In this post, I consider a bar of infinite length with a finite charge, a charged particle, and examine what is the electromagnetic pull between the two. The situation is no more fuzzy than this:
Given a point on the -axis (representing the charged bar), the distance between it and the charged particle is given by
where is the distance of the charged particle from the charged bar. By Coulomb’s law the scalar force between two charged objects with charges and is
where is the Coulombs’s constant, and is the distance between the two particles.
We assume that the charged bar has constant charge density: all subchunks of equal length has equal charge. Now it is easy to see that if basic bar component of length has the charge of , we can write
Since and are considered constants, the above expression approaches zero as .