GRAVITY MAGNETISM AND  LIGHT

The Role of Subnuclear and Subelectron Interactions

Ó 1998 Ralph Sansbury

 Send Comments to r9ns@verizon.net

 

Introduction                                                                         1

 

I  Magnetism and Electrodynamics

 

     Forces Between Currents and Charged Foils      7

     Ampere's Formula and Transverse Electrostatic Dipoles        9

     Orbital Systems Inside Electrons and Atomic Nuclei    14

     Kaufmann's Experiment                                                                 17

     Orbital Systems Inside Electrons and Atomic Nuclei (continued)     18

     Quarks                                27

     Fixing Bohr's Theory                     30

     Resistance and Magnetoresistance                                        34     

 

 

II  Measurements of the Speed of Light        

   Spaceprobe Communications    41  

   Bradley's Measurement 44

    Roemer and Halley Versus Cassini  51

    Fizeau Foucault and Michelson                                    57

    Interference Measurements  of the Speed of Light         63

    A Modern Version of Fizeau's Experiment          68

    Radiation and Induction                           72

      

 

III  The Magnetic Effects of Gravity                                          85

 

Appendix

   

    Bradley                      106

    Roemer                      120

    Halley                         124             

    Fizeau                                  131               

    Foucault on Fizeau                         133

    Michelson                  136

    Ferromagnetism, Diamagnetism and Paramagnetism                      139

   Graneau Effect                                                                                145

    Hall Effect                                                                                      147   

References                                                                          150

 

Diagrams and Illustrations  listed in index link,

http://mysite.verizon.net/r9ns/

 

 

 

 

 

                  

 

 

 

 

 

 


INTRODUCTION

 

   This book is about evidence for charge polarization inside electrons and atomic nuclei. Such polarization can  be shown to imply that the gravitational force between two objects is an electrostatic dipole force where the dipole lengths increase with their separation and similarly for the magnetic force between a pair of current carrying wires or magnetic elements. Also that the speed of light delay up to one second is associated with charge polarization inside the  electrons and atomic nuclei of the receiver.

   We will examine first the  implications of this theory for two of the most influential discoveries in the history of physics.  The first influential discovery was Roemer’s so called measurement of the speed of light (1676) and the second was  Kaufmann’s (1903) measurement of the apparent increase of the mass of beta electrons as their velocity increased. The experts of the times in these specific sorts of measurements, proposed alternative interpretations of these measurements.  But preference was given to the opinions of a larger number of scientists whose expertise lay elsewhere and we now accept their interpretations.

   Let's summarize briefly the two discoveries.  First, Roemer’s measurement of the speed of light required that light be a wave front or a group of moving particles. That is, Roemer's measurement required that reflected Sunlight, reflected from the surfaces of Jupiter's moons, traveled as a wave front or particle for about 40 minutes using Bradley's value (or 55 minutes using Roemer's value) until it reached the Earth. By which time an observer on the Earth would have moved with the Earth a substantial distance, sometimes from under clouds, to a location with an unclouded view of the night sky. Until Bradley(1728), the most knowledgeable astronomers at the time like Cassini, thought that Roemer’s results could equally well have been due to changes in the viewing position of the Earth relative to Jupiter.  Roemer's measurement did not require constant exposure of the light receiver to the light source during the emission of light. But nothing could block the reception of light at the expected time of arrival.

    In contrast, Fizeau’s measurement of light speed involved light focused to pass through successive gaps in a spinning toothed wheel to a mirror about 5 miles from the light source and then reflected back through the same or another gap or blocked by a tooth. The measurement was noting that the speed of the wheel when the light reflected back was minimal. Thus the light emitted by the mirror could have been blocked at the time of emission from the mirror as well as the expected time of arrival at the toothed wheel.  This measurement involved a delay of .25 milliseconds for the 5 mile distance  from the mirror to the receiver. Such was the delay implied by the speed of the wheel and the distance between teeth when the light received by the eye was minimal. The implication was that light was only received if there was exposure of the light receiver to the light source, the mirror, during the emission of light from the mirror as well as during the expected time of arrival at the receiver.

