Particle 1 carrying charge \(4 q\) is fixed at the origin of an \(x y\) coordinate system, and particle 2 carrying charge \(q\) is fixed at \((0,0.12 \mathrm{~m})\). Particle 3 carrying \(2.0 \mu \mathrm{C}\) of charge can move along the \(y\) axis. This particle experiences zero electric force when at \(y=0.080 \mathrm{~m}\) and an electric force of \(126.4 \mathrm{~N} \hat{j}\) when at \(y=0.040 \mathrm{~m}\). What is the value of \(q\) ?