Consider an infinite chain of point charges, ±q (with alternating signs), strung out along the x axis, each a distance a from its nearest neighbors. Find the work per particle required to assemble this system. [Partial Answer: −αq2/(4πϵ0a), for some dimensionless number α; your problem is to determine α. It is known as the Madelung constant. Calculating the Madelung constant for 2- and 3-dimensional arrays is much more subtle and difficult.]