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

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!