Earnshaw's theorem doesn't apply here. What you've done is provide a mechanical constraint, namely the plastic that holds the magnets in position. This is analogous to having a hollow cylindrical tube and dropping two cylindrical magnets into it with opposite orientation. Obviously the top one will levitate. It "wants" to flip over, but can't because of the external mechanical constraint of the plastic. Your magnets "want" to flip over, but can't because of the external mechanical constraint of the plastic. It's a nice experiment and it looks cool, but you're not going to violate Earnshaw's theorem because it's derived directly from Gauss' law. You could do similar "violations" with induced currents, servos, diamagnets, gyroscopic stabilization, or strong focusing, all of which are outside the realm of applicability of Earnshaw.
Warning: small amounts of vector calculus ahead. I consulted Griffith's electrodynamics (4th Ed.) as a reference and problem 3.2 asks you to justify Earnshaw's theorem in one sentence. It's referring to the single particle variant: *A charged particle cannot be held in a stable equilibrium by electrostatic forces alone.* You see why, right? Because the Laplacian of the electrostatic potential is zero, hence there is no curvature and hence no extrema, except at the singularities on the sources of charge themselves. *note: Since ferromagnets in the ideal case are governed by an inverse square law like electrostatics and gravity, you can still use Gauss' law to derive the zero Laplacian and justify Earnshaw for any of these.
Harrigan actually designed this same system, identically. As you no doubt have established for yourself, this does not work (in this video there is a point touching so not a complete gap). This configuration cannot settle into true free levitation, the top magnets will always slide off in one direction or another. Given this is true it would make sense to state as much in the description.
I like the experiment and the discussion. But as Ty Stovall pointed out, the problem is that there are other forces involved. Earnshaw's theorem is really a statement about the nature of static magnetic and/or electric fields and charge. By nature, I mean the "shape" of the electric or magnet fields. If there is a local minimum (i.e. "well") in one direction, then in another direction there will necessarily be a slope or even a maximum of the field. There cannot be a "well" in all directions such that a charge will just fall into the well and stay. As Peter DeSimone described early in the video, the theorem seems to apply to more than just point charges (like magnetic rings, etc.) and it is often stated as an explanation. In some sense it is part of a correct explanation but not necessarily a complete or absolutely correct explanation. The Wikipedia quote shown in the video regarding gravity is an incorrect application of Earnshaw's theorem. Earnshaw's theorem does not describe other forces (gravity included) especially in combinations. Since different arbitrary "force fields" can be created which do not obey the rules of the electric and magnetic fields alone, then different arrangements can indeed be created which seem to "defy" one particular physical theorem or law. But that is no more true in this case than claiming that an airplane "defies" gravity by breaking the laws of physics. However, the Wikipedia article does mention that the law can be applied to extended objects, so Ty's assertion that the connecting elements are the problem is not complete either. I assert that it is a combination of the connected system AND gravity. It is gravitational force which is keeping the two components from moving apart and/or flipping around due to electro-magnetic forces. Earnshaw's theorem is not a complete description of the universe in which charges and electromagnetic fields exist. A full description of a physical system often includes other physics, hence, other mathematics. Peter already mentioned in the video the correct consideration of this problem... that Earnshaw's theorem is just misinterpreted.
Really cool that you found a way to make a system which seams to levitate by itself! How is the project going now? i would love to try it myself! What were the dimensions and N types of the magnets used? Thanks for this sick stuff!!
Stijn IJssel de Schepper thanks! i have moved on to other projects, but i suppose i should come back to this one at some point and see if i can improve it. i don't remember the exact magnet dimensions; i bought them in bulk on Amazon. i recall that the outer diameter of the "pucks" was the same as the inner diameter of the "doughnuts". cheers!
Very nice Pete! This made me think about levitating a single puck magnet. The magnetic well caused by a toroid seems to be a very stable configuration for the puck magnet, only flipping is not prevented. So what if we rigidly attach a weight to the puck magnet such that the centre of gravity is low enough that flipping is prevented. In my imagination this would work, do you see any problems with this setup?
