (Lorenz gauge) wave equation 1 ∂2A 4π ∇2A − = − J. (4) c2 ∂t2 c Suppose that the Hertz polarization vector p has oscillatory time dependence, −iωt p(x,t)=pω(x)e .
    [Show full text]
  • Units in Electromagnetism (PDF)
    Units in electromagnetism Almost all textbooks on electricity and magnetism (including Griffiths’s book) use the same set of units | the so-called rationalized or Giorgi units. These have the advantage of common use. On the other hand there are all sorts of \0"s and \µ0"s to memorize. Could anyone think of a system that doesn't have all this junk to memorize? Yes, Carl Friedrich Gauss could. This problem describes the Gaussian system of units. [In working this problem, keep in mind the distinction between \dimensions" (like length, time, and charge) and \units" (like meters, seconds, and coulombs).] a. In the Gaussian system, the measure of charge is q q~ = p : 4π0 Write down Coulomb's law in the Gaussian system. Show that in this system, the dimensions ofq ~ are [length]3=2[mass]1=2[time]−1: There is no need, in this system, for a unit of charge like the coulomb, which is independent of the units of mass, length, and time. b. The electric field in the Gaussian system is given by F~ E~~ = : q~ How is this measure of electric field (E~~) related to the standard (Giorgi) field (E~ )? What are the dimensions of E~~? c. The magnetic field in the Gaussian system is given by r4π B~~ = B~ : µ0 What are the dimensions of B~~ and how do they compare to the dimensions of E~~? d. In the Giorgi system, the Lorentz force law is F~ = q(E~ + ~v × B~ ): p What is the Lorentz force law expressed in the Gaussian system? Recall that c = 1= 0µ0.
    [Show full text]
  • Magnetic Moment of a Spin, Its Equation of Motion, and Precession B1.1.6
    Magnetic Moment of a Spin, Its Equation of UNIT B1.1 Motion, and Precession OVERVIEW The ability to “see” protons using magnetic resonance imaging is predicated on the proton having a mass, a charge, and a nonzero spin. The spin of a particle is analogous to its intrinsic angular momentum. A simple way to explain angular momentum is that when an object rotates (e.g., an ice skater), that action generates an intrinsic angular momentum. If there were no friction in air or of the skates on the ice, the skater would spin forever. This intrinsic angular momentum is, in fact, a vector, not a scalar, and thus spin is also a vector. This intrinsic spin is always present. The direction of a spin vector is usually chosen by the right-hand rule. For example, if the ice skater is spinning from her right to left, then the spin vector is pointing up; the skater is rotating counterclockwise when viewed from the top. A key property determining the motion of a spin in a magnetic field is its magnetic moment. Once this is known, the motion of the magnetic moment and energy of the moment can be calculated. Actually, the spin of a particle with a charge and a mass leads to a magnetic moment. An intuitive way to understand the magnetic moment is to imagine a current loop lying in a plane (see Figure B1.1.1). If the loop has current I and an enclosed area A, then the magnetic moment is simply the product of the current and area (see Equation B1.1.8 in the Technical Discussion), with the direction n^ parallel to the normal direction of the plane.
    [Show full text]
  • Magnetic & Electric Dipole Moments
    Axion Academic Training CERN, 1 December 2005 Magnetic & Electric Dipole Moments. Yannis K. Semertzidis Brookhaven National Lab •Muon g-2 experiment d c •EDMs: What do they probe? q •Physics of Hadronic EDMs θ •Probing QCD directly (RHIC), & indirectly (Hadronic EDM) •Experimental Techniques dsr v r r = μr × B + d × E dt Building blocks of matter Force carriers Muons decay to an electron and two neutrinos with a lifetime of 2.2μs (at rest). dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Quantum Mechanical Fluctuations •The electron particle is surrounded by a cloud of virtual particles, a …soup of particles… •The muon, which is ~200 times heavier than the electron, is surrounded by a heavier soup of particles… dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt A circulating particle with r charge e and mass m: μr, L r • Angular momentum e, m L = mvr e r • Magnetic dipole μr = L moment 2m μ = IA dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt For particles with intrinsic angular momentum (spin S): e r μr = g S 2m The anomalous magnetic moment a: g − 2 a = 2 dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt In a magnetic field (B), there is a torque: r τr = μr × B Which causes the spin to precess in the horizontal plane: dsr r =×μr B dt r ds v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Definition of g-Factor magnetic moment g ≡ eh / 2mc angular momentum h From Dirac equation g-2=0 for point-like, spin ½ particles.
