Four tiny insulating beads are constrained to lie along a straight, frictionless rod. The beads are fixed at equal separations s, so that the distance between adjacent beads is s. You are given three different charge assignments to the beads as shown below (left-to-right order along the rod):
Assignment A +q−q+q−q
Assignment B +q+q−q−q
Assignment C +2q−q+q0 (the fourth bead is neutral)
No external fields are present, and only the listed charges interact.
a. Rank the total electric potential energy of the four-bead system for the three assignments from the most positive value to the most negative value. Use the format A > B > C, inserting “=” if any are equal.
b. Explain the reasoning behind your ranking, explicitly addressing how both (i) opposite-sign versus like-sign interactions and (ii) the presence of a neutral bead influence the total potential energy.