A conducting sphere `S_1` of radius `r` is attached to an insulating handle. Another conduction sphere `S_2` of radius `R` is mounted on an insulating stand. `S_2` is initially uncharged. `S_1` is given a charge `Q` brought into contact with `S_2` and removed. `S_1` is recharge such that the charge on it is again `Q` and it is again brought into contact with `S_2` and removed. This procedure is repeated `n` times.
a. Find the electrostatic energy of `S_2` after `n` such contacts with `S_1`.
b. What is the limiting value of this energy as `nrarroo` ?

Answer

(i) `U_(n)=(q_(n)^(2))/(8 pi epsi_(0)R)` here `q_(n)=(QR)/(r)[1-((R)/(R+r))^(n)]`
(ii) `U_(infty)=(Q^(2)R)/(8 pi epsi_(0)r^(2))`