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Geometry |
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Authors: Theophilus Agama
In this paper we study the global electrostatic energy behaviour of mutually repelling charged electrons on the surface of a unit-radius sphere. Using the method of compression, we show that the total electrostatic energy $U_k(N)$ of $N$ mutually repelling particles on a sphere of unit radius in $mathbb{R}^k$ satisfies the lower boundbegin{align} U_k(N)gg_{epsilon}frac{N^{2}}{sqrt{k}}.onumberend{align}.
Comments: 9 Pages.
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[v1] 2022-07-14 00:51:48
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