Superconductivity with Weber's Electrodynamics: the London
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Experimental Confirmation of Weber Electrodynamics Against Maxwell Electrodynamics
Experimental confirmation of Weber electrodynamics against Maxwell electrodynamics Steffen Kuhn¨ steff[email protected] April 25, 2019 This article examines by means of an easily reproducible experiment whether Maxwell electrodynamics or the almost forgotten Weber electro- dynamics of Carl Friedrich Gauss and Wilhelm Weber is correct. For this purpose, it is shown that when charging a capacitor with two very flat and horizontally aligned plates a force on a permanent magnet should arise be- tween the plates which differs in both theories diametrically in its direction. Subsequently, the measurement setup is described and, based on the mea- surement results, it is determined that Maxwell electrodynamics contradicts the experiment. The result of the experiment suggests that all aspects of modern physics should be subjected to a careful and critical review. Contents 1 Introduction2 2 Basics 3 2.1 The force between two uniformly moving point charges...........3 2.1.1 Weber force...............................3 2.1.2 Maxwell force..............................3 2.2 Forces between current elements.......................5 2.3 Magnetic forces in a wire gap.........................5 2.4 Solution of Maxwell's equations for a wire stub............... 10 3 Experiment 13 3.1 Experimental setup............................... 13 3.2 Measurement results and evaluation..................... 15 1 4 Summary and conclusion 17 1 Introduction Maxwell's equations have been very successful in describing electromagnetic waves for more than one hundred years. Their rise to the sole theory of electromagnetism be- gins with an article by James Clerk Maxwell in 1865 [Maxwell, 1865]. In this article he shows that from the complete set of Maxwell's equations, including the displacement current, a wave equation can be derived in which electromagnetic disturbances of the field propagate at the speed of light. -
Technical Note 1
Gravito-Electromagnetic Properties of Superconductors - A Brief Review - C. J. de Matos1, M. Tajmar2 June 20th, 2003 Starting from the generalised London equations, which include a gravitomagnetic term, the gravitational and the electromagnetic properties of superconductors are derived. A phenomenological synthesis of those properties is proposed. Table of Contents I) Introduction................................................................................................2 II) Generalised London equations .................................................................2 II-a) Second generalised London equation .............................................3 II-b) First generalised London equation..................................................3 III) Gravito-electromagnetic properties of SCs .............................................3 III-a) Generalised Meissner effect ..........................................................4 III-b) SCs do not shield gravitomagnetic and / or gravitational fields....5 III-c) Generalised quantum fluxoid condition ........................................6 III-d) Supercurrents generated by GM fields..........................................7 III-e) Generalised London moment.........................................................8 III-f) Electric conductivity of SCs in a gravitational field......................9 III-g) Electrical fields in accelerated SCs .............................................13 IV) Conclusion.............................................................................................14 -
New Magnetosphere for the Earth in Future
WSEAS TRANSACTIONS on ENVIRONMENT and DEVELOPMENT Tara Ahmadi New Magnetosphere for the Earth In Future TARA AHMADI Student At Smart High School Kurdistan, Sanandaj, Ghazaly Street No3 IRAN [email protected] Abstract:- All of us know the earth magnetic field come to be less and this problem can be a serious problem in future but now we find other problems that can destroy our planet life or in minimum state can damage it such as FTE theory , solar activities , reversing magnetic poles, increasing speed of reversing that last reverse, reducing magnetic strength ,finding leaks in magnetosphere ,etc. some of these reasons will be factors for increasing the solar energy that hit to the Earth and perhaps changing in our life and conditions of the Earth . In this paper , I try to show a way to against to these problems and reduce their damages to the Earth perhaps The Earth will repair himself but this repair need many time that humans could not be wait. In the past time magnetic field was reversed but now we are against to the other problems that can increase the influence of reversing magnetic field for the Earth and all these events can be a separated problem for us, these problem may be can not destroyed humans life but can be cause of several problems that occur for our healthy and our technology in space. This way is building a system that produce a new magne tic field that will be in one way with old magnetic field this system will construe by superconductors and a metal that is not dipole. -
The Meaning of the Constant C in Weber's Electrodynamics
