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

(a) `U_(2)=(a^(2)Q^(2))/(8 pi in_(0)R) ((1-a^(n))/(1-a))` where `a=R/(r+R)` (b) `U_(2) (n rarr oo) =(RQ^(2))/(8pi in_(0) r^(2))`