Chapter 23, Problem 50CP

Identical thin rods of length 2a carry equal charges +Q uniformly distributed along their lengths. The rods lie along the x axis with their centers separated by a distance b > 2a (Fig. P23.30). Show that the magnitude of the force exerted by the left rod on the right one is

$F=\left(\frac{k_e{Q}^2}{4a^2}\right)\ln \left(\frac{b^2}{b^2-4a^2}\right)$

Figure P23.50