Home made monopoles
Barry Adams
Home made magnetic monopoles
============================
Contrary to popular belief , magnetic monopoles exist and are easy to
make . Take a Steel hemisphere and cut a concentric hemisphere cut of the
middle , now magnetize the hemisphere such that the domains of the object
are aligned with the north (south) pole pointing outwards. Now stick two of
the hemispheres together forming a sphere (glue strong enough to resist
the magnetic repulsion of the hemispheres is required) you now have your
magnetic monopole :-) , since any observer will see the object having a north
pole only (unless they cut it open).
Of course the configuration is unstable and the domains will slowly try
to rearrange themselves to a more stable state. And the magnetic force still
decays like a dipole. Such objects might to useful as frictionless bearings.
Barry Adams
michael kagalenko
Newsgroups: sci.physics
Path: lynx!mkagalen
From: mkag...@lynx.dac.northeastern.edu (michael kagalenko)
Subject: Re: Home made monopoles
Message-ID: <1993Jan23.2...@lynx.dac.northeastern.edu>
Organization: Northeastern University, Boston, MA. 02115, USA
References: <1jr3ui...@mirror.digex.com>
Date: Sat, 23 Jan 1993 23:19:42 GMT
Are you just kidding or want us to insert your name into our Kill-files ?
John C. Baez
> ============================
>
> Contrary to popular belief , magnetic monopoles exist and are easy to
>make . Take a Steel hemisphere and cut a concentric hemisphere cut of the
>middle , now magnetize the hemisphere such that the domains of the object
>are aligned with the north (south) pole pointing outwards. Now stick two of
>the hemispheres together forming a sphere (glue strong enough to resist
>the magnetic repulsion of the hemispheres is required) you now have your
>magnetic monopole :-) , since any observer will see the object having a north
>pole only (unless they cut it open).
Cute - I hope you are joking and, more importantly, that everyone realizes
this! I myself am usually scrupulously honest in pointing out that all my
designs for antigravity machines etc. are flawed and that the real point
is to find the error.
Daniel Seeman
inside of the sphere)" does not affect the problem. Just because we "know" the
South Pole exists in the volume cavity inside doesn't mean we can actually
"see" it. Hmmmm, it seems a bit like an illusion to me (smoke and mirrors to
be sure) but the application may be useful. The application sure does satisfy
the apparent identifying criterion (compass always points one way near the
monopole). I would like to hear other opinions (experiences) with this idea.
dks.
Uwe Hollerbach
No. Actually, even this won't happen. The actual configuration of the
magnetic field will be as follows: there will be two regions at the
poles of the sphere where the north-seeking end of the compass needle
will be attracted to the sphere, and around the equator of the sphere
there will be a region where the south-pointing end of the needle will
be attracted to the sphere. This is actually one kind of quadrupole
configuration, I believe. If it were possible to hide the south poles
in the cavity like this, it would in fact _be_ a monopole (more
technically, the magnetic field would have a monopole component, in
addition to having other components). Best regards,
--
Uwe Hollerbach u...@acm.princeton.edu or u...@alumni.caltech.edu
"In His infinite mercy, Allah does not subtract from one's alloted span those
hours which are spent in contemplation of net.news. All praise be to Allah."
-- an obscure commentator on the early work of Al-Khowariszmi
David E. Brahm
> Home made magnetic monopoles
> [Glue together 2 hemispheres each magnetized with "North" at its pole]
dse...@novell.com (Daniel Seeman) writes:
> ...Just because we "know" the South Pole exists in the volume cavity
> inside doesn't mean we can actually "see" it...
I don't know who's serious and who's joking here, but for the record,
Adams's construction is not a monopole (I believe it's a quadrupole).
Field lines outside the sphere emerge from each pole and re-enter at the
equator; "glue" doesn't stop them! You can't make something that violates
Gauss's Law of Magnetism (del.B=0) by superposing things that obey it.
