Six cylindrical magnets arranged N-S-N-S-N-S formed into a ring hold shape?

[Ntstanch]

I was wondering why, when I arrange six cylindrical magnets, about 1inch long and 1/5th inch wide each (neodymium magnets) in a hexagon shape by arranging them into a chain of N-S-N-S-N-S (top or bottom... with the other end obviously being opposite in arrangement) and connecting them into a hexagon shaped ring, they hold their form. I have some theories which hold (held) up well until I reach(ed) a dead end (dead due to insufficient comprehension, not due to it being that 'okay, this is wrong' death)... but what I want is something to help prove myself wrong outright concerning my theory, or just make SOME form of progress. However, after all this time (it's been about 1.5 years since I hit a 'wall') asking a physics professor or other students no progress has been made (I go to Michigan Tech).

When trying to visualize this model: http://upload.wikimedia.org/wikipedia/commons/0/0d/VFPt_Solenoid_correct2.svg ... with how the magnets are arranged, I can't visualize a reason for why they hold together so well. It is somewhat tricky to get them into the hexagon shape, but once established they can be easily collapsed with just two fingers and minimal force, or, they can repel as though you were trying to force two weak repelling poled magnets together. So, what would really be appreciated is as much explanation concerning why they would hold together so well. You can toss the ring into the air and catch it, and it is still in the hexagon shape... like I said, the arrangement is, for the most part, very stable. I just can't visualize why.

 

[Simon Bridge]

The way to understand would be to do the math for a ring of six magnets which is not a perfect hexagon.

Simplified - the close poles attract each other strongly and distant poles repel. So the magnets, except for the close poles, will try to move apart.

 

[Ntstanch]

The way to understand would be to do the math for a ring of six magnets which is not a perfect hexagon.

Simplified - the close poles attract each other strongly and distant poles repel. So the magnets, except for the close poles, will try to move apart.

I understand that (minus a lot of the math). However the thought experiment leading me to believe it would work and spending the money to test this and a few other things was meant to form a deeper understanding of magnetism. I'm less interested in the math and more interested in the visual/intuitive portion of why the standard magnetic field model allows for this. When visualizing this as a three dimensional construct and factoring in the magnetic field lines (image linked in the original post) and field strengths it really just doesn't seem to make sense.

It's true that they hold together, provable by either experiment or mathematics... but that's just observation of the behavior. It doesn't explain much else or elaborate on understanding, other than it being a repeatable fact, and being measurable to prediction before the need to experiment (most of the time... vector calculus, especially fluids, seem to be far more loose than math applied to other areas). What I'm interested in is a thought experiment heavy explanation as to why they hold together. Not a math heavy depiction of why they hold together given certain boundaries.

I'm trying to take more of a Michael Faraday approach to it... understandable to people who aren't well versed in mathematics.

 

[Simon Bridge]

Mathematics is the language of physics - if you refuse to learn this language then you will not be able to understand it. Sorry.

I gave you the Faraday explanation and you are not happy with it. Again, I cannot help that. The truth is seldom convincing, sadly.

Magnets are not simple intuitive things.
Your common sense is not likely to help - which is why we understand them in terms of field lines and attraction. Drawing the field-lines carefully is one way of "doing the math". If the shape were not a hexagon, there would be an unbalanced force ... the hexagon is the shape where the forces balance.

There are other shapes for six magnets which are also stable.
You can stack them, for example.

Perhaps you'll be able to understand why the hexagon is stable by observing what happens to the field-lines in iron-filings when you distort the shape.

The rest seems to me you are looking for an analytic description of how magnets work - one that does not just describe the results of experiment. Sorry - not how empiricism works.

 

[Ntstanch]

Mathematics is the language of physics - if you refuse to learn this language then you will not be able to understand it. Sorry.

I gave you the Faraday explanation and you are not happy with it. Again, I cannot help that. The truth is seldom convincing, sadly.

Magnets are not simple intuitive things.
Your common sense is not likely to help - which is why we understand them in terms of field lines and attraction. Drawing the field-lines carefully is one way of "doing the math". If the shape were not a hexagon, there would be an unbalanced force ... the hexagon is the shape where the forces balance.

