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## Homework Statement

A crystal is a periodic lattice of positively and negatively charged ions.

(a) Consider an infinite one-dimensional crystal of alternating charges +q and −q, separated by distance d:

**(+q)**--

_{d}--

**(-q)**--

_{d}--(

**+q)**--

_{d}--

**(-q)**--

_{-d}--

**(+q)**--

_{d}--

**(-q)**--

_{d}--

**(+q)**--

_{d}--

**(-q)**--

_{d}--

**(+q)**--

_{d}--

**(-q)**--

_{d}--

**(+q)**--

_{d}--

**(-q)**--

_{d}-- [...]

What is the potential energy per ion?

## Homework Equations

This is a second year electricity and magnetism problem set that I'm attempting ( found my professor's previous problem sets online, I haven't started the actual course - it starts in the Fall)

From first year, I know that the potential energy between two charges is V= kq

_{1}q

_{2}/r

## The Attempt at a Solution

I know I definitely don't have the answer (might need someone to "talk" me through it ) but this is what I was thinking.

If there is an infinite number of (+q) and (-q) sets , I could take an infinite sum of the potential of one set (so between one +q and -q )and then divide out by the number of ions. If n is the number of (+q) and (-q) sets then the number of ions would be 2n?

This seems wrong though, because there is potential between q1 and q2 and then q1 and q3 and q3 and q2, so on and so forth.