Question: Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated a particles. For what value of q/Q>0.5 will the electrostatic force between the two parts have 1/5 of the maximum possible value? Attempt: F = [ k(Q-q)(q) ] / r^2 dF/dq = (k/r^2) d/dq(Qq - q^2) = (k/r^2)(Q-2q) = 0 Q - 2q = 0 q = (1/2)Q --> Thus, this will give me the maximum electrostatic force between the two particles. However, the question is asking about the situation where it is 1/5 of the maximum value. So, F = [ k(Q-q)(q) ] / r^2, and using q = (1/2)Q or 2q = Q, F/5 = [k(2q - q)(q)] / 5r^2 = (kq^2) / 5r^2 --> This is 1/5 of the maximum force. Thus, to find q/Q: F = [ k(Q-q)(q) ] / r^2 = (kq^2) / 5r^2 and I found q/Q to be 0.83333. This answer is wrong, however. Can anyone point me in the right direction?