Four identical point charges are fixed at the four vertices of a square of side…
PHYSICS · Subjective · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
Four identical point charges +q are fixed at the four vertices of a square of side a placed in vacuum.
(a) Starting from first principles, derive an expression for the total electrical potential energy U0 of this four-charge configuration.
(b) A fifth charge Q is to be placed at the centre of the square such that the total electrical potential energy of the five-charge system becomes zero. Derive the required value of Q in terms of q.
(c) Using your result from part (b), find the work that would have to be done by an external agent to assemble all five charges from infinity at their specified locations.
(d) Comment on whether the configuration obtained in part (b) is energetically stable or unstable with respect to small displacements of the central charge. Give a reason for your answer.