There are two conducting spheres of different charge and a conducting wire. After they are connected by the wire, charge flows between the spheres. The charge distributes itself so that the spheres are at the same potential, but I have not been able to find an explanation for this. Why wouldn't the charge be distributed so that the electric field is the same, since that is what is moving the charges in the wire?
Voltage is electrical pressure. Think about two tanks of water, one big and other small both connected by a pipe. Now if you connect the two, water will flow between the two till the level is same in the two tanks. Similarly, charge will flow till the metal sphere are at same potential.