A laboratory demonstration involves assembling four identical point charges of value…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A laboratory demonstration involves assembling four identical point charges of value q at the corners of a square of side length a. The charges start infinitely far apart, and an external agent moves them slowly so that no kinetic energy remains when the configuration is complete.
After completing the demonstration, the instructor repeats the process with the same magnitude charges but arranges them so that each charge is adjacent to two charges of opposite sign (i.e., the pattern +q,−q,+q,−q around the square).
(1) Calculate the total work Wsame done by the external agent in assembling the first configuration (all charges +q). Express your answer in terms of k, q, and a.
(2) Calculate the total work Walt required for the second configuration (alternating signs). Express your answer in the same variables and provide the exact numerical coefficient.
(3) Using your results, determine the ratio WsameWalt. Explain what this ratio indicates about the relative amounts of electrical potential energy stored in the two charge distributions.
(4) Suppose the instructor wishes to modify the alternating–sign square so that the net work required to assemble it is zero. Propose and justify one change to the magnitudes or signs of the charges (keeping four point charges on the square’s corners) that would accomplish this goal.