This result dating to 1842 asserts that a charge in a static electrostatic field can never be in a stable equilibrium. In spite of many partial results a complete proof was first given in 1987. The present talk concerns generalizations from Section 116 of Maxwell's treatise. There Maxwell explains why a rigid charged body or a perfect conducting body or a dielectric body in a static field can never be in a stable equilibrium. We prove the result for conductors and dielectrics. The charged rigid body remains open.

This joint work with G. Allaire appeared in the Archive for Rational Mechanics in 2017. Speaker(s): Jeff Rauch (Umich)