Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 4 / 10A / b / i

The three fixed charges are related by rotations through $2\pi /3$ about the origin. Their three Coulomb's law forces on a charge placed at the origin have equal magnitudes and directions separated by $2\pi /3$, so their vector sum vanishes. Thusis an equilibrium point.