Talk:Earnshaw's theorem

message: I'm leaning toward reworking the first few paragraphs of the article to be more precise with respect to certain concepts: force versus potential energy, electric fields versus magnetic fields and the need to invoke other properties of these fields besides zero divergence. In particular, the article should be clear that magnetic fields are not inverse square force fields (or even force fields, per se - a magnetic field vector gives the potential energy of the reference dipole rather than the force on the reference dipole). In addition to zero divergence, it is also necessary to invoke either conservation of energy or zero curl (or possibly both for magnetic fields). If anyone is interested we can work together to craft some changes. Otherwise, I'll just have a go myself sometime in the next couple weeks. Compbiowes (talk) 05:27, 19 April 2008 (UTC)
thread_title:  More precise language in introductory paragraphs 

message: I have a question:
consider this problem:
Four poin charges q are placed on the corners of a square and one poin charge q is placed on the center of the square.
We want to consider the eqiblirium of centeral point charge in the direction of one diagonals of the square.
If you investigate low displasment, you can see that this charge has stabel equiblirium!
What is the connection of this problem with the Earnshaw's theorem ?
:That wouldn't be a stable configuration.  — Omegatron 14:41, 12 January 2006 (UTC)
replies: text: It's not stable in a plane either.  The test charge will shoot out in between two of the fixed charges, if it is the same polarity, or be attracted to one of them, if it's the opposite polarity.  It's an equilibrium, but it's not a stable equilibrium. — Omegatron 16:19, 22 January 2006 (UTC)
replies: text: You can visualize the potential in 2 dimensions as an infinite rubber sheet.  The 4 charges are vertical sticks underneath, pushing up the sheet to make peaks.  The saddle point between the sticks will be higher than the plane far away, so a marble placed there will tend to roll through one of the 4 valleys between the sticks.  You can generalize this image to any number of charges/sticks, with negative charges being sticks pushing the sheet down to make a hole.  There will be saddle points between the sticks, where a marble could sit stationary, but the slightest disturbance will cause it to either roll into one of the holes, or roll out into the plane far away.  As Omegatron says, unstable equilibria.  -- Chetvorno 03:16, 5 March 2006 (UTC)
replies: text: Continuing the rubber sheet analogy, imagine connecting the tops of the sticks with pieces of string so the strings hold up ridges in the rubber sheet. If the strings are connected diagonally then the surface of the rubber sheet will not have any depressions (a marble would be unstable). If the strings are connected along the sides and if the rubber sheet has weight then the rubber sheet will sag in the middle forming a depression (where a marble would be stable). Basically, either stability or instability is possible depending on the precise form of the potential. Playing around with MatLab and a point charge potential, I get the result that for this two dimensional case there will be a depression where a marble would be stable. Compbiowes 20:50, 20 October 2006 (UTC)

text: Possibly your introduction of weight in the rubber sheet, and/or strings, enabled you to create a depression.  To be analogous to a potential, the rubber sheet has to be uniform and of negligible weight itself, stretched tight, like a trampoline.  Under those conditions it shouldn't be possible to create a stable point with sticks. --Chetvorno 01:50, 24 December 2006 (UTC)

text: I calculated this gray-scale image of a slice of the potential surface around four point charges.  Compbiowes 17:28, 22 October 2006 (UTC)
thread_title:  a contradiction 

message: This isn't true on a periodic space right? I mean, I would think that 4 electrons on the surface of a sphere would spread out uniformly, forming a tetrahedron. 98.156.185.48 (talk) 03:08, 6 January 2024 (UTC)
replies: text: That is called Thomson problem.--ReyHahn (talk) 10:11, 6 January 2024 (UTC)
replies: text: Very interesting! Thank you. I guess for 3D periodic space the minimum configurations correspond to Bravais lattices 98.156.185.48 (talk) 21:01, 6 January 2024 (UTC)
thread_title:  Periodic space