I'm hoping this is an appropriate question for this forum since its related to coursework. If not, sorry in advance! I've been going through Purcell and managed to get through the first two chapters (with unanswered questions here and there but still looking!) but with Chapter 3 (Conductors & Capacitors), I've hit a dead end when it comes to solving ANY problem. I've tried watching various YouTube videos and different resources but it seems like I just end up being familiar with specific examples and cases rather then how to apply the Uniqueness Theorem (or even Gauss). For example, this video right here has an example: http://www.youtube.com/watch?v=gKf2szoEEBE&t=13m34s My questions are: 1) What new knowledge does equating the two conductors to having no charge offer? After some head scratching, I can see why that's the only other case, outside of the infinite possibilities of distributing charge on the surface and the varying magnitudes of the charge. 2) What exactly are the boundary conditions? My rudimentary understanding is that the potential is constant for the surface and(/or?) charge in a conductor can be distributed in any manner. 3) I'm also having specific trouble applying Gauss' Theorem and Uniqueness Theorem together. I've read somewhere a cavity within a conductor has an electric field of zero but when I try to think about concentric spherical shells, I'm not sure if it holds true. 4) Also, is Gauss' Theorem only applicable for some sort of infinite entity? For example, a finite line charge SHOULD have an electric field in the direction of its extension so there is a flux but with infinite fields, the argument is they cancel out at the ends? Or is this correct.