Why dF/dq is equal to zero for the force to be maximum in the problem below:A charge Q is divided into two parts of qand Q-q if the coulomb repulsion between them when they are seprated is to be maximum the ratio of Q/q should be

It''s a basic result. For a point to be local maximum, the tangent at that point must be zero. Tangent is given by dF/dQ. 

Approve if i helped :)

R/2^1/2

IT IS BECAUZ THE AREA UNDER THE CURVE OF FORCE VS CHARGE GRAPH GIVE POTENTIAL AND DF/DQ GIVE TANGENT AT A PARTICULAR POINT AND IF SLOPE OF TANGENT AT A POINT IS 0 OR MINIMUM THEN FORCE WILL BE MAXXXXXXXXX..........