Really cool that you found a way around Earnshaw's Theorem! But this is not a counter example. According to scienceworld.wolfram.com, Earnshaw's Theorem states that, "A collection of point charges cannot be maintained in an equilibrium configuration solely by the electrostatic interaction of the charges." Though your system is definitely in a stable equilibrium state, the fact that the magnets are held together by an apparatus means that there there is a nonmagnetic force acting on them.
Dude! I am pretty sure that the Earnshaw's theorem especially states that a stable equilibrium cannot be achieved 'solely' by electrostatic field. So the magnetic levitation statement is often incompletely understood, because the earth's gravitational field cannot be neglected which balances the magnetic forces forces by us here on earth. Hence, the actual magnetic levitation misinterpretation should be corrected. I read +Cade Perkins' post after typing the whole thing, but I'm totally in agreement with him.
Hi Peter. "Contain" a pole of the magnets by iron & aluminium foils (several, alternated, 0,3mm or so each one of them), leting you get more stability in your experimenting. Try it, please.
I am not sure about your experiment sir because you have places an object on top which is enough to stop the flipping of magnets , but I do appreciate the efforts you have put into it , and this can be proved with just one magnet levitating on the other there is no need for a triangular structure.
There is a VERY easy way of levitating something using a fixed magnetic field (permanent magnet): use a diamagnetic material. This is not as much of a loophole as it is a material for which the theorem can't be applied.
Fun to consider the idea that physical law has been violated, but this demonstration as others have said does not violate Earnshaw's theorem. Other forces are active here, and therefore the premises of Earnshaw's theorem are not satisfied (and thus Earnshaw's theorem doesn't apply).
beautiful stuff, yeah the torque required to flip it over will be way too much. Will be awesome if you can increase that gap, try using neodymium magnets XD
This is quite interesting but if you check out U.S. Patent #5319336 you will see Mr. Alcon actually used aluminum to manifest a locked levitated system. Langley Group at NASA (Nelson Groom) were very impressed. Energy savings for a train system is much much better than the existing levitated systems in use today. The annual International Symposium for Eddy Currents would be most interested in the field of eddy flux lines manifesting from this assembly. Also includes magnetic propulsion & braking systems. Worth taking a look at.
I'm a 11 grader in hopes of comming up with ways to maximize repulsion between any orientation of magnets for my local science fair. If anyone knows of any website to assist me that would be pretty cool. Thank you.
+KrispyGomaha all i can tell you is, if you stack a bunch of magnets together, their magnetic force will combine, and the repulsion will be much stronger. ;-)
and there are mani more ways to levitate normal magnets i found mi own way to levitate them and i worck now to make a generator but im missing the things i need it wil take me time until i ghet em all miself
if i ever get around to making another video on this topic, it will involve an improved prototype. no sense making another vid of this same device, seeing as how narrow the gap was. people would just continue to question its veracity. if i make another vid, it will be because i achieved a gap sufficiently wide that there is no doubt. but, seeing as i'm just a few weeks away from graduating summa cum laude, and seeing that i just launched a new venture ( www.MuzzleSafe.com ) that is garnering investors, winning awards, and is about to launch a commercial product, i can't say when that will be. cheers.
Harrigan proposed this idea in his patent. It does not work. You've deluded yourself into thinking that the gap is small but in fact at least part of the top member is touching the bottom somewhere.
thanks, i will look into that. i haven't played with it for years, but i was never able to achieve a definitively large gap, so that would explain that.
Earnshaw's theorem doesn't apply here. What you've done is provide a mechanical constraint, namely the plastic that holds the magnets in position. This is analogous to having a hollow cylindrical tube and dropping two cylindrical magnets into it with opposite orientation. Obviously the top one will levitate. It "wants" to flip over, but can't because of the external mechanical constraint of the plastic. Your magnets "want" to flip over, but can't because of the external mechanical constraint of the plastic.
It's a nice experiment and it looks cool, but you're not going to violate Earnshaw's theorem because it's derived directly from Gauss' law. You could do similar "violations" with induced currents, servos, diamagnets, gyroscopic stabilization, or strong focusing, all of which are outside the realm of applicability of Earnshaw.
Warning: small amounts of vector calculus ahead.
