Why Magnetic Monopole Has Not Been Found
ralph sansbury
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:
F=(2)(9)(10^9)/((rc)^2)(ids sinaacosb)(i'ds'sina') - (1/2)(ids
cosa)(i'ds'cosa'))
G=(3)(9)(10^9)/r^4)(-(pds cosaa cosb)(p'ds'cosa') + 2(p ds
sinaa)(p'ds'sina'))
Consider the examples of parallel current segments(collinear
dipoles) and collinear
current elements(parallel dipoles)
Fr = + 3p1p2/4(pi)(etasubzero)r^4
Fr = -6p1p2/4(pi)(etasubzero)r^4
The forces F and G are equivalent except for the placement of
the factor "cosb" if p=ri/c* and p'=ri'/c* where c* = (3^1/2)c
where c denotes the velocity of light and the currents are
denoted i and i'.. It may be that the square root of three factor
is related to the fact that we have ignored the equal transverse
dipole component perpendicular to the other transverse dipole
component we first considered. But it is clear from a glance at
the diagrams of these forces that in summation over a complete
circuit, the cosb factor must be sometimes positive and sometimes
negative and these quantities must add up to zero. In the
language of vector calculus used in texts on electromagnetism,
the curls of F and G are equal although their divergences and
gauges may be different.
We should note also that the dipoles p and p' increase with r
consistent with observations of magnetoresistance. Later we show
that another representation of the dipoles similar in this
respect and that gives the same pair-wise ponderomotive force is
preferable; that is p=ri^2/i'c* and p'=((i')^2)(r)/ic*. However
to make the analysis easier to understand we will use initially
the simpler representation. Consider the case of two parallel
vertical wires and the transverse force per unit charge from one
wire on the second. Here and in other references to the
transverse force component we shall mean along a line drawn
between parallel vertical current carrying wires. The other
transverse component is perpendicular both to the longitudinal
current and to the first transverse component; both components
are of equal magnitude.
The transverse force of one wire on the other may make the
transverse dipole more longitudinal and less transverse according
to a process described later. This may reduce the effective size
of the transverse dipole in the second wire produced by a given
emf field E. Hence the magnetic effect is reduced for a specified
voltage V=Ed, where d denotes the distance between any two points
along a current carrying wire for which we want to know the
voltage. The voltage is the sustained potential difference
between these points due to the resistance in the wire.
Similarly for the effect of the second wire on the first. We
should note that as r and so rv/c* increases for a specified emf
the current flow and, v, the subsequent velocity in the direction
of current or electron flow of charge e=(1.6)10^-19 Coulombs and
mass m=(9.1)10^-31kg. must decrease as a consequence of a reduced
time between collisions and so that rv/c* where neAv=i does not
increase beyond the distance between lattice ions which is
approximately one Angstrom (10^-10meters).
Note nevA is the amount of charge flowing per sec through a
cross section area, A, of a wire and the dipole, associated with
a cross section of diameter equal to the wire diameter and width
equal to the distance between atoms, one Angstrom, and denoted
ds, is (r)(nevA)ds/c*; n of course denotes the density or number
of free electrons per meter cubed in mks units. Suppose that the
dipole inside each nucleus and free electron was of length rv/c*
and charge e then nAds is the number of such nuclei and free
electrons contributing to the total dipole associated with the
current segment ds.
This seems at first strange. Over typical values of current and
voltage, and for what amounts to a standard distance between
current carrying wires when their ponderomotive forces are
measured by what is called an galvanometer or ammeter, current is
proportional to voltage; also the time between thermal collisions
is constant for a range of temperatures. We will discuss this
problem later as well as the problem of unique dipoles associated
with segments of current when different pairwise forces between
three or more current segments occur.
