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
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
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
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
In another experiment an Ampere Balance in modified form was
used. The Ampere Balance was obtained from Cenco, a
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 (
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'))
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