Two conducting spheres having radii R₁ and R₂ are placed widely apart from one another. Determine their individual capacitances. Furthermore, if a metal wire connects the spheres, what is the capacitance of the combination? (Consider the setup in terms of series-parallel connections.)

Step-by-step solution

The capacitance of an isolated spherical conductor of radius R is given by C = 4 ₀ R . For the two spheres of radii R₁ and R₂ , their individual capacitances are C₁ = 4 ₀ R₁ and C₂ = 4 ₀ R₂ . When the two spheres are connected by a metal wire, they acquire the same potential. The second plate for each spherical capacitor is considered to be at infinity, which is at a common zero potential. This means the two capacitors are effectively connected in parallel. The equivalent capacitance of the combination is the sum o