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Stomfi
2007-Jan-24, 05:18 AM
I have two questions from my 10 year old's mind.

She wants to know what the magnetic field would look like in a magnetised moebius strip. That is a strip of magnetic material, say 1 metre by 2cm by 1mm thick with each end joined but with a half twist in the strip so that there is only one surface and only one edge.

The other question is how much volts and amps would it take to make a steel pin filled plastic 6 mm tube surrounded by spaced electric coils, straighten so it was rigid.
This is a design for a small eight legged robot such that the coils can be turned on and off individually to create straights and bends and thus movement of the whole machine.

JohnD
2007-Jan-24, 08:17 PM
Stomfi,
No one who knows better has answered, so I'll have a go.

Imagine a flat bar magnet, then one that is a square rod, then a rod with a hexagonal section, then a round section. Is the field different in each case? I suspect not, except possibly very close to the edges of the bar/rod, which the round section rod does not have. So the section of the bar/rod is irrelavent.
Now put a 180 degree twist in the middle of each. The field will again be identical, except close the edges and what is more in the case of the round section - there is no twist! (We are imagining an ideal topological world here). The rod and so the field around it would be the same as one with no twist.
So, a rod magnet and one with a pre-Moebius twist will have the same field. Therefore a moebius ring magnet and a stright one will also have the same field. The poles at each end pay no attention to the orientation of the end. There would be a field with lines of magnetic force that pass through the hole and around the outside, in a magnetic torus - a doughnut.

John

hhEb09'1
2007-Jan-26, 02:47 AM
JohnD, I get the idea that your twist is like this, and then the ends are brought together North to South:

NNN NNN
! ! ! !
! ! ! !
! ! => X
! ! ! !
! ! ! !
SSS SSS

But I got the impression that Stomfi might be thinking of this

NNNNNNNN SSSSSSSS
! \ / !
! X !
! / \ !
SSSSSSSS NNNNNNNNThen the ends are brought together, South to North, and North to South.

JohnD
2007-Jan-26, 09:14 AM
hh,
You're right about my mental image of making a 'moebius' magnet. Remember that the twist extends all the way along the length of the magnet, not just at a torsion in the middle.

I think that your image, in which the twist occurres across the breadth of the magnet (it helps me to visualise a 'sheet' rather than a 'bar' magnet) would be topologically the same as two bar magnets laid side to side, with the opposite poles ajacent. These would experience a strong force joining them them, as their fields joined. The twisted magnet would not seperate longitudinally as the lines would be 'stretched' along the length of the magnet. You could cut it in half along the length and it would still stick together!
On bringing the ends together, there would be a strong torque to not only seperate the ends, but also to undo the twist, caused by the compressed field.

I don't know any way to visualise 3D magnetic fields, except possibly magnetic fluids, with wwhich I have no experience. This site shows how to make your own: http://www.lord.com/Portals/0/MR/DIY-MRFluid.pdf
Perhaps your daughter would like to experiment, Stomfi?

John

Swift
2007-Jan-26, 03:21 PM
This actually reminds me of a type of material that I worked on many years ago called a Spin glass (http://en.wikipedia.org/wiki/Spin_glass), though here we are talking about the spin alignments at the atomic level.

In a normal ferromagnetic, the spins want to line up parallel to each other.
http://www2.uni-siegen.de/~anchem/bilder/cooperativemagnetism1.jpg

In an antiferromagnet, the spins of nearest neighbors line up anti-parallel.
http://www.aacg.bham.ac.uk/images/antiferromagnetism.gif

A spin glass is a type of antiferromagnet with either an amorphous (random structure of a glass) or has a symmetry such that the spins on the individual atoms can't completely satisfy the anti-parallel state (the three arrows in the diagram below can't all be oppositely oriented to each other.
http://www.physics.emory.edu/faculty/boettcher/_sping.jpg.
This means the material can never reach a minimum stable energy state and leads to some interesting magnetic properties.

JohnD
2007-Jan-26, 06:30 PM
All,
It may be bad form to quote yourself, but I failed to make a point. I said:

You could cut it in half along the length and it would still stick together!
and omitted to say, "in contrast to a straight bar (or sheet) magnet that you cut from pole to pole. That would spring apart, as the two seperate fields established themsleves!

Swift,

John

Swift
2007-Jan-27, 12:27 AM
Swift,

John
Unfortunately, for Ms. Stomfi, my knowledge is about magnetism at the atomic level, not so much the macro-physics. I think a lot of it will depend upon the orientation of the magnetic field in the sheet; I suspect what will happen be very dependent upon that. If you describe the field as a vector, with north being the arrow of the vector, and starting with the non-twisted sheet (pre-mobius), is the field perpendicular to the plane of the sheet, or parallel to either the length or the width. I think you will have three different cases.

Stomfi,
I think this would be a terrific science project for your daughter. It would appear that one can purchase all sorts of flexible magnets (http://froogle.google.com/froogle?q=flexible+magnets&hl=en&safe=off&sa=X&oi=froogle&ct=title). Personally, I am much more an experimentalist than a theoretician. Hope you try it and let us know the result.

Stomfi
2007-Jan-28, 02:44 AM
I see you've used the Moebius effect to turn me into a mother. That was clever.
It's actually a grand daughter and Stomfi may not be woman.

One can make a Moebius Strip with a long strip of plain paper making the twist and sticking the ends together to make a circle. Using a pen to draw a line down the middle without taking the pen off the surface, ends up with what appears to be a line on either side. Cutting down the line with a pair of scissors creates one large circle.

It is the initial circle that has only the one surface and one edge that my grand daughter is interested in. She knows she can do the experiment if she could find the materials, but she'd rather find out how to know before she does it, the same as for the second problem.

hhEb09'1
2007-Jan-28, 03:01 AM
She knows she can do the experiment if she could find the materials, but she'd rather find out how to know before she does it, the same as for the second problem.What materials do you think you need? I ask because a lot of people don't realize that a lot of the "sheet" magnets are not aligned across the sheet.

JohnD
2007-Jan-28, 09:54 AM
Stomfi,

"I see you've used the Moebius effect to turn me into a mother. That was clever. It's actually a grand daughter and Stomfi may not be woman."

Don't be so touchy!

No one here has made any assumptions about your gender, and only reasonable ones about your relationship to the young lady. You said "my 10 year old" and "she", so isn't it reasonable to refer to her as Ms.Stomfi, as if she was your daughter?

How about filling a flexible plastic tube with iron filings, and magnetising it? Or rather several tubes, duct taped together to approximate to a flat sheet? That could then be twisted and 'joined' with tape?

John