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

  1. Dec 31, 2013 #1
    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!
     
  2. jcsd
  3. Jan 1, 2014 #2

    Simon Bridge

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  4. Jan 2, 2014 #3
    Triangular dipyramid :uhh: 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!
     

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  5. Jan 2, 2014 #4

    Simon Bridge

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    Nice find!
     
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