so let it be at a distance x from the half of line ab

the force will be         and this will be along the hpothenese    the horizontal components of te forces will cancel each other out

and the total force will be the sum of the vertical component of the forces  =

and here    r²=x²+d²/4                    and costhetha=

solving we get          Qx/(x²+d²/4)^3/2

for MAXIMUM value     d/dx  x/(x²+d²/4)^3/2=0

solve and get the answer