    [Show full text]
  • Induced Magnetic Dipole Moment Per Unit Volume [A/M]
    Electromagnetism II (spring term 2020) Lecture 7 Microscopic theory of magnetism E Goudzovski [email protected] http://epweb2.ph.bham.ac.uk/user/goudzovski/Y2-EM2 Previous lecture The electric displacement field is defined as Gauss’s law for the electric displacement field: or equivalently For linear, isotropic and homogeneous (e.g. most) dielectrics, Boundary conditions: and , leading to Energy density of the electric field: 1 This lecture Lecture 7: Microscopic theory of magnetism Magnetization and magnetic susceptibility Magnetic properties of atoms; the Bohr magneton Theory of diamagnetism Theory of paramagnetism 2 Types of magnetism In external magnetic field, materials acquire non-zero magnetization , i.e. induced magnetic dipole moment per unit volume [A/m]. For isotropic homogeneous materials, the magnetic susceptibility is defined as Magnetism is linked to the charged constituents in materials: 1) orbital angular momenta of electrons; 2) spin angular momenta of electrons; 3) spin angular momenta of nuclei (a much smaller contribution). Three main types of magnetic materials Diamagnetic: M is opposite to external B; small and negative. B Paramagnetic: M is parallel to external B; small and positive. B Ferromagnetic: very large and non-linear magnetization M. Permanent magnets are magnetized in absence of external B. 3 Magnetic properties of atoms (1) A fundamentally quantum effect: classical physics predicts absence of magnetization phenomena. Ze Bohr’s semiclassical model Angular momentum of the electron: e Magnetic dipole moment of a current loop (lecture 1) (T is the rotation period; S is the area; e>0 is the elementary charge) Gyromagnetic ratio of electron orbital motion: 4 Magnetic properties of atoms (2) Quantization of angular momentum: Quantization of the magnetic moment of electron orbital motion: Bohr magneton: Electron spin (intrinsic angular momentum): The associated magnetic moment is B, therefore the gyromagnetic ratio is twice larger than for orbital motion: e/m.
    [Show full text]
  • Equivalence of Current–Carrying Coils and Magnets; Magnetic Dipoles; - Law of Attraction and Repulsion, Definition of the Ampere
    GEOPHYSICS (08/430/0012) THE EARTH'S MAGNETIC FIELD OUTLINE Magnetism Magnetic forces: - equivalence of current–carrying coils and magnets; magnetic dipoles; - law of attraction and repulsion, definition of the ampere. Magnetic fields: - magnetic fields from electrical currents and magnets; magnetic induction B and lines of magnetic induction. The geomagnetic field The magnetic elements: (N, E, V) vector components; declination (azimuth) and inclination (dip). The external field: diurnal variations, ionospheric currents, magnetic storms, sunspot activity. The internal field: the dipole and non–dipole fields, secular variations, the geocentric axial dipole hypothesis, geomagnetic reversals, seabed magnetic anomalies, The dynamo model Reasons against an origin in the crust or mantle and reasons suggesting an origin in the fluid outer core. Magnetohydrodynamic dynamo models: motion and eddy currents in the fluid core, mechanical analogues. Background reading: Fowler §3.1 & 7.9.2, Lowrie §5.2 & 5.4 GEOPHYSICS (08/430/0012) MAGNETIC FORCES Magnetic forces are forces associated with the motion of electric charges, either as electric currents in conductors or, in the case of magnetic materials, as the orbital and spin motions of electrons in atoms. Although the concept of a magnetic pole is sometimes useful, it is diácult to relate precisely to observation; for example, all attempts to find a magnetic monopole have failed, and the model of permanent magnets as magnetic dipoles with north and south poles is not particularly accurate. Consequently moving charges are normally regarded as fundamental in magnetism. Basic observations 1. Permanent magnets A magnet attracts iron and steel, the attraction being most marked close to its ends.
