I admit that I have something of a block when it comes to Electromagnetism, but this question is so basic it's really bugging me. So time to throw my pride aside.
I have a member at PHF that asked me if an exterior non-uniform charge distribution can create an electric field inside a closed surface. My initial answer was "no" based on Gauss' Law because I could swear I've done a number of them. However it is true that a single point charge outside the surface generates an electric field inside the surface. My problem is that the net flux through the surface is 0, but I thought that implied that E was also 0? There's a big flaw in my reasoning but I can't seem to find it.
Addendum: As I've been typing there's something that's trying to worm its way into my head. I've leave the question as posted. If I figure it out I'll let you all know the hows and whys.