Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What is their individual capacitance? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series-parallel connections.
The radius of conducting sphere 1 =R1
Radius conducting sphere 2 =R2
First, we need to calculate the capacitance of isolated charged sphere.
Formula used :
The capacitance of a sphere is given by the formula
Where
C is the capacitance of the capacitor
ε₀ is the permittivity of the free space is ε₀=
Taking limits as aR and b∞, Capacitance of charged sphere is found by imagining the concentric sphere with an infinite radius having some -Q charge).
The capacitance of isolated charge sphere is
The capacitance of isolated charge sphere 1 is
The capacitance of isolated charge sphere 2 is 
If the two spheres are connected by a metal wire, then the charge will flow one sphere to another up to their potential becomes the same.
The potential will be the same only when they are connected in parallel. So two spheres are connected by a metal wire in parallel.
The capacitance of individual spheres of radius R1 and R2 is C1=4πε₀R1 and C2=4πε₀R2 respectively.
Combinational capacitance when charged spheres are connected by a wire is 4πε₀R1+R2).