Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 2 / 16D / c / Solution

Successive reflections in the two grounded planes require four charges:Their total charge and electric dipole moment vanish. Applying the second-order expansion from part (a), the terms proportional to $a^2{x}^2$, $b^2{y}^2$, and $a^2+b^2$ also cancel, while the mixed terms add. ThusThis is an electric quadrupole potential.