Suppose we have two negative charges, one located at the origin and carrying charge −9e, and the other located on the positive x-axis at a distance d from the first one and carrying charge −36e. Determine the location, polarity and magnitude of a third charge whose placement would bring the entire system into equilibrium.

It would have to be in between the two charges and be positive for force on 9e to be zero

k 9e q/x^2= k 36e 9e /d^2

q/x^2 = 36e/d^2

q = 36e x^2/d^2

Now we need force on 36e to be zero

k 36e q/(d-x)^2 = k 36e 9e/d^2

q/(d-x)^2 = 9e/d^2

36 x^2/d^2 = 9/d^2 (d-x)^2

36 x^2 = 9 (d-x)^2

x=d/3

q = 36e (d/3)^2/d^2 = 36e/3^2 = 4 e

answer:

put more,