--
Staccato signals of constant information, | David Brahm, physicist
A loose affiliation of millionaires and | (br...@cco.caltech.edu)
billionaires and Baby ... |---- Carpe Post Meridiem! --
These are the days of miracle and wonder, | Disclaimer: I only speak
And don't cry, Baby, don't cry, don't cry. | for the sensible folks.
Jonathan Scott
doesn't work. If you have a hollow sphere made of material which was
totally uniformly magnetized along radial lines, the effect of closing
the sphere would be to exactly cancel out the magnetic field. If it was
less than perfect, you would have patches of north and south pole over
the surface, giving equal flux into and out of the sphere.
That is, of course, unless you put a monopole inside it...
Jonathan Scott
jonatha...@vnet.ibm.com or jsc...@winvmc.vnet.ibm.com
Benjamin Weiner
>bd...@digex.digex.com (Barry Adams) wrote,
>> Home made magnetic monopoles
>> [Glue together 2 hemispheres each magnetized with "North" at its pole]
Actually I think Adams meant hemispheres magnetized radially outward,
so that for each one, the field lines point out of the hemispherical
surface and in through the flat part.
>dse...@novell.com (Daniel Seeman) writes:
>> ...Just because we "know" the South Pole exists in the volume cavity
>> inside doesn't mean we can actually "see" it...
>I don't know who's serious and who's joking here, but for the record,
>Adams's construction is not a monopole (I believe it's a quadrupole).
>Field lines outside the sphere emerge from each pole and re-enter at the
>equator; "glue" doesn't stop them! You can't make something that violates
>Gauss's Law of Magnetism (del.B=0) by superposing things that obey it.
This last statement is quite correct and applies to the radially-magnetized
version as well. I might as well blow the punchline, maybe some people will
benefit. Consider Gauss's law of magnetism: usually one writes this as
div B = 0.
This is true at any point; hence no point can have net outflow/inflow
of magnetic field lines. But it's also true of surfaces; remember the
integral form of Gauss's law of magnetism.
integral(B dot dS) = 0,
where the integral is over a closed surface and dS is a surface element, and
"0" = zero is the enclosed magnetic charge. (Inspired by my high-school
calc class using "plus an arbitrary constant, zero" for indefinite integrals.)
Take this integral over a sphere just at the surface of the magnetized
sphere, and you see that if B is everywhere outward then the integral
cannot be zero, so no dice. In fact given that the arrangement maintains
spherical symmetry the B-field will vanish everywhere, by symmetry
arguments.
John Brawley
A > Organization: California Institute of Technology, Pasadena
A > > Home made magnetic monopoles
A > > [Glue together 2 hemispheres each magnetized with "North" at its
A > pole]
A >
A > I don't know who's serious and who's joking here, but for the record,
A > Adams's construction is not a monopole (I believe it's a quadrupole).
A > Field lines outside the sphere emerge from each pole and re-enter at
A > the
A > equator; "glue" doesn't stop them! You can't make something that
A > violates
A > Gauss's Law of Magnetism (del.B=0) by superposing things that obey it.
This mean you cannot make one of these no matter what? (of -course-
that's what you mean.... It just seems like it ought to work, say, if
you provided serrated (as in rabbeted) perimeter edges... You mean
that no matter how tight you make the seams, the field would "leak"
through the (say, nanometer wide) join line? What would happen to
the sphere _if_, say, you managed to get a perfect join (theoretically
speaking)? Would the field "leak" through somwhere else? Metal
fatigue and shatter? What? What? (I'd thought on this idea several
years ago... I wanted to make a "floating ball" that sat in a
concave all-(south or north) "dish" shaped field (no problem), and
had all the outside of the sphere the same polarity. I wasn't
trying to make a monopole, just a neat thing with earth's geographical
features painted on it. Floating like that, tiny breezes ought to
trun it. Now here you come poking terrible holes in my neat little
floating globe idea! Gad. <grin> Tell me: what if I drilled tiny
holes all over it? Would that allow me to have, say 95% of the outer
surface all one polarity, with the other polarity's flux lines all
bunched together in the holes, like they do in a ring magnet?
