Find the capacitance of a system of two indentical metal balls of radius `a` if the distance between their centres is equal to `b`, with `b gt gt a`. The system is located in a uniform dielectric wtih permittivity `epsilon`.

Explanation

When `b gt gt a` the charge distribution on each spherical conductor is practicaly unaffected by the presence of the other conductor. Then, the potential `varphi_(+) (varphi_(-))` on the positive (respectively negative) charge conductor is
`+ (q)/(4pi epsilon_(0) epsilon a) (- (q)/(4pi epsilon_(0) epsilon a))`
Thus `varphi_(+) - varphi_(-) = (q)/(2pi epsilon epsilon_(0) a)`
and `C = (q)/(varphi_(+) - varphi_(-)) = 2pi epsilon_(0) epsilon a`.
Note : if we require terms which depend on `(a)/(b)`, we have to take account of distribution of charge on the conductors.