There are other shapes for six magnets which are also stable.
You can stack them, for example.

Perhaps you'll be able to understand why the hexagon is stable by observing what happens to the field-lines in iron-filings when you distort the shape.

The rest seems to me you are looking for an analytic description of how magnets work - one that does not just describe the results of experiment. Sorry - not how empiricism works.

Guess I'm more a fan of imagination/creativity and a general intuitive visual-spatial perception of things which can be observed and experimented with (physically or as thought experiments). I also don't recall being unhappy with your Faraday explanation... I just saw it as obvious. My intuition lead me to believe that they would stay in that form, but not by using the standard model to visualize it, and math was not involved or needed (it would be to further map it out and expand on it, but I'm not trying to go in that direction). Aside from that, how do you think Faraday produced the thinking which allows you to suggest that I stare at the direction of iron fillings in order to better understand this? New ideas and new science doesn't seem to come from taking advice like what you've given me.

Either way we're in totally different schools of thought.

 

[Simon Bridge]

I just saw it as obvious

Is there anything wrong with obvious explanations?

Aside from that, how do you think Faraday produced the thinking which allows you to suggest that I stare at the direction of iron fillings in order to better understand this?

Because that is what he did. He set up experiments and demonstrations which isolated the phenomina he wanted to study, and made careful observations. He wa s famous for it and gave such demonstrations well into old age.

New ideas and new science doesn't seem to come from taking advice like what you've given me.

What, from observation and contemplation? New scientific ideas cannot come any other way.

 

[Ntstanch]

Is there anything wrong with obvious explanations?
Because that is what he did. He set up experiments and demonstrations which isolated the phenomina he wanted to study, and made careful observations. He wa s famous for it and gave such demonstrations well into old age.
What, from observation and contemplation? New scientific ideas cannot come any other way.

No, an obvious explanation isn't (wasn't) an issue. I just pointed out how this, "I gave you the Faraday explanation and you are not happy with it." was incorrect.

Yes, he set up experiments, and demonstrations and did what I try to do when I have the time (tech disallows free time... most of the time). However, he didn't use/repeat old experiments to try and better explain whatever it was he was trying to understand. He used original experiments which he thought up on his own, with the help of old knowledge... but my point was that staring at iron fillings got old in High School. I work at trying to understanding what's happening in the iron fillings, and the fields, approaching it similar to how he did (natural philosophy, experimenting-etc).

Observation and contemplating deep inside the 'box' seem to yield fewer new ideas. Thinking inside the box seems to be what you had suggested as absolutely necessary. New math comes after new understanding as far as I've noticed. Granted math can help towards new understanding. However I doubt mapping out the field strength mathematically is going to yield a fantastic new epiphany regarding the tricky nature of magnetism, electromagnetism, or other relative ism's.

I usually come here hoping for more outside the box approaches to why the fields (or number theory, set theory) function or behave as they do. Inside the box thinking wore me out years ago.

Edit: Also, Faraday is my hero. I've even read a book filled with correspondents between him and others. I think he may have been made of kindness.

 

[Simon Bridge]

However, he didn't use/repeat old experiments to try and better explain whatever it was he was trying to understand.

But he did repeat them when he was demonstrating to someone else ... especially when they were known to his as very illustrating of what he wants to explain. Which is what I'm doing, except I cannot demonstrate the experiments for you - you have to do it.

I usually come here hoping for more outside the box approaches to why the fields (or number theory, set theory) function or behave as they do. Inside the box thinking wore me out years ago.

Then I imagine you are frequently frustrated. Have you read the forum rules?

When you ask about well established and well studied phenomina - I can only respond with the well established models and science.

Perhaps if you would illustrate where your understanding falters and I could match the description better to your learning style?

I had a look at some of your other posts to see what sort of approach you prefer and the others have been most successful where you have described your understanding of the situation - like with the hot-air balloon - and they have filled in the gaps. Perhaps if you described the way you are thinking about these magnets, I'd have a better understanding of what you need explained and how?

 

[Ntstanch]

Then I imagine you are frequently frustrated. Have you read the forum rules?