Proe. Int. conf. "Galileo Back in Italy - II" (Soc. Ed. Androme-:ia, Bologna, 2000), pp. 23-36, R. Monti (editor) The Meaning of the Constant c in Weber's Electrodynamics A. K. T. Assis' Instituto de Fisica 'Gleb Wat.aghin' Universidade Estadual de Campinas - Unicamp 13083-970 Campinas, Sao Paulo, Brasil Abstract In this work it is analysed three basic electromagnetic systems of units utilized during last century by Ampere, Gauss, Weber, Maxwell and all the others: The electrostatic, electrodynamic and electromagnetic ones. It is presented how the basic equations of electromagnetism are written in these systems (and also in the present day international system of units MKSA). Then it is shown how the constant c was introduced in physics by Weber's force. It is shown that it has the unit of velocity and is the ratio of the electromagnetic and electrostatic Wlits of charge. Weber and Kohlrausch '5 experiment to determine c is presented, emphasizing that they were 'the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchhoff and Weber obtained independently of one another, both working in the framev.-ork of \Veber's electrodynamics, the fact that an electromagnetic signal (of current or potential) propagate at light velocity along a thin wire of negligible resistivity. Key Words: Electromagnetic units, light velocity, wave equation. PACS: O1.55.+b (General physics), 01.65.+g (History of science), 41.20.·q (Electric, magnetic, and electromagnetic fields) ·E-mail: assisOiCLunicamp.br, homepage: www.lCi.unicamp.brrassis AA. VV•. -
Electrodynamics of Superconductors Has to According to Maxwell’S Equations, Just As the Four-Vectors J a Be Describable by Relativistically Covariant Equations
Electrodynamics of superconductors J. E. Hirsch Department of Physics, University of California, San Diego La Jolla, CA 92093-0319 (Dated: December 30, 2003) An alternate set of equations to describe the electrodynamics of superconductors at a macroscopic level is proposed. These equations resemble equations originally proposed by the London brothers but later discarded by them. Unlike the conventional London equations the alternate equations are relativistically covariant, and they can be understood as arising from the ’rigidity’ of the superfluid wave function in a relativistically covariant microscopic theory. They predict that an internal ’spontaneous’ electric field exists in superconductors, and that externally applied electric fields, both longitudinal and transverse, are screened over a London penetration length, as magnetic fields are. The associated longitudinal dielectric function predicts a much steeper plasmon dispersion relation than the conventional theory, and a blue shift of the minimum plasmon frequency for small samples. It is argued that the conventional London equations lead to difficulties that are removed in the present theory, and that the proposed equations do not contradict any known experimental facts. Experimental tests are discussed. PACS numbers: I. INTRODUCTION these equations are not correct, and propose an alternate set of equations. It has been generally accepted that the electrodynam- There is ample experimental evidence in favor of Eq. ics of superconductors in the ’London limit’ (where the (1b), which leads to the Meissner effect. That equation response to electric and magnetic fields is local) is de- is in fact preserved in our alternative theory. However, scribed by the London equations[1, 2]. The first London we argue that there is no experimental evidence for Eq. -
Arxiv:0807.1883V2 [Cond-Mat.Soft] 29 Dec 2008 Asnmes 14.M 36.A 60.B 45.70.Mg 46.05.+B, 83.60.La, 81.40.Lm, Numbers: PACS Model
Granular Solid Hydrodynamics Yimin Jiang1, 2 and Mario Liu1 1Theoretische Physik, Universit¨at T¨ubingen,72076 T¨ubingen, Germany 2Central South University, Changsha 410083, China (Dated: October 27, 2018) Abstract Granular elasticity, an elasticity theory useful for calculating static stress distribution in gran- ular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived based on the hypothesis that granular medium turns transiently elastic when deformed. This theory includes both the true and the granular tempera- tures, and employs a free energy expression that encapsulates a full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. For the special case of stationary granular temperatures, the derived hydrodynamic theory reduces to hypoplasticity, a state-of-the-art engineering model. PACS numbers: 81.40.Lm, 83.60.La, 46.05.+b, 45.70.Mg arXiv:0807.1883v2 [cond-mat.soft] 29 Dec 2008 1 Contents I. Introduction 3 II. Sand – a Transiently Elastic Medium 8 III. Jamming and Granular Equilibria 10 A. Liquid Equilibrium 10 B. Solid Equilibrium 11 C. Granular Equilibria 12 IV. Granular Temperature Tg 13 A. The Equilibrium Condition for Tg 13 B. The Equation of Motion for sg 14 C. Two Fluctuation-Dissipation Theorems 16 V. Elastic and Plastic Strain 17 VI. The Granular Free Energy 18 A. The Elastic Energy 20 B. Density Dependence of 22 B C. Higher-Order Strain Terms 23 D. Pressure Contribution From Agitated Grains 25 E. The Edwards Entropy 27 VII. Granular Hydrodynamic Theory 28 A. -
Weber's Electrodynamics and the Hall Effect