    It is interesting to note that Bradley’s observations could be explained  not in terms of  the light  delay from the star but  in terms of the light delay from  a secondary source, the refractive glass, the objective lens of the meter long telescope as the light crossed  a focal point to the eyepiece in front of the eye.  That is, the northerly star passed into view of the meter long telescope as the Earth was moving at 29km/s in the orbital plane beneath the star  at the time when the Earth’s rotational motion was at right angles to it orbital motion and to a  plane formed by a longitudinal line (meridian) of the Earth and the telescope. If we use the 3(108) m/s value for light speed then it  took about 3 nanoseconds for the light from the star image when it first appears over the edge of the objective lens and then at  successive points across the objective until it passes from view, to reach the eye. During this time in each case, the Earth had moved 10-5  meters south or north and so the same star in the two cases appeared to be coming not from directly overhead but slightly different positions in the sky. That is, the change in position implied a specific speed of light in the meter long tube relative to the known orbital speed of the Earth.

   Thus in the case of the Bradley and Fizeau measurements, the delays in the perception of light are nanoseconds or milliseconds and not 40 or 55 minutes in the case of Roemer’s measurement and the receiving eye was exposed to the refracted image at the time of secondary emission from this piece of glass regarded as the source.

    In any case, Maxwell’s theory of light transmission and delay in 1861 based on Kirchoff’s theory of  transmission in an aerial coaxial cable(1857), both a few years after Fizeau’s measurement in 1849, showed that Fizeau’s light speed measurement agreed roughly,  not only with the Bradley, Roemer values but also with the ratio of the magnetic force constant, :0 =4B(10 -7 ) to the electric force constant, g0 where 4Bg0 = 9(109). That is, the force between parallel wires a meter apart carrying currents of 1 Amp or 1 Coul/s is 10-7 Newtons and the force between two charged spheres each carrying one Coulomb of charge is 9(109)Newtons.  And that light speed was a fundamental constant relating magnetism to electricity, c2 = 4Bg0/4B(10 -7 ).

   It is necessary to point out here that communications with distant space probes, radar reflections off the moon or  distant planets, etc., do not confirm Roemer's measurement as they would seem to at first glance.

  Radar range measurements and the Global Positioning Satellite System involving one way delays of less than a second seem to be well substantiated but  radar signals bounced off the moon are faint and have an error range that makes a  one second one way  delay possible. More distant radar reflections eg Venus etc involve waiting a few seconds or numerous minutes for reflection or echo require that the data received must be statistically analysed from noise and is to some extent ‘chosen’ so as to confirm what is otherwise observed or which does not contradict what is otherwise observed. In most cases many different starting times are assumed when comparing the “received” voltage changes over time with the sent pattern of voltage changes over time until the most “similar” time series is determined.(In the summation or integration of sets of time series, the random noise cancels out and small repeated signals at regular intervals, add. But these finite patterns may have nothing to do with the topography of the radar target and have not been precisely compared with other independent photographs or less distant radar range measurements of the target.

   Communications between spacecraft and the Earth use streams of bits that are modulations of GHz sine waves and the further away the craft the more repetitions are needed of the same bit as part of an alphanumeric code, a sequence of which codes constitutes the information sent. So the time it takes for a bit to be a confirmed signal is greater than the speed of light delay.

   The location of a distant space craft is determined by several methods and a computer algorithm that in effect throws out any estimate that doesn’t agree with the rest, produces an estimate that is used to position the receiving antenna.  Hence the speed of light estimate, apparently used, need not be used to track the position of the craft.  Preference may be given to estimates from the mass and initial acceleration of the space craft and the gravitational influences of  the sun and nearby planets etc., from astronomical observations from the space craft of its surroundings, from the Doppler shift with respect to the Earth, etc., with previous estimates of positions to estimate subsequent positions according to basic Newtonian mechanics.

  The speed of light  implies a Doppler shift in frequency but a Doppler shift could also occur as a result of the change in relative velocity between source and receiver etc.. That is, a Doppler shift does not imply the speed of light even though an increased delay in the reception of light as the distance between source and receiver increases does imply the Doppler shift.