To see that the combined forces of many small electrostatic
dipoles in 1) two parallel fairly closely spaced wires and 2) two
parallel pairs of oppositely charged surfaces separated by a thin
dielectric or 3) one such composite pair of charged surfaces and
a current carrying wire, can produce a measureable, ponderomotive
force we will consider a quantitatative example. Consider a
current element, ds, along the direct current carrying conductor
of length,s. We project the electrostatic dipole
pds=rids/(3^1/2)(c) to obtain, p sina ds, and on a perpendicular
to r to get, p cosa ds. We define in the angle between the
electrostatic dipole Pds' at point R and the extension of the
line r as 90-a' where a' = a. Then the force between the
electrostatic dipoles Pds' and pds along r projected on D and
integrated over ds is the integral over ds of
[( (3)(9)10^9)(dl)(-pP(cosa)^2+2pP(sina)^2 sina]ds
Since(r)(-da)=ds sina so ds=(r/sina)da , we can write this as the
integral over da of
[2(9)(10^9)(3ds) ((sin2a - (1/2)cos2a) (ri/(3^1/2))c)P/r^3]da
Since rsina=D, we can write this integral and integrate over
possible values of , a, from zero to 90 degrees
2K((sina)^2 -(1/2)(cosa)^2)((sina)^2)da/D^2 =
1.96(9)(10^9)(i/(3^1/2)c)Pds'/D^2=F
The dipole-per-meter length here is P = Qd = CVd =
((1.1)(10^-11)(A)/ d)(V)(d)
This seems to account for one of the experiments previously
mentioned involving measurements of small attractive forces
about 10^(-7to -5) Newtons, between uncharged current carrying
wires(900Amps to 25Amps) and a charged cm^2 foil(2kV) and in
another experiment, two oppositely charged foils separated by a
thin, eg 1mm dielectric(.42kV). The attraction appeared to
increase with increasing currents in one direction contrary to
the accepted theory that the magnetic force of current carrying
wires was independent of the electrostatic force of charged
conductors (Note that induced oppositely directed currents cause
repulsion).
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 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.
>
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.
It turns out that the similarity between the magnetic force
in Ampere's general formulation and the force of electrostatic
dipoles can be made into an identity if these dipoles transverse
to current elements expand as the distance between the current
elements increases.
A reason for this to occur is that the transverse field of the
dipole say in one current element interferes with the production
of the dipole in a parallel current element by the longitudinal
field causing the current.
Sam Wormley
ralph sansbury
I guess you are referring to the negative result as stated
recently:
"NEW LIMITS ON THE MASS OF MAGNETIC MONOPOLES have been
established in an experiment at Fermilab.( No evidence for the
monopole itself but new constraints on what its mass must be if
it does exist: at least 600 GeV if the monopole is a spin-0
particle and 900 GeV if its spin is 1/2.)
The equations written down by James Clerk Maxwell in the
19th century are not symmetric with respect to electric and
magnetic forces. They can be made symmetric if there exists a
magnetic monopole, a particle, comparable to the electron, with
an isolated north or south magnetic pole (all known magnets are
dipoles, possessing both south and north poles)."
The point is that the reason for the lack of symmetry is that
the magnetic force and its dipole characteristics are derived
from the fact that the magnetic force can be ascribed to the
observed poles of the electric dipole.
As explained in the above post and in
http://www.bestweb.net/~sansbury/book01.html
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"Sam Wormley" <swor...@mchsi.com> wrote in message
news:3DDC0069...@mchsi.com...
>
> See:
http://www.google.com/search?q=%22Magnetic+Monopole%22+site%3Awww
.aip.org+update
Richard
>
> I guess you are referring to the negative result as stated
> recently:
> "NEW LIMITS ON THE MASS OF MAGNETIC MONOPOLES have been
> established in an experiment at Fermilab.( No evidence for the
> monopole itself but new constraints on what its mass must be if
> it does exist: at least 600 GeV if the monopole is a spin-0
> particle and 900 GeV if its spin is 1/2.)
> The equations written down by James Clerk Maxwell in the
> 19th century are not symmetric with respect to electric and
> magnetic forces. They can be made symmetric if there exists a
> magnetic monopole, a particle, comparable to the electron, with
> an isolated north or south magnetic pole (all known magnets are
> dipoles, possessing both south and north poles)."
>
> The point is that the reason for the lack of symmetry is that
> the magnetic force and its dipole characteristics are derived
> from the fact that the magnetic force can be ascribed to the
> observed poles of the electric dipole.
> As explained in the above post and in
> http://www.bestweb.net/~sansbury/book01.html
You have it backwards, the electrostatic field is a randomized vector
(magnetic) field. The force on your test charge will be given precisely
by:
-F = mu_o I q' [ ( v _e / 2 ) -v_q' ] / ( 2 pi d )
where v_e is the drift rate in the conductor, and v_q' is the speed of
the test charge wrt the conductor.
When v_q' = 0 the equation reduces to:
-F = mu_o I v _e q' / ( 4 pi d )
A very very small force. I didn't follow your description, so could you
explain in detail how you filtered this force out from the inductive
force? If you have found a method that accomplishes this, then a quick
look at the equation will show that if the force were known, that the
actual drift rate of the current can be derived, viz.:
v_e = -F 4 pi d / (mu_o I q')
Note also that for any given current, that the force on the test charge
will increase with increasing drift rate, meaning that a poor conductor
will amplify the force vs. that generated by a good conductor, given the
same current.
