How to find distance between 2 charges, with no force given?

[Blooper]

Homework Statement

Three charges q1 q2 and q3 are set along the x-axis. q1 is at the origin and q2 is at r = 11.3mi

If q1 = +2.0C, q2 = +1.5C, and q3 = -2.3C, where must q3 be placed so that the net force on it is zero? In other words, the position of q3 is r3 = di, and you must find d. Answer in meters.

Homework Equations

F = k(q1*q2)/r^2

The Attempt at a Solution

I believe if I was given the force between the two, this question would be easy, but since no force is given, I'm not sure how to rearrange Coulomb's Law to isolate r (distance).

 

[haruspex]

I believe if I was given the force between the two, this question would be easy,

The actual values of the forces are irrelevant. All that matters is that they balance.
However, you do have enough information to find the forces in terms of the unknown coordinate.
Write out the expressions for the two forces.

 

[BesselEquation]

Homework Statement

Three charges q1 q2 and q3 are set along the x-axis. q1 is at the origin and q2 is at r = 11.3mi

If q1 = +2.0C, q2 = +1.5C, and q3 = -2.3C, where must q3 be placed so that the net force on it is zero? In other words, the position of q3 is r3 = di, and you must find d. Answer in meters.

Homework Equations

F = k(q1*q2)/r^2

The Attempt at a Solution

I believe if I was given the force between the two, this question would be easy, but since no force is given, I'm not sure how to rearrange Coulomb's Law to isolate r (distance).

Start by writing ΣF = 0 for the system, from there, solve for the uknown r