   A spacecraft moving at a very slightly decreasing or increasing velocity wrt a receiving station on Earth  will show a Doppler shift of (1+v/c)f where f is a frequency generated by the spacecraft and v is the positive or negative velocity.

   The speed of light assumption  implicitly involves the assumption that weak and strong sources from the same distance arrive with the same delay. The possibility for a greater delay for the weak source is somehow compensated by weaker delay making influences proportional to the weaker intensity of the source.

   As the weak or strong source moves further from the receiver, there is no change in the delay making influences proportional to the intrinsic intensity of the source but there is a change in distance that reduces the strength of the received signal. Hence as a spacecraft moves further radially from the Earth, its signal gets weaker and the delay is assumed to increase by Dr/c.

   But suppose that as ‘r’ increases beyond a certain value, eg 16,500 miles or .09 seconds- where the geostationary satellites are, the delay in the arrival of a signal increases somewhat less than r/c and that beyond 186,282 miles the delay does not continue to increase. Could there still be a Doppler shift proportional to Dr/cDt, yes but this does not necessarily imply that there is an added delay, Dr/c, before the radiation from the emitter reaches the receiver. That is, the hypothesis that light is the movement of waves,particles or probabilistic particles implies a Doppler shift but this is not an if and only if implication.

  We discuss later in the section on radiation and induction, using Maxwell’s equations and the hypothesis of charge polarization inside atomic  nuclei and inside electrons,  the way in which a longitudinal sine oscillation of charge inside atomic nuclei of a receiver produces a transverse oscillation of charge within the nuclei that in turn produces a greater longitudinal oscillation of charge in the opposite direction.  And subsequent oscillating forces from the source are weaker and too weak  to change what is happening in these nuclei and start to act on other nuclei producing a subsequent oscillation of charge there. And that this process once started from some outside influence may continue for a time without additional outside influence. Also, as the amplitude of charge oscillation in a receiver increases in this way, successive, weak, sine oscillations at the same frequency  and phase like those initially produced by the same oscillating outside force,  are given a boost by the previous buildup of charge oscillation. This is the familiar resonance effect.  And if the later set of oscillations and modulations is just a repetition of the previous set, then when the later sequence rises above noise, this is tantamount to the initial radiation having arisen above noise.

  In the radiation and inductance section we derive an exponential increase in the rms amplitude of the induced oscillation of charge assuming this model that could explain delays of up to one second eg one way delays based observed from returning blips on a plane’s or ship’s radar screen.

  Where is the energy and information in a stream of radar data sent to a distant spacecraft in the, supposedly hundreds of seconds before it reaches the spacecraft?  We argue that signals from the spacecraft are received within seconds after they are sent from the spacecraft and not hours later. The constant transmissions from these spacecraft of a pure sine wave carrier oscillation at a specific frequency can be regarded as being received by one of three receiving stations  that is facing the spacecraft at the time of reception. Such transmissions are in addition to data uplinks and downlinks. http://flux.aps.org/meetings/YR99/CENT99/vpr/layoa03-02.html

   We argue that the estimates of spacecraft position based on assuming much larger speed of light delays before such signals are received may have led to the apparent increase in the gravitational attraction of the spacecraft to the earth implied by these estimates.
    Such receptions and the difference between consecutive receptions a minute apart are used to determine the Doppler shift caused by the relative motion of the Earth (29km/s+-.456km/sec) and the spacecraft( eg 36km/s).   For example the difference between successive receptions is near zero when the motion of the receiving station on Earth is perpendicular to a line from the spacecraft to the receiving station. This motion, the sum of the orbital and rotational motions, is perpendicular when both the rotational and orbital motions are parallel or at an angle such that the total motion is perpendicular to craft-Earth line.

   And 24 hours later, receptions at the same receiving station may be nearly the same when both the orbital and rotational motion of the Earth are again nearly both perpendicular to this line. But at times when the line from the spacecraft to the Earth’s orbital path is not perpendicular to it and  the rotational motion is perpendicular to this line, then frequencies received by the same station 24 hours apart will be different, the moreso the less perpendicular the craft-orbital path line is to the orbital path.

