14a: It is impossible to have a stable equilibrium in electrostatics. This idea is known as Earnshaw's Theorem. Let's prove this fact. Assume that at a particular point P that

a charge Q is in a stable equilibrium. Think about the direction of È necessary for the equilibrium. Now use Gauss' Law with a spherical gaussian surface centered on P. Show that this leads to a contradiction. b: Imagine a square in the xy plane with a point charge Q fixed at each corner. Now put latest charge q in the exact center of the square. Imagine that you push q in some direction and then release it from rest. For what direction(s) would the charge move back toward the center of the square (in other words, the system is stable to perturbations in those s directions)? Similarly, for what direction(s) would the charge move further away from the center3