When you ask about well established and well studied phenomina - I can only respond with the well established models and science.

Perhaps if you would illustrate where your understanding falters and I could match the description better to your learning style?

Will be busy until Saturday... which at best will give me time to try and word the question as best I can, but for as much purpose as I figure is needed I understand the current model. And I probably would be frequently frustrated, but my solution to that is to ease into the "out of the box" approach. Most of my questions are fairly level headed, but occasionally I like to try and mix theories against each other (how I try and understand it Vs. what different theories I've learned (or have yet to be learn)).

I had a look at some of your other posts to see what sort of approach you prefer and the others have been most successful where you have described your understanding of the situation - like with the hot-air balloon - and they have filled in the gaps. Perhaps if you described the way you are thinking about these magnets, I'd have a better understanding of what you need explained and how?

Again... it's difficult to explain without showing the experiments I had made and without my notes. An atmospheric physicist I occasionally talk to (not a student of his) about this sort of stuff was sort of lost (this was like a year ago), and also didn't have the time to play with the theory really, said my best option would be to get well acquainted with vector calculus and fluids. He also said he was a physicist in spite of his math skills (we both use our fingers frequently when doing math... literally). And I don't think the maths for three dimensional fluids have been invented yet. So, yeah. I'll try and explain it as best I can when I have time. Thanks.

 

[marcusl]

I was wondering why, when I arrange six cylindrical magnets, about 1inch long and 1/5th inch wide each (neodymium magnets) in a hexagon shape by arranging them into a chain of N-S-N-S-N-S (top or bottom... with the other end obviously being opposite in arrangement) and connecting them into a hexagon shaped ring, they hold their form. I have some theories which hold (held) up well until I reach(ed) a dead end (dead due to insufficient comprehension, not due to it being that 'okay, this is wrong' death)... but what I want is something to help prove myself wrong outright concerning my theory, or just make SOME form of progress. However, after all this time (it's been about 1.5 years since I hit a 'wall') asking a physics professor or other students no progress has been made (I go to Michigan Tech).

When trying to visualize this model: http://upload.wikimedia.org/wikipedia/commons/0/0d/VFPt_Solenoid_correct2.svg ... with how the magnets are arranged, I can't visualize a reason for why they hold together so well. It is somewhat tricky to get them into the hexagon shape, but once established they can be easily collapsed with just two fingers and minimal force, or, they can repel as though you were trying to force two weak repelling poled magnets together. So, what would really be appreciated is as much explanation concerning why they would hold together so well. You can toss the ring into the air and catch it, and it is still in the hexagon shape... like I said, the arrangement is, for the most part, very stable. I just can't visualize why.

The drawing you link to shows the magnetic field in and around a coil of wire, which is not a good model for your system. It is more appropriate to think of a cylindrical bar magnet as having an equivalent magnetic charge on each end, one positive and the other negative. (I forget whether + corresponds to N or S, I think S, but in any case it doesn't matter to the reasoning that follows.) The charges are fixed on the ends of the metal and are not free to move. These aren't real magnetic charges (magnetic monopoles haven't been found to exist) but in physics we often replace a complex system with a simple equivalent that allows us to solve for the right behavior.

Just as with electric charges, opposite (+ -) magnetic charges attract each other while like (+ + or - -) repel. Once you get your magnets into a ring, the assembly is "meta-stable", which we can understand by examining a single magnet (call it "2") and its neighbors ("1" and "3"). 2 is pulled towards its neighbors (and vice versa), touching each one at a single point located towards the center of the ring, such that the flat ends make an angle with respect to each other. 2's + flat end is attracted to 1's - flat end, and its field energy would be reduced if it rotated so that their ends rested flat against each other. For that to happen, though, 2 would have to pull away from the magnet at the other end (3), which would increase the field energy there by a greater amount than is gained by resting flat against 1. (In fact, the highest energy configuration is when all magnets are separated a long way apart.) This scenario is repeated at all six magnets with the result that the minimum energy of an ensemble in an approximate ring is minimized when the shape is, exactly, a ring. The ring is in equilibrium. Note that its energy is not necessarily the lowest possible for 6 magnets, but it is the lowest for magnets that you forced into a near-ring shape. It is stable to small perturbations (hence "meta-stable") because of the energy difference ("activation energy") mentioned.

