Four point charges are to be located at the corners of a square of side that lies in…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential
Problem
Four point charges are to be located at the corners of a square of side a=6.0cm that lies in the xy–plane with its center at the origin. Starting from infinity, the charges are placed sequentially in the following order:
• Charge A: +4.0μC at the upper right corner (+a/2,+a/2)
• Charge B: −4.0μC at the upper left corner (−a/2,+a/2)
• Charge C: +4.0μC at the lower left corner (−a/2,−a/2)
• Charge D: +4.0μC at the lower right corner (+a/2,−a/2)
(a) Derive an algebraic expression, using k, q, and a, for the net work an external agent performs while bringing in Charge B after Charge A is already fixed at its corner.
(b) Determine the numerical value of the work found in part (a).
(c) Calculate the additional work required to bring in Charge C, given that Charges A and B are fixed.
(d) Compute the additional work required to bring in Charge D, completing the square configuration.
(e) Using your preceding results, obtain the total electric potential energy of the fully assembled four–charge configuration.
(f) Suppose Charge A were doubled to +8.0μC while the other three charges remained unchanged. Without re–calculating every pair interaction, explain how the total potential energy would scale relative to the value found in part (e).