I was having a discussion with my friend the other day. He had just attended a lecture about Paul traps. He told me that the Paul trap potential has a stationary point in the middle, which is a saddle point, and that the 2 pairs of opposite poles are oscillating between being positive and negative, such that the 'hills' and 'valleys' of the potential are constantly switching place. Then anything placed near the saddle point will find itself on a slope most of the time and thus be relatively trapped. When i asked why it had to be a saddle point and not just a constant minimum, he said that it was because it is impossible to create a consant electromagnetic potential well. I remember hearing a bit about this during my introductory electromagnetism course. But that was well over a year ago and i can't remember the argument for this. A google search didn't give me anything either. So is there a law or an equation you can point me to, which will make this obvious to me? Maybe it comes out easily from one of Maxwell's equations. I took EM1 and EM2 (which makes it slightly embarassing that i don't know this) so you know my prerequisites for understanding your explanations.