# 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: \( \ln(1+x)=-\sum_{k=1}^{\infty} (-1)^{k} \frac{x^{k}}{k}\).