Determine the capacitance of a system consisting of a metal ball of radius `a` and an infinite conducting plane separated from the centre of the ball by the distance `l` if `l gtgta`.

Explanation

As in 0.109 we apply the method of image. Then the potential difference between the +vely charged sphere and the conducting plane is one half the nominal potential difference between the sphere and its image and is ltbr. `Delta varphi = (1)/(2) (varphi_(+) - varphi_(-)) = (q)/(4pi epsilon_(0) a)`
Thus
`C = (q)/(Delta varphi) = 4pi epsilon_(0) a`. for `l gt gt a`.