PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential
Problem
Four identical point charges, each of magnitude q, are fixed at the corners of a square of side length a. The charges are initially infinitely far apart and are brought in one at a time until the square is fully assembled.
(1) Derive an expression for the total electric potential energy Usq of the completed configuration in terms of k, q, and a. Show all steps in your reasoning.
(2) Express your final answer in the most compact exact form possible, combining like terms and factoring numerical coefficients where appropriate.
(3) Explain briefly whether the work you calculated depends on the specific assembly path chosen, and justify your answer using appropriate electrostatic principles.