# Ring magnets levitation question

1. Aug 24, 2011

### carmatic

consider the image i have uploaded, it shows 4 ring-shaped magnets of different sizes
each pair of concentric magnets are held in position relative to each other, and the lower pair is also affixed to the ground, i.e. the upper pair of magnets is free to move

blue and red faces show the polarity of the magnets, and furthermore assume that the magnetic strength is uniform across the magnets, like any good magnet should be.... it can be seen that the pair of magnets will be repelling each other

the outer upper magnet is smaller than the outer lower magnet, while the inner upper magnet is larger than the inner lower magnet

my question is, if the upper pair of magnets are released exactly directly above the lower pair, will they be in a stable magnetic levitation?

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Last edited: Aug 24, 2011
2. Aug 24, 2011

### DaveC426913

It will flip over and then stick together. You could prevent this by setting it spinning quickly enough for gyroscopic forces to take effect.

3. Aug 24, 2011

### carmatic

ah thanks, i have forgotten to consider flipping

but what if the upper magnets levitating at a height which is less than the radius of the outer upper magnet, so that in order to flip the upper magnets will have to be raised above their equilibrium height?

Last edited: Aug 24, 2011
4. Aug 24, 2011

### DaveC426913

Alternately, you could make three of these and rigidly link them into a triangle.

5. Aug 24, 2011

### carmatic

thanks for your input, i can see that making a triangle shape out of 3 of these four-ring-magnet arrangements is quite elegant, it could be used for things like creating a very vibration-free platform if diamagnetic conductors are placed so that currents are induced in them when they are exposed to fluctuations in the magnetic field due to the vibration of the lower magnets, and so will cancel out or absorb the vibrations

another idea i have is to 'hang' an object with considerable mass but with negligible magnetic activity below the upper magnets, this would cause the center of mass to be lower than the center of lift , and i think it should also prevent flipping from happening
i am trying to find a way so that i can have a resistance-free rotating platform

6. Aug 24, 2011

### DaveC426913

Yes. Many ideas would work. But it would be cool to tweak the thing down to its most basic and simplest components. The more self-contained the unit is, the more elegant, economical and marketable it would be.

Hanging a mass below the centre-line would be quite awkward for most purposes to which you might want to put the thing.

7. Aug 24, 2011

### carmatic

so in terms of keeping it simple... would simply getting the upper pair of magnets to levitate low enough so that it could not flip without being raised , work?

i understand that theres definitely a relationship between the levitation height and the radii and maybe thickness of the magnets, which would mean that the levitation height would have to be less than the radius of the upper magnets, because the attraction of the magnets is enough to transiently lift the upper magnets in the process of flipping it over
am i right?

8. Aug 24, 2011

### DaveC426913

Lowering it won't make it less flippy - well, not a lot less flippy anyway - it's still unstable.

9. Aug 24, 2011

### Delta Kilo

Stable http://en.wikipedia.org/wiki/Magnetic_levitation" [Broken]. I have one of these, it's really cool.

Last edited by a moderator: May 5, 2017
10. Aug 24, 2011

### DaveC426913

I have seen a levitation that is not spin stabilized. It is quite delicate, but there in no question it was levitating.

OK, actually suspended. Does that count?

Last edited by a moderator: May 5, 2017
11. Aug 24, 2011

### Delta Kilo

Well, not really. It's an active feedback system. It has batteries and on/off switch in the base. When the power goes out the globe falls down.

12. Aug 24, 2011

### DaveC426913

Yes. I don't see that as a disqualifier.

13. Aug 24, 2011

### Delta Kilo

Well it's no longer a static arrangement of permanent magnets, which was what the OP was asking about.
It has an electromagnet and a control circuitry in it.

14. Aug 24, 2011

### carmatic

the floating globe uses an AC current to create a rapidly fluctuating magnetic field which is such that the region of lowest energy for a magnet, oriented in some way within the globe, is slightly above where the globe is, to account for the pull of gravity... earnshaw's theorem says that it is not possible to stably levitate static magnets, and having a rapidly fluctuating magnetic field means its not a static at all

i was thinking that by using some way of imposing a mechanical constraint, such as rigidly making 3 of these ring arrangements into a triangle, or having a ballast, would also exempt it from earnshaw's theorem

but having the rings levitate low enough so that flipping is not possible, yet having the lower magnets wider apart so that the upper magnets would be repulsed from any horizontal displacement, seems like a special case...

15. Aug 25, 2011

### DaveC426913

OK well, what difference does it make what Earnshaw says if, in the end, we have a levitating object?

His theorem applies to a specific case, namely permanent magnets, and presumably a simple configuration. This, on the other hand, is an engineering problem.

16. Aug 25, 2011

### chrisbaird

No configuration of static permanent magnets, no matter how cleverly arranged, can produce stable levitation. While exploiting symmetries may seem intuitively to create equilibrium points (just add more rings!), it will always be a point of unstable equilibrium, like trying to balance a ball on the tip of a stationary spear.

17. Aug 25, 2011

### DaveC426913

Right. Intuitively, I first thought that the triangle of structures might work (we're talking permanent magnets here). Upon reflection, you're surely right. The whole device won't remain stationary; it will simply slide off to the side and then collapse, positives to negatives.

You could produce a stable configuration if you physically constrained the device (say, by placing it in a cylinder, so it couldn't slide off) however, that's a pretty limited form of levitation, since it would physically be in contact (if minutely) with the container wall.

18. Aug 27, 2011

### carmatic

thanks for the replies, people

i get it that there needs to be some form of non-magnetic constraint to stabilize a magnetic levitation

but with having a pair of rings both at the top and at the bottom... suppose that the gap between the bottom rings are wide enough that the top rings can fit between them, both pairs of rings will avoid overlapping each other and collapse into the same plane because the magnets are attracted side-on... if the formerly upper pair of magnets fit loosely in the lower magnets, the upper magnets will be displaced to the side until contact is made with the lower magnets... but if it is a snug fit, then the magnets will be perfectly centered

then suppose the top and bottom pairs of rings having the same diameters , this is the balancing a ball on a spear situation

but what if there is an intermediate state between these , that there is repulsion from the partial overlap of magnets, yet there is an attraction towards the center caused by the fractions of the magnets which do not overlap

now, if there is nothing holding the upper pair of magnets fixed relative to each other and enforce the gap between them, then it is reasonable that there would be no stability whatsoever

Last edited: Aug 27, 2011
19. Sep 2, 2011

### carmatic

is it ok for me to put out a request for someone who regularly works with physics simulation packages to do a quick check for how valid this is?

20. Sep 4, 2011

### carmatic

actually yes you guys are right, ive installed a 2d static modelling program and it does indeed say that any offset will produce a net force in the direction of the offset

however, the machine i have which these magnetic rings are part of , is a spinning machine

my next question would be if the rings were spinning, but too slow to have any appreciable gyroscopic effect compared to the magnetic forces....
also, supposing that the rings of magnets are instead discrete magnets arranged regularly as a ring

if this ring of magnets were to be surrounded by a 'cylinder' of non-ferromagnetic conductive material such as aluminum, the non homogenous rotating field would induce eddy currents in the cylinder , which would in turn oppose the movements of the magnets...

due to the non linear relationship between flux density and distance, i think that the rotation as well as the induction effect would act to center the ring of magnets... but this would come at an energy loss for as long as the frequency of induction is low enough for the induction to take place... the higher the rate of rotation, the higher the frequency of induction , the less current is induced and therefore the less energy loss

am i correct?