   Such an analysis of the archived data  leads to a different sequence of positions  of the spacecraft with less error than the assumption that the received signals arrived from  positions where the spacecraft was 5 or  10 hours or so earlier.

   It is important to note that the sequence of positions of the Pioneer10 spacecraft that were used to show a small gravitational anomaly that was evident after 1980 were not positions based on data from minute by minute communications with the spacecraft from the time of launch but rather from  estimates of positions after the Jupiter contact in 1973 based on the standard speed of light assumption and with the data from 1987 to 1998, 5 to 10 hour delays between signals sent and received.  I was  told that  after
the Jupiter encounter in 1973 and the radical change in direction of the Pioneer 10 at that time,  it was difficult to reconcile the preceding  minute by minute sequence that had begun with the launch in 1972.

   The criteria for the validity of the new estimation procedure was presumably that it predicted subsequent positions with the least possible error. The lack of documentation of this procedure is regrettable.

   I have asked nasa for this documentation and for an analysis of the Doppler data assuming that the data is received a few seconds after it was sent from the spacecraft. But to no avail.

 

    The cumulative effect interpretation of light speed delay makes Einstein’s valiant effort to save Maxwell’s theory from the Michelson Morely experiment, with dilations and contractions of space-time, unnecessary. In fact if we view light as the cumulative effect of instantaneous forces at a distance, Maxwell’s premise of an invisible massless field conveying electric and magnetic influences from a source to a receiver is also rendered  unnecessary.

   The problems of the photon theory, of the wave photon duality or of the probabilistic photon are similarly avoided. The probabilistic photon theory begs the question of what actually happens in the process of emission and reception of a photon. Also and perhaps more importantly, the photon theory does not explain how a photon can move like a particle and yet not have the other characteristics essential to the definition of a particle, like its mass.

   One might object that a cumulative instantaneous force theory does not explain how forces can occur between objects which are not touching.  The answer to this is that sure, human beings must touch things to move them. But the primitive human experience includes magnetic and electrostatic attractions and repulsions between things which are not touching.     

    Consider the force between charged particles such as leaves of tin foil on a simple electroscope. The leaves are fastened together at the top by, say, an aluminum paper clip. The aluminum clip and the top part of the leaves are charged. The bottom parts of the leaves are free to move apart and they do because similarly charged particles repel each other. The formula for this repulsion is an inverse square force similar in form to Newton's gravitational force and in the fact that it can act in a vacuum. It is not necessary here to postulate a propagating field or the movement of photons.

    In fact if we were to postulate the existence of undefined entities unnecessarily we would stand in violation of the scientific method specifically of Occam's principle of parsimony.

    Hence the cumulative effect interpretation of light would, having fewer assumed entities, be preferable to the present theory of light if we could show Roemer's so called  measurement etc., to be attributable to other causes. We will discuss these causes  in the section on light speed measurements.

   The second fundamental discovery in the history of physics that we will consider in terms of charge polarization inside atomic nuclei  has to do with the apparent increase of mass of beta electrons as they approached the speed of light.  Beta electrons (electrons emitted by nuclei of radioactive atoms) of various speeds near the speed of light were observed.  Their increasing responsiveness to a magnetic field as their velocity increased was seen, unexpectedly, to slack off when the velocity increased beyond a specific amount. The rate of increase of the response, as the velocity increased, unexpectedly decreased. Instead of being attributed to changes in some previously unobserved quality of magnetic responsiveness, these changes were attributed to increasing  inertia or mass. The force producing the velocity somehow after some threshold point produced an increase in mass also.       

    Kaufmann, the one person who had most familiarity with this sort of experiment objected that the data seemed to require different values for the inertial mass  in different directions. But his objections were ignored in favor of the simpler explanation offered by Special Relativity whose success in explaining the Michelson Morely experiment was in its favor.