Weber’s Electrodynamics and the Hall Effect Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (June 5, 2020) 1Problem In 1846, Weber used a model of electric current as moving electric charge (of both signs) to give an instantaneous, action-at-a-distance, “microscopic” force law, from which Amp`ere’s force law between current-carrying circuits could be deduced.1 In Gaussian units, the force on electric charge e due to moving charge e is, according to Weber, 2 ee 2 ∂r r ∂2r Fe,Web er = − 1 − + ˆr, (1) r2 c2 ∂t c2 ∂t2 where r = re −re,andc is the speed of light in vacuum. Following Amp`ere, Weber supposed that the force between two moving charges (current elements) is along their line of centers, and obeys Newton’s third law (of action and reaction). This contrasts with the Lorentz force law, which does not obey Newton’s third law in 2 general, ve e × , Fe,Lorentz = Ee + c Be (2) 3 where the fields Ee and Be are given by the forms of Li´enard and Wiechert. Until the late 1870’s the only experiments possible with electric currents were those in which the currents flowed in complete circuits (as studied by Amp`ere). The first step to- wards a larger context of electric currents was made by Rowland [52, 65] (1876, working in Helmholtz’ lab in Berlin), who showed that a rotating, charged disk produces magnetic effects. More importantly, Rowland’s student Hall (1878) [55] showed that an electric con- ductor in a magnetic field B perpendicular to the current I develops an electric potential 1References to original works are given in the historical Appendix below. -
The London Equations Aria Yom Abstract: the London Equations Were the First Successful Attempt at Characterizing the Electrodynamic Behavior of Superconductors
The London Equations Aria Yom Abstract: The London Equations were the first successful attempt at characterizing the electrodynamic behavior of superconductors. In this paper we review the motivation, derivation, and modification of the London equations since 1935. We also mention further developments by Pippard and others. The shaping influences of experiments on theory are investigated. Introduction: Following the discovery of superconductivity in supercooled mercury by Heike Onnes in 1911, and its subsequent discovery in various other metals, the early pioneers of condensed matter physics were faced with a mystery which continues to be unraveled today. Early experiments showed that below a critical temperature, a conventional conductor could abruptly transition into a superconducting state, wherein currents seemed to flow without resistance. This motivated a simple model of a superconductor as one in which charges were influenced only by the Lorentz force from an external field, and not by any dissipative interactions. This would lead to the following equation: 푚 푑퐽 = 퐸 (1) 푛푒2 푑푡 Where m, e, and n are the mass, charge, and density of the charge carriers, commonly taken to be electrons at the time this equation was being considered. In the following we combine these variables into a new constant both for convenience and because the mass, charge, and density of the charge carriers are often subtle concepts. 푚 Λ = 푛푒2 This equation, however, seems to imply that the crystal lattice which supports superconductivity is somehow invisible to the superconducting charges themselves. Further, to suggest that the charges flow without friction implies, as the Londons put it, “a premature theory.” Instead, the Londons desired a theory more in line with what Gorter and Casimir had conceived [3], whereby a persistent current is spontaneously generated to minimize the free energy of the system. -
Some Analytical Solutions to Problems Using London Equations
Module 3 : Superconductivity phenomenon Lecture 2 : Solution of London equations and free energy calculations Solution of London Equations for sample cases Flat slab in a magnetic field Consider a flat superconducting slab of thickness in a magnetic field parallel to the slab. The boundary condition is that field match at . Subject to this condition, the solution to the London equation , where is the microscopic value of the flux density, is easily determined to be a superposition of two exponentials. The result can be written as (13) Clearly, the minimum value of the flux density is attained at the mid-plane of the slab where it has a value . The field variation inside a superconducting slab is shown. Averaging this internal field over the sample thickness one gets (14) Let us consider the limit . This leads to deep inside the superconductor. In the other limit, i.e., , we expand . Therefore, approaches . Since , we get (15) As a consequence, magnetisation measurements can be made on thin films of known thicknesses and the penetration depth can be estimated from such measurements. Since the magnetisation is reduced below its Meissner value, the effective critical field for a thin sample is greater than that for bulk. The difference in the free energy between the normal state and the superconducting state is (16) For the case of complete flux expulsion, the above difference in free energies is (17) This energy, which stabilises the superconducting state is called the condensation energy and is called the thermodynamic critical field. For a thin film sample (with a field applied parallel to the plane) we get, (18) In terms of the bulk thermodynamic critical field (19) Critical current of a wire Consider a long superconducting wire having a circular cross-section of radius . -
Unipolar Induction and Weber's Electrodynamics