It is possible to force the ring to assume another state by pushing with your fingers--you probably get a long chain or a double chain, which has the lowest energy for magnets not in a ring. When you press, your body does enough work to overcome the activation energy we talked about above. The magnets are forced to move out of equilibrium, and they snap into a new minimum energy configuration (equilibrium) appropriate to the new configuration.

A proper analysis would calculate forces and field energies, but such calculations are often non-trivial when magnetic materials are involved. Hence I have provided the descriptive explanation above.

 

[Simon Bridge]

Thank you marcusl.

I suppose working with the energy stored in the magnetic field between the poles would be a way to examine this - the bigger the angle between the flat pole-ends of the bar magnets the bigger the volume the field-lines have to go through, the bigger the energy stored there. (Though the field is not uniform in such a gap.)

Two magnets would click together so their ends are flat to each other - minimizing the energy stored between them. For more than two magnets, the minimum energy of the system would be to stack them + - + - etc and if the collection were given a good shake they would try to do that. But force them to an orientation, like a loop, then the minimum energy of the system needs also to minimize the energy at each join ... which makes all the angles the same (for same volume enclosed).

Numerically: for six magnets, we need to know how the energy stored in the field varies with different angles for each of the six angles in an arbitrary six-sided shape. This means a 6D phase space of angles with an energy assigned to each point.

The problem restricts us to only those combinations of angles which will allow the magnets to form a closed path - i.e. the sum of the angles is twice pi. We'd need to minimize the energy stored over this "surface". (Actually I suspect this simple model has a constant total energy stored so this means minimizing the energy stored in each corner simultaneously... which should intuitively mean all the angles have to be the same.) Anyone want to try it and see?

Another take - equivalent - would be to pick a point in the phase space and then evolve the system (the rule being that the next point has to be one with lower energy). The result would be oscillatory solutions around the equilibrium perfect hexagon ... so the IRL result would be a wobbly hexagon. (try this for many points and color-code according to the results - would this be be a fractal?)

A physical model would be to make rectangular blocks out of wood or plastic or some similarly non magnetic material the same size and shape as the bar magnets, drill a hole down their lengths and string them onto a length of elastic whose unstretched length is smaller than the sum of the lengths of the blocks. Tie it off in a loop. The elastic simulates the magnetic field between the poles. There are some similar stable points - like if you flatten the loop - but what it likes to do is form a near-perfect hexagon.

These are all still "in the box" as (to me) they are just other ways of expressing the balance of forces I wrote about first. But maybe this way of writing is clearer to OP?

Aside: The N pole is usually considered + (field lines radiate away from it).
You're right, it doesn't matter here.

 

[Ntstanch]

It is possible to force the ring to assume another state by pushing with your fingers--you probably get a long chain or a double chain, which has the lowest energy for magnets not in a ring. When you press, your body does enough work to overcome the activation energy we talked about above. The magnets are forced to move out of equilibrium, and they snap into a new minimum energy configuration (equilibrium) appropriate to the new configuration.

You can force the ring into a "flattened" shape, which resists and rebounds into its original hexagon form even if you pinch them together physically. This is when you have the 'west' side (one cylinder) as a - and east side (one cylinder) as a +. Leaving the two magnets on the top or "north" as having positive left and negative right, and below them a mirrored positive right and negative left.

So, when pushing the + - (north) and -+ (south) with - (west) and + (east), the structure holds firm for forces applied at most angles... Thought if you press on the east and west sides it immediately collapses into (most of the time) a two column and three row stack of row 1 being either - top + bottom... row 2 + top - bottom and row 3 - top + bottom. Or the opposite.

Though, in the former example of pressing them together no amount of physical force will stop it from going back to it's original ring shape save for breaking them or fusing them together (by hand that would require godlike strength). But a very light amount of force, in the latter example, is required to break the ring.

Another take - equivalent - would be to pick a point in the phase space and then evolve the system (the rule being that the next point has to be one with lower energy). The result would be oscillatory solutions around the equilibrium perfect hexagon ... so the IRL result would be a wobbly hexagon. (try this for many points and color-code according to the results - would this be be a fractal?)