   We will discuss Kaufmann's reasons  later and show that a better explanation is that there is a change in magnetic responsiveness as the speed of a charged particle increases to the speed of light. The explanation is better because it requires fewer assumptions and is consistent with new discoveries in nuclear physics.

    The increasing number of premises and circumlocutions in modern physics are due to the mistaken interpretations of Roemer’s and of Kaufmann’s measurements. When Faraday and Maxwell first imagined invisible lines of force, wheels and ball bearings to help them understand electromagnetic induction and radiation as implied by Roemer's experiment, it was not inconceivable that such things existed. But even during Maxwell’s lifetime improbable implications of such entities became difficult to ignore. For example the invisible and perhaps vacuous field medium carrying light would have to have the rigidity of iron.

    Despite such problems with field theories, the apparent lack of any alternative to explain the phenomena of radiation, e.g. Roemer’s measurement, has led to even more extravagant claims for fields.

   Physicists like Witten at Harvard, for example believe that latent energy and mass may exist in a complete vacuum, in massless space;  that the existence of fields implies such a possiblity.  Witten calls these things, these vacuous latent mass-energy things, strings.  They are somewhat similar to Wheeler's quantum foam. And other physicists like Kip Thorne at Stanford extending the ideas of John Wheeler, believe there are wormholes in  space-time, since space-time near a large dense star could be severely bent out of shape; also perhaps, that these wormholes may lead to otherwise invisible universes. The mathematical complexity of the justification for these speculations confounds journalists who anyway have to be more concerned with catchy phrases and startling images than with scientific clarity.

   But one doesn’t have to follow a lengthy mathematical argument to see the probable fallacy in such speculations. Regarding latent energy and mass in  vacuous space.  Our only experience of latent energy and mass is in the presence of other mass and not far from such masses, in empty space. For example, radioactive nuclei produce charged particles of lesser mass that move at high velocities. These particles are visible as they move through cloud chambers and cause condensation around them in their successive positions in the moist vapor of the cloud chamber. But sometimes, uncharged particles may be ejected and soon break up into charged particles that seem to appear out of nowhere. But such things are not observed to occur in vacuous space far from the mass of an excited atomic nucleus.

    Hence it is improbable that latent energy and mass can exist in a vacuum.

Regarding wormholes, black holes, and other implications of the General Relativity premise that mass distorts space-time and the premise that the density of imploding mass can increase beyond specific limits.

    The situation is analogous to a rubber band stretched to the limit. One cannot apply indefinitely a linear formula to describe the amount of stretching produced by a given force on a rubber band. At some point the band loses its elasticity and the relation between force and stretch loses its linearity. And at some point the band breaks but the formula keeps grinding out numbers. The linear formula alone is not enough to tell when the band breaks. When extrapolations claim the existence of  stranger and stranger phenomena, it is time, isn't it, to question the validity of the extrapolation and the applicability of one' s basic assumptions and theory.

     Necessary information  is lacking in black hole and wormhole speculations based on the predictions of equations that are observed to be valid for some values of the independent variables. Will these same formula work for unobserved values of the independent variables?  Probably not, especially if the predictions are counter to our previous experience of similar things and events.

    Let us look more closely, also, at the assumptions required for black holes and wormholes. Regarding General Relativity: the effect of the Sun’s mass in delaying slightly the time,  when the eye recognizes  light from a distant star, can be attributed to the effect of the Sun’s mass on the eye or other receiver of the radiation;  that is, we do not have to assume that space time is bent  by large masses as assumed by General Relativity. Similarly the precession of the perihelion of the planets may be attributed to a torque interaction between the planets and the Sun as dipoles; we do not have to assume that space-time is bent. By dipoles here I mean electrostatic dipoles and the evidence of such dipoles will be shown in a later section dealing with gravity.

    Regarding how much a star can collapse given the forces of repulsion between atomic nuclei and parts of atomic nuclei, the evidence of neutron stars with densities 10­14 times that of water or of  the Sun may point to even greater densities and black holes and singularities. But as we have said, when limits are approached and extrapolations are made of  things happening that are unlike anything we observe, it is time to reassess the boundaries of the theory that leads to such extrapolations.

