# Maximum Excursion

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.