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We discuss several results in electrostatics: Onsager's inequality, anextension of Earnshaw's theorem, and a result stemming from the celebratedconjecture of Maxwell on the number of points of electrostatic equilibrium.Whenever possible, we try to provide a brief historical context and references.

Around a theorem of F. Dyson and A. Lenard: Energy Equilibria for Point Charge Distributions in Classical Electrostatics