    [Show full text]
  • Magnetism in Transition Metal Complexes
    Magnetism for Chemists I. Introduction to Magnetism II. Survey of Magnetic Behavior III. Van Vleck’s Equation III. Applications A. Complexed ions and SOC B. Inter-Atomic Magnetic “Exchange” Interactions © 2012, K.S. Suslick Magnetism Intro 1. Magnetic properties depend on # of unpaired e- and how they interact with one another. 2. Magnetic susceptibility measures ease of alignment of electron spins in an external magnetic field . 3. Magnetic response of e- to an external magnetic field ~ 1000 times that of even the most magnetic nuclei. 4. Best definition of a magnet: a solid in which more electrons point in one direction than in any other direction © 2012, K.S. Suslick 1 Uses of Magnetic Susceptibility 1. Determine # of unpaired e- 2. Magnitude of Spin-Orbit Coupling. 3. Thermal populations of low lying excited states (e.g., spin-crossover complexes). 4. Intra- and Inter- Molecular magnetic exchange interactions. © 2012, K.S. Suslick Response to a Magnetic Field • For a given Hexternal, the magnetic field in the material is B B = Magnetic Induction (tesla) inside the material current I • Magnetic susceptibility, (dimensionless) B > 0 measures the vacuum = 0 material response < 0 relative to a vacuum. H © 2012, K.S. Suslick 2 Magnetic field definitions B – magnetic induction Two quantities H – magnetic intensity describing a magnetic field (Système Internationale, SI) In vacuum: B = µ0H -7 -2 µ0 = 4π · 10 N A - the permeability of free space (the permeability constant) B = H (cgs: centimeter, gram, second) © 2012, K.S. Suslick Magnetism: Definitions The magnetic field inside a substance differs from the free- space value of the applied field: → → → H = H0 + ∆H inside sample applied field shielding/deshielding due to induced internal field Usually, this equation is rewritten as (physicists use B for H): → → → B = H0 + 4 π M magnetic induction magnetization (mag.
    [Show full text]
  • Classical Electromagnetic Interaction of a Point Charge and a Magnetic Dipole Moment Is a Poorly Understood Aspect of Classical Physics
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE CLASSICAL ELECTROMAGNETIC INTERACTION OFprovided A by CERN Document Server POINT CHARGE AND A MAGNETIC MOMENT:CONSIDERATIONS RELATED TO THE AHARONOV-BOHM PHASE SHIFT Timothy H. Boyer Department of Physics, City College of the City University of New York, New York, NY 10031 (July 5, 2001) Abstract A fundamentally new understanding of the classical electromagnetic inter- action of a point charge and a magnetic dipole moment through order v2=c2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov-Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not rela tivistic to order v2=c2, does reveal a connection between the electric field of the point charge and hidden momen- tum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1=c4 and hence is negligible in a 1=c2 analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamen- tally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric forcebackatthepointchargewhichi)isoforder1=c2, ii)depends upon the magnetic dipole moment, changing sign with the dipole moment, iii) is odd in the charge q of the passing charge, and i v) reverses sign for charges passing on opposite sides of the magnetic moment.
    [Show full text]
  • Lecture 14-15: Planetary Magnetospheres
    Lecture 14-15: Planetary magnetospheres o Today’s topics: o Planetary magnetic fields. o Interaction of solar wind with solar system objects. o Planetary magnetospheres. Venus in the solar wind o Click on “About Venus” at http://www.esa.int/SPECIALS/Venus_Express/ Planetary magnetism o Conducting fluid in motion generates magnetic field. o Earth’s liquid outer core is conducting fluid => free electrons are released from metals (Fe & Ni) by friction and heat. o Variations in the global magnetic field represent changes in fluid flow in the core. o Defined magnetic field implies a planet has: 1. A large, liquid core 2. A core rich in metals 3. A high rotation rate o These three properties are required for a planet to generate an intrinsic magnetosphere. Planetary magnetism o Earth: Satisfies all three. Earth is only Earth terrestrial planet with a strong B-field. o Moon: No B-field today. It has no core or it solidified and ceased convection. o Mars: No B-field today. Core solidified. o Venus: Molten layer, but has a slow, 243 day Mars rotation period => too slow to generate field. o Mercury: Rotation period 59 days, small B- field. Possibly due to large core, or magnetised crust, or loss of crust on impact. o Jupiter: Has large B-field, due to large liquid, metallic core, which is rotating quickly. Planetary magnetic fields o Gauss showed that the magnetic field of the Earth could be described by: ˆ ˆ B = −µ0∇V (rˆ ) = −µ ∇ˆ (V i + V e ) 0 where Vi is the magnetic scalar potential due to sources inside the Earth, and Ve is the scalar€ potential due to external sources.
    [Show full text]