Two conducting spheres, one having twice the diameter of the other, are separated by a distance large compared to their diameters. The smaller sphere (1) has charge q and the larger sphere (2) is uncharged. If the spheres are connected by a long thin wire and come to equilibrium:

Question

Quizplus · Accepted Answer

When the wire connects the two spheres, charge will flow from sphere 1 to sphere 2 until they both reach the same potential. Since the spheres are made of the same material and are in the same environment, their capacitances are proportional to their radii. Thus, since sphere 2 has twice the diameter of sphere 1, its capacitance is four times larger than sphere 1's capacitance. Therefore, it will require four times the amount of charge to have the same potential as sphere 1. Because of this, charge will flow from sphere 1 to sphere 2 until the potential of both spheres is equal. Thus, choice A is correct, as both spheres will have the same potential after reaching equilibrium.

Two Conducting Spheres, One Having Twice the Diameter of the Other