An engineer is comparing two methods of arranging four identical point charges
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
An engineer is comparing two methods of arranging four identical point charges, each of magnitude q=1.0μC, inside a vacuum chamber of side length 0.50m. In Configuration I, the charges are placed at the four corners of a square of side 0.50m. In Configuration II, the charges are placed at the center of each side of the same square.
For each configuration, the charges are initially infinitely far apart and are brought in one at a time by an external agent that performs the minimum possible work consistent with electrostatic forces.
(a) Derive a general expression for the total electric potential energy of four identical charges located at the vertices of a square of side s.
(b) Using your result from part (a), calculate the total energy for Configuration I.
(c) Derive an expression for the total electric potential energy of four identical charges located at the midpoints of the sides of a square of side s (Configuration II).
(d) Compute the total energy for Configuration II using s=0.50m, and compare it quantitatively to Configuration I.
(e) Based on your comparison, recommend which configuration should be chosen if the engineer’s goal is to minimize stored electric potential energy. Justify your recommendation with reference to the calculations and physical reasoning.