Final answer:
The capacitance of two isolated conducting spheres far apart from each other is proportional to the sum of their radii. This is because each sphere's capacitance is considered separately and directly related to its own radius.
Step-by-step explanation:
The capacitance of two separate conducting spheres is determined by their sizes. When two spheres are far apart, such that they do not influence each other, the capacitance of each sphere is proportional to its radius. If the two spheres were to form a spherical capacitor, the capacitance of the combined system would depend on both radii, but since they are far apart, we consider them individually. Therefore, when considering the capacitance of two isolated spheres, it is proportional to the sum of the radii of the two spheres.
It is important to note that while the capacitances of more complex systems, such as parallel-plate, spherical, or cylindrical capacitors, have specific relationships with dimensions like plate area and separation distance, the question here refers to two isolated spheres. In such a case, each sphere's capacitance is independent and can be considered separately.
For a single conducting sphere, the capacitance C is given by C = 4πε₀r, where ε₀ is the permittivity of free space and r is the radius of the sphere. For the radii r1 and r2, the total capacitance when considered as isolated spheres would be proportional to r1 + r2, which is the sum of the radii.