     The reassessment involves observing evidence for charged  particles inside electrons and atomic nuclei orbiting at supraluminal speeds and what that implies, particularly with regard to accepted hypotheses regarding 1)Ampere's theory of magnetism, 2) the wave/photon and probabilistic photon theories of electromagnetic radiation, 3)the quantum theory of atomic energy levels and of magnetic phenomena, 4)exchange forces and the quark theory of Gell Mann, 5) Einstein's special theory of relativity and mass energy transformations   6) Newton's  theory of gravity and Einstein's general relativity theory.

    One is led to the conclusion that all the forces of nature including gravity, magnetism and the weak and strong nuclear forces are derived from a single force, the electrostatic force.

  

 

 

 

I   MAGNETISM and ELECTRODYNAMICS

 

Forces Between Currents and Charged Foils

 

   According to the received wisdom, there should be no force between a charged object and a current carrying wire except that caused by electrostatic or electromagnetic induction.   This is essentially the theory of magnetism formulated by Ampere, Biot, Savart, Faraday and others.

   I carried out a number of experiments that seemed to show that this is not the case; that the electromagnetic force might be a form of electrostatic force. The experiments involved measurements of forces between uncharged current carrying wires and charged pieces of metal, for example oppositely charged metallic surfaces separated by a dielectric. The forces appeared to increase with increasing currents and to reverse direction with a reversal of the direction of the current  contrary to  the accepted theory  that the magnetic  force of current carrying wires was independent of the electrostatic force of charged conductors.

   These effects are not easy to detect because as the current in a wire is  turned on, a  momentary current is induced in the nearby small square piece of metal even with slits cut in it to minimize this effect, and so there  occurs a brief weak magnetic repulsion  between the wire and the piece of metal independent of the direction of the current.   Also the charged piece of metal induces charge displacement in the wire and so the resulting constant stronger attraction increases as the separation, between the  piece of metal and the wire, is reduced.

   But small observed repulsions occurred in spite of such attraction producing inductions when the current was moving in one direction. The experiments involved measurements of small repelling and attractive forces, about 10-7to-5 Newtons, between uncharged current carrying wires ( 900Amps to 25Amps) and a charged cm2 foil carrying a charge of 2kV.

   In another experiment  an Ampere Balance in modified form was used. The Ampere Balance was obtained from  Cenco, a Chicago supplier of  laboratory demonstrations for schools. The Ampere Balance consists of a horizontal wire about one cm in diameter and 30cm long fixed between two dielectric (plastic) supports and connected to a dc power source. Above this current carrying wire is another wire of the same length forming one side of a three sided square wire circuit. The fourth side of the square is a dielectric two by four piece also 30cm long whose ends were metal triangular prisms.

    The blade end of each prism rested on a metal step carved into a metal post about 3cm high. So the fourth side of the square and the horizontal U shaped wire circuit could pivot back and forth; weights could also be attached to the opposite side of the dielectric bar so as to position the base of the U at a desired position above the straight wire. When currents were passed through both wires the movement of U shaped piece upward or downward showed the Amperian force between current carrying wires.

   By replacing the U shaped wire with thin wooden dowels glued together to produce the same shape and by attaching to the base of the U a pair of thin copper strips separated by a 1mm thick dielectric tape whose long edge faced the equally long straight wire it was possible to test for the existence of a force between a current carrying wire and an electrostatic dipole. That is when the copper strips were charged say to a potential difference of .42 kV we formed a chain of dipoles in the horizontal plane and parallel perhaps to transverse dipoles in the current carrying wire below them. The hypothesis that currents produce electrostatic dipoles transverse to the currents is discussed in detail below

     The vertical 1 mg attraction/repulsion of the two sets of parallel/antiparallel dipoles was easily observed.  Note that the horizontal torque due to the interaction of the potential difference along the current carrying wire and the chain of dipoles was not possible to observe given the experimental design implemented here.

   The observed forces appeared to increase with increasing currents contrary to the accepted theory that the magnetic force of current carrying wires is independent of the electrostatic force of charged conductors.

