- #1

fluidistic

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## Homework Statement

The configuration is as follows: there's a charge q separated by another charge q (the distance is a) which is separated by a charge -q. And it continues to infinity. The distance of separation is always "a" and all the charges are linearly situated. I must show that for r>>a, the potential can be written as [tex]V(r)=k \left [ \frac{q}{r}+\frac{2qa}{r^2} \right ][/tex]

**2. The attempt at a solution**

I'm a bit confused about the distribution of charges. On the sketch, there's "..." after the 3 first charges. Hence I guess the configuration is q---q---(-q)---q---q---(-q)---q...

My other doubt is... what did they take as V(0)? It seems like the first charge, but I'm not sure. My intuition tells me what I'll have to depreciate terms of order greater than 2 at some moment.

The potential of a single charge q is [tex]\frac{kq}{r}[/tex]. Of the 2 first charges of the problem: [tex]\frac{kq}{r}+\frac{kq}{r+a}[/tex]. Of the 3 first: [tex]\frac{kq}{r}+\frac{kq}{r+a}-\frac{kq}{r+2a}[/tex]. But I don't think I'm going into the right direction to solve the problem.

I'd appreciate a very little tip. Thanks.