Direct Email:
john.b...@f9.n8012.z86.toadnet.org
FIDONet: John Brawley, 1:100/435
PO Box 224, Eureka, MO, 63025-1134
Data (BBMsgSys) (314) 938 5285
"Sit down before Fact like a little child...."
--T.H. Huxley
Leigh Palmer
mci...@husc8.harvard.edu writes:
>One or the other. The idea was essentially to make a spherical
>shell out of magnetic dipoles. In the limit of an infinitely
>rigid sphere and infinitely robust dipoles, pushing the hemispheres
>together would take an infinite amount of energy; the force you
>need diverges as the edges get closer. A real hemisphere is only
>finitely strong and is made of stuff whose magnetic dipoles will
>reorient if the energy difference is large enough. So at some
>point, either a hemisphere will break or the field will leak
>through the surface (probably the latter, I'd guess).
I don't know how you obtained that "infinite energy" solution. It is
certainly incorrect. The correct solution, B = 0 everywhere, is the only
spherically symmetric solution to div B = 0, has been posted elsewhere in
this group. No superstrong materials are required, but the thing is
practically infeasible, cute though it would be.
Leigh
Matt McIrvin
>This mean you cannot make one of these no matter what? (of -course-
>that's what you mean.... It just seems like it ought to work, say, if
>you provided serrated (as in rabbeted) perimeter edges... You mean
>that no matter how tight you make the seams, the field would "leak"
>through the (say, nanometer wide) join line? What would happen to
>the sphere _if_, say, you managed to get a perfect join (theoretically
>speaking)? Would the field "leak" through somwhere else? Metal
>fatigue and shatter? What? What?
One or the other. The idea was essentially to make a spherical
shell out of magnetic dipoles. In the limit of an infinitely
rigid sphere and infinitely robust dipoles, pushing the hemispheres
together would take an infinite amount of energy; the force you
need diverges as the edges get closer. A real hemisphere is only
finitely strong and is made of stuff whose magnetic dipoles will
reorient if the energy difference is large enough. So at some
point, either a hemisphere will break or the field will leak
through the surface (probably the latter, I'd guess).
As long as the magnetic field obeys Maxwell's equations, the thing
can't be constructed at all.
(I'd thought on this idea several
>years ago... I wanted to make a "floating ball" that sat in a
>concave all-(south or north) "dish" shaped field (no problem), and
>had all the outside of the sphere the same polarity. I wasn't
>trying to make a monopole, just a neat thing with earth's geographical
>features painted on it. Floating like that, tiny breezes ought to
>trun it. Now here you come poking terrible holes in my neat little
>floating globe idea! Gad. <grin> Tell me: what if I drilled tiny
>holes all over it? Would that allow me to have, say 95% of the outer
>surface all one polarity, with the other polarity's flux lines all
>bunched together in the holes, like they do in a ring magnet?
I think there are actually proofs to the effect that you can't stably
levitate something this way with permanent magnets alone. You may have
seen a gadget sold in science-toy stores which has a levitating
spindle; one end of the spindle bumps up against a mirror, and that
stabilizing mirror is what makes the whole thing possible. Without
it the spindle couldn't be stable.
The right way to do this would be to make the floating ball out of an
ordinary permanent magnet, and levitate it above a slab of high-
temperature superconductor in a pool of liquid nitrogen!
--
Matt McIrvin
David E. Brahm
> ...I wanted to make a "floating ball" that sat in a concave all-(south or
> north) "dish" shaped field (no problem), and had all the outside of the
You not only wanted to make a monopole (the sphere), you wanted to make a
("dish-shaped") field in which all field lines converged to a stable point
without putting a source at that point! You can't do that even with
electric fields (or electric fields plus gravity). Gauss's Law(s)
generically disallow any such static "floating" constructions, to wit:
| (*1*) No static (electro-magnetic-gravitational) field configuration |
| in empty space will hold an object in stable equilibrium. |
Yet, almost the very object you describe, a "floating globe", is sold in
novelty stores (for $200 or so). The clever designers used non-static
fields, which get feedback from the globe's position. Also, a magnet will
float stably above a superconductor, which somehow manages to pull the same
stunt automatically, without any clever designers.
