I'll be honest, I've never really understood the "why" of Earnshaw's Theorem. Why can't a charged particle be held in equalibrium with only electrostatic forces? If I have six charges arranged in at the corners of a hexagon and put a charge at the center, why can't it just stand there since the electric field is zero at that point? What is the reasoning/justification for this theorem? Does it apply to gravitostatic forces as well?