Of the charge Q on a tiny sphere, a fraction @ is to be transferred to a second , nearby sphere. The spheres can be treated as a particle

What value of @ maximizes the mag F of the electrostatic force b/w the two spheres???

 hi,

let @ fraction is transferred to other sphere , charge on the other will be = Q@

   charge remained  on the  first one = Q -Q@ = Q(1-@)

   force between the spheres , F = 

                                              = k . Q@ *    Q(1-@) /  r^2

       let k / r^2 be another const k2

  F  =    k2  Q@ *    Q(1-@)

dF/d@ = k2 . Q^2 ( 1 - 2@) 

d^2 F / d@^2 = k2 . Q^2 ( - 2)

      so for a max.   put dF/d@ = 0 

  gives ,  @ = 1/2 

 for this  d^2 F / d@^2 is also <0

so for @ =1/2 we will have max. force