Two small spheres, each carrying a net positive charge, are separated by 0.400 m. You have been asked to perform measurements that will allow you to determine the charge on each sphere. You set up a coordinate system with one sphere (charge q₁) at the origin and the other sphere (charge q₂) at x = +0.400 m. Available to you are a third sphere with net charge q₃ = 4.00 × 10^-6 C and an apparatus that can accurately measure the location of this sphere and the net force on it. First you place the third sphere on the x-axis at x = 0.200 m; you measure the net force on it to be 4.50 N in the +x-direction. Then you move the third sphere to x = +0.600 m and measure the net force on it now to be 3.50 N in the +x-direction.

(a) Calculate q₁ and q₂.

(b) What is the net force (magnitude and direction) on q₃ if it is placed on the x-axis at x = -0.200 m?

(c) At what value of x (other than x = {q) could q₃ be placed so that the net force on it is zero?