5 positivly charged particles on sphere, min energy configuration, rel

[Spinnor]

Assume 5 charged particles (charge 1) constrained to live on the surface of a sphere are in a configuration that minimizes electrostatic potential energy. Are there configurations that are stable but that are not the minimum energy configuration?

A simple computer program could quickly(?) examine many random configurations and slowly map out the potential energy surface E(θ_1,phi_1,θ_2,phi_2,θ_3,phi_3,θ_4,phi_4,θ_5,phi_5)?

There must be more elegant(less computer time) ways to find the minimum energy configuration?

Has this problem been solved?

Edit, E above is a function of only 8 variables, we can always let one particle be at the north pole?Thanks for any help!

 

[Simon Bridge]

It's called "the Thomson Problem".
http://en.wikipedia.org/wiki/Thomson_problem

 

[Spinnor]

It's called "the Thomson Problem".
http://en.wikipedia.org/wiki/Thomson_problem

Triangular dipyramid Nice and symmetric, I should have seen that. Things probably get more interesting with larger numbers. From the link above check out a fun Java app at,

http://thomson.phy.syr.edu/thomsonapplet.php

Check out the screen shot and add a charged particle and watch the charges rearrange to I assume the lowest energy configuration. Still would like to know if there are stable relative minimum.

Edit, I think you have to hit the Auto button on the app to get the configuration to minimize energy?

Thanks for your help!

 

[Simon Bridge]

Nice find!