Suppose a particle with charge q is confined to the x-axis but moves completely freely along that axis. It interacts electrostatically with two charged particles (with the same charge q) anchored to positions y=±L, respectively, along the y-axis.
(a) Find an expression for the system’s potential energy Vx as a function of L, the Coulomb constant 1/4πε0, q, and the sliding object’s position x.
(b) Find any equilibrium point or points for this Vx, and specify whether each is stable or unstable