A physical model would be to make rectangular blocks out of wood or plastic or some similarly non magnetic material the same size and shape as the bar magnets, drill a hole down their lengths and string them onto a length of elastic whose unstretched length is smaller than the sum of the lengths of the blocks. Tie it off in a loop. The elastic simulates the magnetic field between the poles. There are some similar stable points - like if you flatten the loop - but what it likes to do is form a near-perfect hexagon.

These are all still "in the box" as (to me) they are just other ways of expressing the balance of forces I wrote about first. But maybe this way of writing is clearer to OP?

Aside: The N pole is usually considered + (field lines radiate away from it).
You're right, it doesn't matter here.

http://www.youtube.com/watch?v=2ghBUcQG1lQ&feature=related -- (going outside the box now) I try and imagine this sort of force for the balance of the cylinders. Except this video would require nearly exact opposite forces lined perfectly. If these forces were, to some extent, at play in the magnets it would help explain why the exchange of force and energy is so well kept and balanced. And many other visual theories concerning the fields, along with why the theory convinced me that I could flip the pole on my compass with just two magnets and a quick motion, along with other things.

I also like to imagine the field of a single magnet as being something like this: http://apod.nasa.gov/apod/image/1006/redrectangle_hst_big.jpg ... (not saying it is, but eliminating or strengthening my theory by extreme amounts relies on a comprehension of what is going on in the center of those mirrored vortexes. Right now my best guess is that there is simply an extraordinarily efficient motion which holds itself well for a very long time. Though I need to believe myself much more than I currently do before it's worth considering any further without being told as to why it may or may not hold up under scrutiny.

Lastly... what you are saying does make sense to me well enough, however it would be more beneficial for my perspective to be scrutinized for what it is. I know that when openly going outside the box there is little safety around people who have far more experience than myself. Sometimes the professors I speak with remind me of the catholic school nuns who despised curiosity and questioning... in which case I simply thank them for their time and go. Other times I get ones who enjoy my sort of curiosity and do their best to help. I don't disappoint them and am not the type to "grind my axe"... or "troll" people.

 

[Simon Bridge]

I try and imagine this sort of force for the balance of the cylinders.

Um ... the video shows vortexes in a fluid: how would this relate to static magnetic fields?

If these forces were, to some extent, at play in the magnets

That is a pretty big "if"

it would help explain why the exchange of force and energy is so well kept and balanced.

Only it is not needed - we have a well-established EM field theory for that which is good enough to produce some quite tricky bits of technology - including the computer you are using to read PF.

I also like to imagine the field of a single magnet as being something like this:[Nasa pic]

... the NASA pic is just a glowy light pattern that looks nothing like a magnetic field for a bar magnet - what is it supposed to be of?

What is ti that leads you to believe that these images are useful for visualizing what happens in the balance of six magnets?

Though I need to believe myself much more than I currently do before it's worth considering any further without being told as to why it may or may not hold up under scrutiny.

That would be the opposite of scientific method - working out what is wrong with an idea is the first step ... there are very many possible ways that things could be, and the vast majority of them are wrong.

We can imagine all kinds of pretty pictures and patterns, even enjoy doing so, but that does not make them plausible let alone true or relevant. Part of the discipline in science is sticking to what the Universe shows us is happening at the expense of what we'd like. Anyway - the Universe usually has a better imagination than us and always knows more physics than we do.

If you want to know how things are known to work and the limits of what is known then I can help, but if you want to pursue fantastic claims and speculations I wish you luck and much enjoyment.

 

[Ntstanch]

Um ... the video shows vortexes in a fluid: how would this relate to static magnetic fields?

What is ti that leads you to believe that these images are useful for visualizing what happens in the balance of six magnets?

In short, this: http://www.scribd.com/doc/34317/Spintronics-The-Secret-World-of-Magnets-2006-by-Howard-Johnson -- By the time I had pretty much lost all momentum in making any progress while failing to destroy my curiosity in alternative concepts for more or less all of my highly enjoyable and imaginative ideas I came across this, and they appear to have at least confirmed the biggest part of what I was pondering (fluid like motion and vortexes being relative to magnetic fields). They also seem credible in their experience and what not.

