PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Four identical positive point charges, each of magnitude q, are fixed at the corners of a square of side length L. A physicist wishes to remove the charge at the top right corner (call this charge q4) from the square. Two different proposals are considered:
• Proposal 1: Move q4 very slowly to an infinite distance away along a straight line perpendicular to the plane of the square.
• Proposal 2: Move q4 very slowly to a point located a distance h directly above the center of the square, keeping the other three charges fixed in their original positions.
Assume h>0 and h≪L so that q4 remains relatively close to the square in Proposal 2.
(a) Derive an expression, in terms of k, q, and L, for the initial total electric potential energy of the four–charge configuration before q4 is moved.
(b) For Proposal 1, derive the work that must be done by an external agent to remove q4 to infinity. Express your result using k, q, and L.
(c) For Proposal 2, derive an expression for the new total electric potential energy of the four–charge system after q4 has been moved to the point a distance h above the center of the square. Keep your answer in symbolic form and include all contributing pairs.
(d) Compare the work required in Proposals 1 and 2. Discuss, with reasoning based on your derivations, which proposal requires the external agent to do more work and why.