Final answer:
The voltage at the surface of the two connected metal spheres will be the same because the system must be an equipotential due to the thin wire connection. The charge rearranges so that the surface charge density is inversely proportional to the radius of each sphere, resulting in uniform electric potential across both surfaces.
Step-by-step explanation:
When two metal spheres, connected by a thin wire, have different radii, and they are far apart, the charge will redistribute till each sphere has the same electric potential (voltage). According to the relationship given by 01 R₁ = 02 R₂, the surface charge density is inversely proportional to the radius of the sphere. Considering both spheres reach an equipotential due to the wire connection, the voltage at the surface of both sphere A (with radius R₁) and sphere B (with radius 2R₁ or R₂) will be the same despite their differing sizes. This result is consistent with the concept that the electric potential for a charged sphere only depends on the total charge and the radius, not the distribution of that charge over the surface. As such, the charge will arrange itself in such a way that the voltage is uniform across the surfaces of both spheres due to their conductive connection.