There are three fixed (immobile) charged particles in the \(xy\)-plane: a particle with charge \(+q\) at \((x,y) = (0,1)\), a particle with charge \(-q\) at \((x,y) = (-1,0)\), and a particle with charge \(-q\) at \((x,y) = (1,0)\).
In addition, there is a free (movable) charge of \(+q\) initially at rest at \((x,y) = (0,0)\).
If the net Coulomb force from the three fixed charges is the only force influencing the free charge, determine the maximum distance the free charge travels from the origin \((0,0)\) before it starts to come back.
Give your answer to 2 decimal places.
Details and Assumptions:
- Neglect units and assume that all physical equations take their simplest possible forms.