Two conducting spheres with radii $$r_1 = 5\ \text{cm}$$ and $$r_2 = 10\ \text{cm}$$ are initially isolated. The first sphere has charge $$Q_1 = 3\ \text{nC}$$, and the second has charge $$Q_2 = -1\ \text{nC}$$. If the spheres are connected by a thin conducting wire and then separated, what will be the final charge on the smaller sphere?