How Far is Charge C from Charge A When the Force on It Is Zero?

[BuBbLeS01]

Homework Statement

Charge A and charge B are 3.00 m apart, and charge A is +2.00 C and charge B is +3.00 C. Charge C is located between them at a certain point and the force on charge C is zero. How far from charge A is charge C?

Homework Equations

The Attempt at a Solution

I am reviewing for my final and I can't remember how to do this! I wanted to use...
F = K*Q1*Q2 / r^2
But I can't have 0 in the denominator so I know I am missing something obvious...but I am not seeing it.

 

[lzkelley]

you're solving for when the NET force is zero. let A be charge of A, B be charge of B, and C for C, etc. distance d apart. so the distance from C to A is R1, and C to B is R2 then R1 + R2 = d.
and the 2 forces need to equal each other - i.e. F1 = kAC/(R1^2) = kBC/(R2^2) does that make sense?

 

[BuBbLeS01]

Well yea but I don't have R2? So I tried using like R2 = 3- R1 but I can't get that to work...

 

[lzkelley]

thats how you have to do it, R1 and R2 are linked by the constant d (3 in this case). you'll end up with a binomial or something that you can solve numerically if nothing else.
A/(R1^2) = B/(3-R1)^2