I consulted Griffith's electrodynamics (4th Ed.) as a reference and problem 3.2 asks you to justify Earnshaw's theorem in one sentence. It's referring to the single particle variant: *A charged particle cannot be held in a stable equilibrium by electrostatic forces alone.* You see why, right? Because the Laplacian of the electrostatic potential is zero, hence there is no curvature and hence no extrema, except at the singularities on the sources of charge themselves.
*note: Since ferromagnets in the ideal case are governed by an inverse square law like electrostatics and gravity, you can still use Gauss' law to derive the zero Laplacian and justify Earnshaw for any of these.
thank you for the wise and thoughtful reply! that appears to be the consensus.
Just learnt about Earnshaw's theorem and here I am to watch how to break it. ;p
Oh same ,,, came here from griffiths electrodynamics :p
Harrigan actually designed this same system, identically. As you no doubt have established for yourself, this does not work (in this video there is a point touching so not a complete gap). This configuration cannot settle into true free levitation, the top magnets will always slide off in one direction or another. Given this is true it would make sense to state as much in the description.
I like the experiment and the discussion. But as Ty Stovall pointed out, the problem is that there are other forces involved. Earnshaw's theorem is really a statement about the nature of static magnetic and/or electric fields and charge. By nature, I mean the "shape" of the electric or magnet fields. If there is a local minimum (i.e. "well") in one direction, then in another direction there will necessarily be a slope or even a maximum of the field. There cannot be a "well" in all directions such that a charge will just fall into the well and stay. As Peter DeSimone described early in the video, the theorem seems to apply to more than just point charges (like magnetic rings, etc.) and it is often stated as an explanation. In some sense it is part of a correct explanation but not necessarily a complete or absolutely correct explanation. The Wikipedia quote shown in the video regarding gravity is an incorrect application of Earnshaw's theorem. Earnshaw's theorem does not describe other forces (gravity included) especially in combinations. Since different arbitrary "force fields" can be created which do not obey the rules of the electric and magnetic fields alone, then different arrangements can indeed be created which seem to "defy" one particular physical theorem or law. But that is no more true in this case than claiming that an airplane "defies" gravity by breaking the laws of physics. However, the Wikipedia article does mention that the law can be applied to extended objects, so Ty's assertion that the connecting elements are the problem is not complete either. I assert that it is a combination of the connected system AND gravity. It is gravitational force which is keeping the two components from moving apart and/or flipping around due to electro-magnetic forces. Earnshaw's theorem is not a complete description of the universe in which charges and electromagnetic fields exist. A full description of a physical system often includes other physics, hence, other mathematics. Peter already mentioned in the video the correct consideration of this problem... that Earnshaw's theorem is just misinterpreted.
Cool! Have you done more experiments since this?
well that's great. congratulations for your efforts! hope that you will be recognized with it soon :)
Really cool that you found a way to make a system which seams to levitate by itself!
How is the project going now? i would love to try it myself! What were the dimensions and N types of the magnets used?
Thanks for this sick stuff!!
Stijn IJssel de Schepper thanks! i have moved on to other projects, but i suppose i should come back to this one at some point and see if i can improve it. i don't remember the exact magnet dimensions; i bought them in bulk on Amazon. i recall that the outer diameter of the "pucks" was the same as the inner diameter of the "doughnuts". cheers!
Very nice Pete! This made me think about levitating a single puck magnet. The magnetic well caused by a toroid seems to be a very stable configuration for the puck magnet, only flipping is not prevented. So what if we rigidly attach a weight to the puck magnet such that the centre of gravity is low enough that flipping is prevented. In my imagination this would work, do you see any problems with this setup?
I was thinking about the exact same thing. Is this experiment already disproven by somebody or?
Really cool that you found a way around Earnshaw's Theorem! But this is not a counter example. According to scienceworld.wolfram.com, Earnshaw's Theorem states that, "A collection of point charges cannot be maintained in an equilibrium configuration solely by the electrostatic interaction of the charges." Though your system is definitely in a stable equilibrium state, the fact that the magnets are held together by an apparatus means that there there is a nonmagnetic force acting on them.
Dude! I am pretty sure that the Earnshaw's theorem especially states that a stable equilibrium cannot be achieved 'solely' by electrostatic field. So the magnetic levitation statement is often incompletely understood, because the earth's gravitational field cannot be neglected which balances the magnetic forces forces by us here on earth. Hence, the actual magnetic levitation misinterpretation should be corrected. I read +Cade Perkins' post after typing the whole thing, but I'm totally in agreement with him.
briliant one of those why didn't i think of that moments lol
Can this help in a new design for Ion Traps in Mass Spectrometers?
