1. Prove, without using Gauss's law, that the field inside an infinitely long, uniformly charged cylinder is zero. 2. Electric field of a charged surface 3. My lead is that from a given point, I draw a very narrow cone to any piece of area on the cylinder, with distance r away.. That creates a piece of area dA, and assuming the charge density is σ0, that piece of area is inducting a field given by E = k*σ0*dA / r^2. Now I've tried to continue the line to the other end, but couldn't manage to come up with anything that would cancel the field.. Any help?