Three identical metallic beads A, B, and C possess charges \(q_{1}, q_{2}\), and \(q_{3}\), respectively. All the three beads are affixed on a meter scale where A lies at \(0, B\) lies at \(60 \mathrm{~cm}\), and C at \(100 \mathrm{~cm}\). In this configuration, if all the three beads attain electrostatic equilibrium, then find the charge ratios of \(q_{2}\) to \(q_{3}\).