Electric Field and Electrostatics

Answer
$K*e^2/r^2 = K*2e^2/(R-r)^2$
$(R-r)^2 = 2r^2$
$R^2- 2Rr +r^2 -2r^2 =0$
$r^2 + 2Rr -R^2 =0$
$r = -R +sqrt{(R^2+R^2)} = -R +R*sqrt{2} = 0.414*R = 0.41421*43.70 =18.1011 nm$
$f = K*e^2/r^2 =9*10^9*(1.6*10^{-19})^2/(18.1011*10^{-9})^2 =7.03*10^{-13} N$