The work required for adding a charge to an infinite charge distribution

Deeviance

1. The problem statement, all variables and given/known data

Find the energy required to add an additional charge to the chain
in the limit where the total number of charges approaches infinity.

So, I have a equidistant linear charge distribution like + - + - + -..... where the total number of charges approaches infinity. The charges are being brought from an infinite distance to there spot in the charge distribution.

What is the energy required to add a charge on to the "end" of it?

2. Relevant equations

Electric force = k(Q1Q2)/d^2
work = Integral of (Fdot Dr) from path begin to path end


3. The attempt at a solution

I wish I could more here, but its one of these problems that I can't set up, so I can't really give an attempted solution but here are my thoughts.

(backed up by nothing but my intuition)

It will be a finite number as most of the force due to charge distribution will cancel out.

It will be close to the amount of energy required to add a charge to a single charge distribution because of the cancellation.



Any direction would be much appreciate.

clem

Use potential. The work equals q V.
V is an infinite sum of alternating sign with terms like 1/n.