Electric field inside an infinitely long cylinder.

AI Thread Summary
The discussion focuses on proving that the electric field inside an infinitely long, uniformly charged cylinder is zero without using Gauss's law. A method involving drawing a narrow cone from a point to the cylinder's surface is presented, where the electric field contribution from a differential area is calculated. The challenge arises in attempting to sum the contributions from opposite sides of the cylinder, as they do not cancel out due to varying distances. It is noted that if the point is not on the cylinder's axis, the cone will intersect different areas at different distances, complicating the analysis. The conclusion emphasizes the difficulty in achieving a net field of zero using this approach.
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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?
 
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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.
 
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