UNIPOLAR INDUCTION AND WEBER'S ELECTRODYNAMICS Andre K T. Assis,1,2 and Daria S. Thoberl lJnstituto de Fisica 'Gleb Wataghin', Universidade Estadual de Campinas, Unicamp, 13083-970, Campinas, Sao Paulo, Brasil Interneis: [email protected], and [email protected] 2Also Collaborating Professor at the Department of Applied Mathematics, HI/IECe, State University of Campinas, 13083-970 Campinas-SP, Brazil INTRODUCTION Unipolar induction is the generation of current on a conductor for the case 1Il which the conductor and the magnet are in relative rotatory motion. A typical case of unipolar induction is shown in figure 1. ¢ I _galvanometer [--@- and circuit A copper B disk _cylindrical NI permanent I magnet I SI Iaxis Figure 1. Apparatus used to investigate unipolar induction. The sliding contacts in A and B connect the galvanometer to the copper disk. Copper disk and magnet are free to rotate. FronJiers of FundamenJa[ Physics, Edited by M. Barone and F. Selleri, Plenum Press, New York, 1994 409 Since Fara.day's experimcnts L of 18:12 on electromagnetic induction on rotating systems there are intense debates concern ing the loration of the scat of the electromotive force (cmfJ 1 . In this work whenever we speak of "rotation" it should be understood "rotation relative to the earth or laboratory." Let us see what happens in the laboratory. \Vhen we rotate only t.he disk an emf is produced on the galvanometer-disk circuit (the magnet is fixed in the laboratory), as wee can see on the galvanometer. When we rotate only the magnet (the disk is fixed in the laboratory) no current flows by the galvanometer. -
Revolutionary Propulsion Research at Tu Dresden
67 REVOLUTIONARY PROPULSION RESEARCH AT TU DRESDEN M. Tajmar Institute of Aerospace Engineering, Technische Universit¨at Dresden, 01062 Dresden, Germany Since 2012, a dedicated breakthrough propulsion physics group was founded at the Institute of Aerospace Engineering at TU Dresden to investigate revolutionary propulsion. Most of these schemes that have been proposed rely on modifying the inertial mass, which in turn could lead to a new propellantless propulsion method. Here, we summarize our recent e↵orts targeting four areas which may provide such a mass modification/propellantless propulsion option: Asymmetric charges, Weber electrodynamics, Mach’s principle, and asymmetric cavities. The present status is outlined as well as next steps that are necessary to further advance each area. 1. INTRODUCTION Present-day propulsion enables robotic exploration of our solar system and manned missions limited to the Earth-Moon distance. With political will and enough resources, there is no doubt that we can develop propulsion technologies that will enable the manned exploration of our solar system. Unfortunately, present physical limitations and available natural resources do in fact limit human ex- ploration to just that scale. Interstellar travel, even to the next star system Alpha Centauri, is some 4.3 light-years away which is presently inaccessible – on the scale of a human lifetime. For example, one of the fastest manmade objects ever made is the Voyager 1 spacecraft that is presently traveling at a velocity of 0.006% of the speed of light [1]. It will take some 75,000 years for the spacecraft to reach Alpha Centauri. Although not physically impossible, all interstellar propulsion options are rather mathematical exercises than concepts that could be put into reality in a straightforward manner. -
Non-Local Electrodynamics of Superconducting Wires: Implications for Flux Noise and Inductance
Non-Local Electrodynamics of Superconducting Wires: Implications for Flux Noise and Inductance by Pramodh Viduranga Senarath Yapa Arachchige B.Sc., Carleton University, 2015 A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE in the Department of Physics and Astronomy c Pramodh Viduranga Senarath Yapa Arachchige, 2017 University of Victoria All rights reserved. This thesis may not be reproduced in whole or in part, by photocopying or other means, without the permission of the author. ii Non-Local Electrodynamics of Superconducting Wires: Implications for Flux Noise and Inductance by Pramodh Viduranga Senarath Yapa Arachchige B.Sc., Carleton University, 2015 Supervisory Committee Dr. Rog´eriode Sousa, Supervisor (Department of Physics and Astronomy) Dr. Reuven Gordon, Outside Member (Department of Electrical and Computer Engineering) iii Supervisory Committee Dr. Rog´eriode Sousa, Supervisor (Department of Physics and Astronomy) Dr. Reuven Gordon, Outside Member (Department of Electrical and Computer Engineering) ABSTRACT The simplest model for superconductor electrodynamics are the London equations, which treats the impact of electromagnetic fields on the current density as a localized phenomenon. However, the charge carriers of superconductivity are quantum me- chanical objects, and their wavefunctions are delocalized within the superconductor, leading to non-local effects. The Pippard equation is the generalization of London electrodynamics which incorporates this intrinsic non-locality through the introduc- tion of a new superconducting characteristic length, ξ0, called the Pippard coherence length. When building nano-scale superconducting devices, the inclusion of the coher- ence length into electrodynamics calculations becomes paramount. In this thesis, we provide numerical calculations of various electrodynamic quantities of interest in the non-local regime, and discuss their implications for building superconducting devices.