That would be the opposite of scientific method - working out what is wrong with an idea is the first step ... there are very many possible ways that things could be, and the vast majority of them are wrong.

I can't break apart an idea without building one up.

If you want to know how things are known to work and the limits of what is known then I can help, but if you want to pursue fantastic claims and speculations I wish you luck and much enjoyment.

I'm trying to gain both. Like what was said before concerning Faraday... the former of your statement (above in quotes) alongside speculation currently perceived as fantastic. If I had a very solid argument for the square nebula and why it behaved as it did after a supernova (forming that shape), along with very specific and scientifically accurate explanations for three dimensional vortexes... well clearly we'd have more to work with. However, I don't, and what I like more often than not is to be told specifically why my idea is wrong logically at the least. In which case I can remove that part of the idea, or the idea entirely.

 

[Simon Bridge]

You realize that Howard Johnsons ideas amount to perpetual motion right?
His Secret World of Magnets has so many misconceptions, and omissions that it is hard to know where to start ... we can easily demonstrate that bar-magnet fields are not like he describes. He rejects iron filings as an indicator, which is silly because it follows directly from the definition of a magnetic field ... but you can do the same experiment with small magnets (as per the definition of the magnetic field) and also disprove what he claims.

How did you determine that these ideas "seemed credible"? What does that even mean?

These ideas have been discussed before.
eg. https://www.physicsforums.com/archive/index.php/t-103813.html

what I like more often than not is to be told specifically why my idea is wrong logically at the least

... however, there are many logical ideas that are also untrue of the world. We test ideas about the world empirically. Google for "philosophy of science".

 

[Ntstanch]

You realize that Howard Johnsons ideas amount to perpetual motion right?

I never figured to associate the two... seems completely illogical to compare any form of motion as perpetual given that sooner or later all motion breaks down, and can be (to my understanding) at best highly efficient motion. Err... so no. I didn't know he associated his ideas with perpetual motion.

How did you determine that these ideas "seemed credible"? What does that even mean?

They seemed credible partially on account of their education, along with the tools they had to map these things out. The information they gathered and theorized matched my own very closely... except I had a budget of about 300$ + thought experiments. And no formal education in the area at all really.

And the fluid video, with the right-left-right-left-right-left vortex motion holding itself together was something I lightly pondered as what might be a possible phenomenon in magnetism, and is what lead me to make the hexagon ring using real magnets in the first place. If the motion was fluid, but mirrored and opposite on the other end of the cylinder, over the length of the magnets the countering forces seemed like they would be equal at most every point allowing for it to behave just as I predicted. Of course I'm well aware that I may have predicted wrong, but still ended up with supporting evidence.

With that, I related to the nebula picture. Primarily, from a better angle: http://www.newscientist.com/data/images/ns/cms/dn11577/dn11577-2_450.jpg
It fit what I had visualized, two vortexes, mirrored... and something in the center that I can't figure out. And from what I've read, no one really knows what is going on in that nebula photo.

These ideas have been discussed before.
eg. https://www.physicsforums.com/archive/index.php/t-103813.html

... however, there are many logical ideas that are also untrue of the world. We test ideas about the world empirically. Google for "philosophy of science".

I know of empirical science and its philosophy, but I like to keep that in mind while contemplating natural philosophy. Also, thank you for the link to this other discussion... I take every effort to be proven wrong/prove myself wrong, but I prefer to be proven wrong similar to having my butt kicked until I know that every punch, take down, kick - etc I attempt is futile. One thing you notice at a tech school is how almost no one has this critical thinking aspect... if a professor told them down is the new up, 95% of a class with 250 students wouldn't even think to question him.

Also, what books would you suggest for the most in depth information of both fluids and magnetism? As a hobby, I do want to know as much well grounded knowledge as can be taught. And I look forward to this website and individuals like yourself to help me refine it... but I will let my imagination and creativity wonder into new perspectives of what is being taught. If I didn't it would just feel like learning to repeat what I was told.