Find Position of Charge 3 in Two Charge System

[fsm]

Homework Statement

Two charged particles, with charges q_1=q and q_2=4q, are located a distance d apart on the x axis. A third charged particle, with charge q_3=q, is placed on the x-axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3.
Find the position of charge 3. Assume that all three charges are positive.

So charge 3 could be inbetween charge 1 and 2, or to the left of charge 1. The problem wants me to find "2 possible VALUES" of charge 3. How can i find a value when no values were given to me in the word problem. THey want the X_3,1, and X_3,2 in terms of Q, D, and K (coulomb constant).

Homework Equations

$$F_{\textrm{2 \,on \,3}} = k\frac{q_2 q_3}{d-x_3} = k\frac{4q^2}{d-x_3}$$
and
$$F_{\textrm{1 \,on \,3}} = k\frac{q_1 q_3}{d-x_3} = k\frac{q^2}{x_3^2}$$

The Attempt at a Solution

For an answer I get 4q^2 and -d

It says that -d is wrong. I figure out what I'm doing wrong.

 

[Kurdt]

First of all I would like to point out that electrostatic force is proportional to the inverse square of distance. Secondly, what is this d - x₃ business? define the force on 3 from 2 as the following and go from there.

$$F_{23}=k\frac{q_2q_3}{x_{23}^2}$$

You will have to work out how to relate that distance with d and the distance from the first charge.

 

[fsm]

I know that electrostatic force is proportional to the inverse square of distance. As for as the d-x_3 business that how the problem is defined and how the problem is to be answered. Those were the constraints put on me. The first two equations are correct because that was part a and part b. I could not continue the rest of the problem if those two equations were wrong. From there I set the two equations equal and get a quadratic equation. 4q^2 is correct and verified. The second part of the answer is where thing are not right.

 

[Kurdt]

Ok sorted I know why its d-x and so forth. I've worked through myself and I get x will be d/3 and -d so I can't see why they say its not correct. Also asking for the answer in terms of k and q is a bit strange since they cancel. Perhaps if you posted your working it would be easier to diagnose the problem.