Here's my question, then: Put an electron in a bowl; by (*1*) there is no
point where it can sit stably, i.e. del.(qE+mg)=0 everywhere. Yet I think
it just sits there anyway (?). Furthermore, a book is just a collection
of nucleons and electrons; it floats stably a few Angstroms above my desk,
no problem. Where does (*1*) break down? Is QM at work here?
Matt McIrvin
>In article <mcirvin....@husc.harvard.edu> Matt McIrvin,
>mci...@husc8.harvard.edu writes:
>>One or the other. The idea was essentially to make a spherical
>>shell out of magnetic dipoles. In the limit of an infinitely
>>rigid sphere and infinitely robust dipoles, pushing the hemispheres
>>together would take an infinite amount of energy; the force you
>>need diverges as the edges get closer.
>I don't know how you obtained that "infinite energy" solution. It is
>certainly incorrect. The correct solution, B = 0 everywhere, is the only
>spherically symmetric solution to div B = 0, has been posted elsewhere in
>this group.
Of course. I was imagining a situation in which the hemispheres were
still separated by some distance, and in which by some miracle the
magnetic field within the ferromagnetic material remained constant.
That's not spherically symmetric; it has a field entering around
the equator which gets progressively more intense as the hemispheres
get closer together. The point I was trying to make is that eventually
something has to give. I suppose I was unclear-- I didn't mean the
zero-distance limit to be taken seriously.
If spherical symmetry is to apply in the final state, obviously B=0
is the only solution. In practice I'd think the result of the
experiment would be spherically nonsymmetric, since it started out
merely axially symmetric. The equatorial regions would probably
reverse polarity, and you'd end up with a quadrupole magnet rather
than the intended monopole. But I have already strayed far beyond
areas in which I know much.
--
Matt McIrvin
Leigh Palmer
mci...@husc8.harvard.edu writes:
>Of course. I was imagining a situation in which the hemispheres were
>still separated by some distance, and in which by some miracle the
>magnetic field within the ferromagnetic material remained constant.
>That's not spherically symmetric; it has a field entering around
>the equator which gets progressively more intense as the hemispheres
>get closer together. The point I was trying to make is that eventually
>something has to give. I suppose I was unclear-- I didn't mean the
>zero-distance limit to be taken seriously.
You've fallen victim to the reification error, Matt. Magnetic fields,
viewed as lines of force something like rubber bands, may have served
Faraday well in his day, but the analogy can only be pushed (or
stretched) so far. One of my favorite tricks to show how intuition can
get one into trouble is to demonstrate what happens in the following case:
Put two long coaxial cylindrical bar magnets with unlike poles close
together but not touching. These particular bar magnets may be thought of
as being made of type II superconducting material with trapped, pinned
trapped magnetic flux tubes running lengthwise through them. Picture the
magnatic field in the region between the adjacent poles. Now rotate one
of the magnets about its axis. What happens?
Answer: the magnetic field lines wind up like rubber bands to produce a
small volume, very intense field between the poles. Perhaps you could use
this to power a flying model airplane!
When I was a graduate student a Bell Labs physicist gave us a seminar in
which he made an error comparable to the one I just illustrated. He had
already got it published it in PRL, so it still counts for him.
Keep the faith!
Leigh
Stephen F. Schaffner
|> In article <mcirvin....@husc.harvard.edu> Matt McIrvin,
|> mci...@husc8.harvard.edu writes:
|> You've fallen victim to the reification error, Matt. Magnetic fields,
|> viewed as lines of force something like rubber bands, may have served
|> Faraday well in his day, but the analogy can only be pushed (or
|> stretched) so far. One of my favorite tricks to show how intuition can
|> get one into trouble is to demonstrate what happens in the following case:
I don't see why Matt made an error. The condition that B = 0
everywhere in the case of spherical symmetry contradicts the assumption
in the problem of a spherically symmetric dipole. This means not that if
you constructed such an object that the field would magically go to zero,
but that you can't construct it at all, or rather that it can only be
constructed if the dipole strength is zero (in the absence of monopoles,
of course). The thought experiment of trying to combine two perfect dipole
hemispheres (or better, taking a spherical dipole with a small hole in it,
and taking the size of the hole to zero, a case that's easier to
integrate) shows the same thing, in this case because the magnetic field in
the gap goes to infinity, and so does the force required to complete the
sphere.
