Chapter 21, Problem 92GP

A one-dimensional row of positive ions, each with charge +Q and separated from its neighbors by a distance d, occupies the right-hand half of the x axis. That is, there is a +Q charge at x = 0, x = +d, x = +2d. x = +3d, and so on out to ∞. (a) If an electron is placed at the position x = −d, determine F, the magnitude of force that this row of charges exerts on the electron. (b) If the electron is instead placed at x = −3d, what is the value of F? [Hint: The infinite sum ${\displaystyle \underset{n=1}{\overset{n=\infty }{\sum }}\frac{1}{n^2}}=\frac{{\pi }^2}{6}$, where n is a positive integer.]