--
Richard
http://www.cswnet.com/~rper
--The dissenter is every human being at those moments of his life when
he resigns momentarily from the herd and thinks for himself.
--Archibald MacLeish
ralph sansbury
"Richard" <no_mail...@yahoo.com> wrote in message
news:3DDC5D82...@yahoo.com...
> ralph sansbury wrote:
> >
> > The point is that the reason for the lack of symmetry is
that
> > the magnetic force and its dipole characteristics are derived
> > from the fact that the magnetic force can be ascribed to the
> > observed poles of the electric dipole.
> > As explained in the above post and in
> > http://www.bestweb.net/~sansbury/book01.html
>
> You have it backwards, the electrostatic field is a randomized
vector
> (magnetic) field.
prefer to discuss physical possibilities eg the possibility of
electrostatic dipoles inside atomic nuclei and inside free
electrons that could account for the magnetic field.
One advantage of this is a reduction in the number of
premises- which is something you seem to want also. That is there
is no need for the premise of an independent magnetic force in
addition to the electrostatic force.
Also since electrostatic poles and dipoles are observed and
magnetic dipoles are observed but magnetic poles are not
observed it would seem preferable to remove the magnetic force
premise than to remove the electrostatic dipole premise.
Richard
Except that the math is not in favor of that argument.
Franz Heymann
"ralph sansbury" <sans...@bestweb.net> wrote in message
news:utq1akj...@corp.supernews.com...
>
[...]
I would
> prefer to discuss physical possibilities eg the possibility of
> electrostatic dipoles inside atomic nuclei and inside free
> electrons that could account for the magnetic field.
Since an electron has an observed magnetic moment, it is impossible
for it to also have an electric dipole moment. It cannot behave like
an axial vector and a polar vector object simultaneously.
[...]
Franz Heymann
Douglas Eagleson
ralph sansbury wrote:
A monopole as defined by the Dirac theory for the
monopole is a condition of the magnetic fields.
And so to find such a condition in nature requires
another theory to define the place it will be
expected. And Dirac never tried the existence
cause question. He just said, such and such
a field condition, is valid.
So, it may never be found in nature until
a person causes the Dirac field.
Why not, go make one. It is only as hard
as the automobile alternator that Dirac never
stated as a field condition. Do you see
the alternator flying around?
Douglas Eagleson
Gaithersburg, MD USA
ralph sansbury
The magnetic dipole moment is normal to the plane of a current
carrying coil and is shown in the snipped post to be equivalent to the
sum of electrostatic dipole moments transverse to the direction of
current flow in the wire coil and associated with each atomic nucleus
and free electron in the wire coil.
That is each electrostatic dipole has a component in the plane of
the coil and perpendicular to the plane of the coil.
The projections of these components on a line from the coil to the
normal line to the center of the coil and then the projection of these
components onto this normal line produce a dipole. The sum of such
dipoles is shown to be equivalent to the magnetic dipole moment in the
quoted discussion below:
Fr = -6p1p2/4(pi)(etasubzero)r^4
ralph sansbury
> A monopole as defined by the Dirac theory for the
> monopole is a condition of the magnetic fields.
>
identify this necessary monopole with the the electrostatic pole of an
electrostatic dipole if the condition that the distance between the
poles increases as the distance between the dipoles increases.
This condition is necessary to change the inverse fourth power force
between electrostatic dipoles to an inverse square force like that
between so called magnetic dipoles.
Such a condition is implied by the interaction between the
electrostatic dipole field of one dipole and the electric field
producing the motion of the other electron or electrons that produces
also transverse charge polarization inside the electron and if there
are atomic nuclei charge polarization inside the nuclei.
The claim that the magnetic dipole of an electron is an axial
vector not a polar vector refers to an orbital electron in an atom and
an axial line perpendicular to the plane of the orbit through the
center of the orbit.
Like free electrons moving in a circular coil, an electron in a
circular oribit experiences charge polarization transverse to its
motion.
The so called spin and orbital magnetic moment components add up to
give a net magnetic moment which is inferred from the effects of
magnetic fields on splitting spectral lines etc. But this so called
magnetic interaction is between electrostatic dipoles in the orbiting
atomic electrons and the electrostatic dipoles in the source of the
applied magnetic field.