Electric field inside an infinitely long cylinder.

[soulreaping]

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 surface3. 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?

 

[HallsofIvy]

If your point is not on the axis of the cylinder, your cone will have two different distances to the cylinder and cover two different areas.