   A discussion of the subject appeared in Electrical Engineering Times (12/28/87). A related patent was accepted by the US patent office (4,355,195). Only one paper of several I submitted was published in the Rev of Scientific Instruments (3/85) and there followed a paper, purporting dishonestly, I thought, to be a duplication of one of these experiments using wires of different lengths, thickness and arrangements  and different orders of magnitude of currents and presenting ambiguous results(Rev. Sci. Instr., D.F. Bartlett 10/90).

   The hypothesis was proposed that the magnetic force was ultimately an electrostatic force between electrostatic dipoles inside the atomic nuclei and free electrons of the conductors and transverse to the currents. The dipoles are produced by subnuclear and/or subelectronic elliptical orbital systems; specifically by the displacement of the average centers of negative and positive charge inside these systems. The magnitude of the dipoles appears to increase with the distance, r, between any two of a pair of dipoles and decreases as the relative size of the other dipole in the pair considered, increased.

    Because the dipoles are not produced by the relative displacement of free electrons and the positive atomic ions and because they are so small and so numerous, all with a common orientation, electrostatic shielding does not shield against this proposed cause of the magnetic force.

   Hence their effect on a nearby conductive piece of metal that is not carrying current is less to pull or push the free electrons in the metal toward one side but to attract or repel equally the similarly oriented electrostatic dipoles inside the nuclei and free electrons of a parallel current carrying conductor on the other side of the conductive piece of metal.

   To see why this is really not so surprising consider two oppositely charged metallic surfaces on opposite sides of a thin narrow strip of plastic tape.

   Suppose the distance between the charged  surfaces of the strip is smaller than the distance between the strip, lying horizontally, and a parallel current carrying wire suspended above it, by a factor of approximately three or more, then the charge of these surfaces interacts-according to Coulomb's law- about ten times less strongly with the free electrons in the parallel current carrying wire than it would if the distance  between the charged surfaces was the same as that between the current carrying wire and the nearer charged surface. That is, pairs of charged surfaces interact as dipoles with other electrostatic dipoles that may be assumed to exist within the nuclei and free electrons of the parallel current carrying wire. When the oppositely charged surfaces are very close to one another, interaction between the linear array of electrostatic dipoles thus formed and a free electron in the wire carrying current can be less than the force between the total electrostatic dipole of the array and an electrostatic dipole inside the free electron or inside the nucleus of the current carrying wire.

     The reason is that any displacement of a free electron in the current carrying wire not in the direction of the sustained potential difference is opposed by pushes from a greater local density of free electrons produced by the selfsame displacement and by pulls from the greater local density of positive charge produced by the same displacement of free electrons.

     This does not happen of course when an electrostatic dipole in one conductor acts on a colinear line of electrostatic dipoles inside the nuclei and free electrons of a parallel conductor. The two parallel conductors then repel each other or attract each other. That is, this action whether a push or a pull acts on the  electrostatic dipoles inside the nuclei in the same direction as it acts on the electrostatic dipoles in the free electrons which thus tend to move together.

    We will show that the similarity between the magnetic force in Ampere’s general formulation and the force of electrostatic dipoles can be made into an identity.

 

 

Ampere's Formula and Transverse Electrostatic Dipoles

  

   The obvious analogy between electrostatic dipoles and magnetic dipoles has led physicists on a century long search for a single magnetic pole without result. The underlying significance of the analogy probably lies elsewhere. For example:

   The similarity between the magnetic force between current carrying segments of wire as formulated by Ampere and the electrostatic force between imaginary electrostatic dipoles transverse to these wire segments, ds and ds' can be expressed as follows(fig 1&2, on the first page of illustrations at the end of the book):

 

F=(2)(9)(109)/((rc)2)(ids sinaacosb)(i'ds'sina') - (1/2)(ids cosa)(i'ds'cosa'))

 

G=(3)(9)(109)/r4)(-(pds cosaa cosb)(p'ds'cosa') + 2(p ds sinaa)(p'ds'sina'))