Minimal energy configurations for charged particles on a thin conducting disc: the perimeter particles

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The lowest energy configurations for N equal charged particles confined to a thin conducting disc have been investigated in detail up to N=160 and in outline for further values up to N=500. For all values of N up to 160 the particle configurations can be described in terms of concentric shells. The number of perimeter particles p appears to be simply related to N and to the mean radius of the outermost internal shell. Justification for these relations is obtained from a simple model based on the well-known distribution of continuous charge on a conducting disc.