Three identical point charges are fixed at the vertices of an equilateral triangle of…
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
Three identical point charges +q are fixed at the vertices of an equilateral triangle of side length a. A fourth point charge Q is placed at the geometric center of the triangle (the point equidistant from all three vertices).
(1) Derive an expression for the total electric potential energy Utot of the four–charge system in terms of k, q, Q, and a. Present your result in fully simplified form.
(2) For the special case Q=−q, determine the numerical factor multiplying kq2/a in your expression for Utot. Leave radicals in exact form rather than decimal form.
(3) Given Q=−q, find the value of a (in terms of k and q) for which the total potential energy is zero. Explain the physical significance of this result with respect to the net work required to assemble the system.