# Electric potential energy question

1. Sep 2, 2009

### fluidistic

I've done an exercise that made me think a bit.
So the electric potential energy of a 1 dimensional crystal (lattice?) formed by alternating ions is about $$\frac{-ke^2 \ln 2}{a}$$. So as it is a negative number, I would have to do some work to separate the charges composing the crystal and the crystal is stable.
But what if the infinite sum is worth $$0$$?
I know that I need no work to take one charged particle from infinity to anywhere, so the electric potential energy of the particle would be $$0$$... but what if I have a system of charged particles with a total electric energy equal to $$0$$? Is this hypothetical system stable? What does that mean that its electric potential is null?