At the beginning of the explanation for this problem, they set up a ratio among the electric field of the smaller sphere, and the electric field of the larger sphere. Why do they do this? The question for this problem states, "Charge is placed on two conducting spheres that are very far apart and connected by a long thin wire. The radius of the smaller sphere is 5 cm and that of the larger sphere is 12 cm. The electric field at the surface of the larger sphere is 590 kV/m. Discover the surface charge density on each sphere."