--
Steve Schaffner ssc...@unixhub.slac.stanford.edu
The opinions expressed may be mine, and may not be those of SLAC,
Stanford University, or the DOE.
John Brawley
On (27 Jan 93) Matt McIrvin wrote to All...
A > From: mci...@husc8.harvard.edu (Matt McIrvin)
A >
A > John.B...@p1.f9.n8012.z86.toadnet.org (John Brawley) writes:
A > >speaking)? Would the field "leak" through somwhere else? Metal
A > >fatigue and shatter? What? What?
A >
A > One or the other. The idea was essentially to make a spherical
A > shell out of magnetic dipoles. In the limit of an infinitely
A > rigid sphere and infinitely robust dipoles, pushing the hemispheres
A > together would take an infinite amount of energy; the force you
A > need diverges as the edges get closer. A real hemisphere is only
A > finitely strong and is made of stuff whose magnetic dipoles will
A > reorient if the energy difference is large enough. So at some
A > point, either a hemisphere will break or the field will leak
A > through the surface (probably the latter, I'd guess).
Thank you! (You also have the honor of being the first person to
cinfirm my access to the INTERNET newsgroups, by the way...)
That's what i was afraid of. Oh, well, one clears the brain of old
dreams, one has more room for new ones... <g>
A > >floating globe idea! Gad. <grin> Tell me: what if I drilled tiny
A > >holes all over it? Would that allow me to have, say 95% of the outer
A > >surface all one polarity, with the other polarity's flux lines all
A > >bunched together in the holes, like they do in a ring magnet?
A >
A > I think there are actually proofs to the effect that you can't stably
A > levitate something this way with permanent magnets alone. You may
A > seen a gadget sold in science-toy stores which has a levitating
A > spindle; one end of the spindle bumps up against a mirror, and that
A > stabilizing mirror is what makes the whole thing possible. Without
A > it the spindle couldn't be stable.
I've seen it. I plan on making a bigger one, out of the two large
speaker magnets I have which are currently sitting on their fields
with a wooden post through the holes. (Ring magnets.) The setup I
have on my mantel has about a pound of steel roller bearings riding
on the upper surface of the upper magnet, and there's still an air
gap of about 3/8 inch between them. I'm waiting for them to "run
down." (Tongue is in cheek.) I do wonder, however, how to understand
that, if they will _not_ run down (no domain reversals) what it is
that they're doing, sitting there opposing gravity... Is the
requirement that energy _must_be_ expended in order to oppose gravity
excluded in this case, since the fields the pound of steel is levitated
by is just the collective fields of the electrons in the magnet? Thus,
the question goes to the electrons' dipole fields? It's really
bothered me, that on the one hand, I'm supposed to accept that gravity
is acceleration-equivalent, and that to oppose it, energy expenditure
is -required-, yet there they sit, blithely ingoring this while I try
to figure out whether or not anything in the magnets themselves have
to be expending energy or not...
A > The right way to do this would be to make the floating ball out of an
A > ordinary permanent magnet, and levitate it above a slab of high-
A > temperature superconductor in a pool of liquid nitrogen!
Workable! Unsellable! Dangerous! Gimme one! Do -not- give one to
my kids! <grin>
Direct Email:
john.b...@p1.f9.n8012.z86.toadnet.org
FIDONet: 1:100/435
TOADnet: 86:8012/9.1
Matt McIrvin
>You've fallen victim to the reification error, Matt.
More likely an idealization error. It's likely that nothing behaves
like the stuff I described.
--
Matt McIrvin