Question

Consider two identical spheres P and Q with charge q on each. A third sphere R of the same size but uncharged is successively brought in contact with the two spheres. What is the new force of repulsion between P and Q?

Answer 1

Charge on two spheres will be equally divided on two sphere each times on touching. 

When R is kept in contact with R, charge q is equally distributed between P and R.

Charge on p = q/2

Charge on  R = q/2

When R is kept in contact with Q, total charge will again be equally distributed.

Initial force of repulsion between P and Q

Final force of repulsion between P and Q