As other commenters have pointed out this doesnt violate earnshaw's theorem. None the less this is very clever.
Hi Peter.
"Contain" a pole of the magnets by iron & aluminium foils (several, alternated, 0,3mm or so each one of them), leting you get more stability in your experimenting. Try it, please.
+Ignacio Valle cool, thanks for the tip! i may just try that.
Peter Alaric
You're welcome.
I am not sure about your experiment sir because you have places an object on top which is enough to stop the flipping of magnets , but I do appreciate the efforts you have put into it , and this can be proved with just one magnet levitating on the other there is no need for a triangular structure.
There is a VERY easy way of levitating something using a fixed magnetic field (permanent magnet): use a diamagnetic material.
This is not as much of a loophole as it is a material for which the theorem can't be applied.
Fun to consider the idea that physical law has been violated, but this demonstration as others have said does not violate Earnshaw's theorem. Other forces are active here, and therefore the premises of Earnshaw's theorem are not satisfied (and thus Earnshaw's theorem doesn't apply).
beautiful stuff, yeah the torque required to flip it over will be way too much. Will be awesome if you can increase that gap, try using neodymium magnets XD
if u did came whit this 4 years ago how come no one seen it ?
Interesting. I built a very similar structure in 2016. Unfortunately, it does not work as described above.
if you have pictures or make a video, please let me know. i'd love to check it out!
This is quite interesting but if you check out U.S. Patent #5319336 you will see Mr. Alcon actually used aluminum to manifest a locked levitated system. Langley Group at NASA (Nelson Groom) were very impressed. Energy savings for a train system is much much better than the existing levitated systems in use today. The annual International Symposium for Eddy Currents would be most interested in the field of eddy flux lines manifesting from this assembly. Also includes magnetic propulsion & braking systems.
Worth taking a look at.
Boss.
Every time you erase something on the board, my tooth hurts =(
the metod i found it have free spin so i can easy make a electricity generator
btw peter gj u are doing nice try to investigate magnets are the future
I'm a 11 grader in hopes of comming up with ways to maximize repulsion between any orientation of magnets for my local science fair. If anyone knows of any website to assist me that would be pretty cool. Thank you.
+KrispyGomaha all i can tell you is, if you stack a bunch of magnets together, their magnetic force will combine, and the repulsion will be much stronger. ;-)
and there are mani more ways to levitate normal magnets i found mi own way to levitate them and i worck now to make a generator but im missing the things i need it wil take me time until i ghet em all miself
Why not show your experiment? You seem to have built all the stuff and say it's levitating but I see no real proof.
the gap was narrow, and at the time i did not have a video camera capable of macro shots, so i took photos and dropped them into the video instead.
Then wish you can update the video someday with a better experiment of the same device, would be nice.
if i ever get around to making another video on this topic, it will involve an improved prototype. no sense making another vid of this same device, seeing as how narrow the gap was. people would just continue to question its veracity. if i make another vid, it will be because i achieved a gap sufficiently wide that there is no doubt. but, seeing as i'm just a few weeks away from graduating summa cum laude, and seeing that i just launched a new venture ( www.MuzzleSafe.com ) that is garnering investors, winning awards, and is about to launch a commercial product, i can't say when that will be. cheers.
@@PeteLaric Great idea and nice effort, but lets face it - it didn't levitate! :)
5225
oh and triangles!!! ILLUMINATI!!!!!!
To me you debunked his theorem, congratulations
you're about 4 years too late, I already came up with this particular method, sorry to burst your bubble
Mario Mackinnon did you by any chance publish your work? i'd be interested to check it out!
Peter DeSimone type in stable levitation with permanent magnets, am about to start the second phase of this very soon
Harrigan proposed this idea in his patent. It does not work. You've deluded yourself into thinking that the gap is small but in fact at least part of the top member is touching the bottom somewhere.
thanks, i will look into that. i haven't played with it for years, but i was never able to achieve a definitively large gap, so that would explain that.