Four point charges are fixed at the corners of a square of side length
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
Four point charges are fixed at the corners of a square of side length a. Beginning at the upper-left corner and moving clockwise, the charges are +Q, −Q, +Q, and −Q.
Neglect all external influences.
(1) Derive a symbolic expression for the total electric potential energy Usquare of the four-charge system in terms of k, Q, and a. Express your result as a single simplified fraction or sum.
(2) Without substituting numerical values, state whether Usquare is positive, negative, or zero, and justify your conclusion by referencing the contributing pairwise interactions.
(3) If the side length of the square is uniformly increased to 2a while the charges remain fixed at the corners, explain qualitatively (without full recalculation) how the magnitude and sign of the total electric potential energy change.