# Breaking the chain

Electricity and Magnetism Level 3

Consider an infinite chain of alternating charges ( $$+q,-q,+q,-q \ldots$$) and spacing $$d$$. It is known that the interaction energy between two neighboring charges is $$E_{p}=-1~\mbox{J}$$. What is the work needed in Joules to remove one of the charges from the chain and place it at infinity?
Hint: $$\ln(1+x)=-\sum_{k=1}^{\infty} (-1)^{k} \frac{x^{k}}{k}$$.

×