Electrostatic force including coulombs law

[th3plan]

Homework Statement

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 1/2 of the maximum possible value?

The Attempt at a Solution

ok i drew a picture and i know that sphere 1 is Q-q , and sphere 2 is q, and i plug into equation

F=k(Q-q)q/r^2

i differentiate and get qQ-2q now what i do from here, to get 1/2 maximum possible value

i know to get maximum i set equal to zero, do i set this equal to 1/2? How would i solve it for q/Q ratio if its equal to 1/2?

 

[granpa]

Q is a constant. just set it equal to 1. same with r.