Electric forces, net force = zero

[johnnyies]

Homework Statement

Three charges lie along the x -axis. The positive charge q1 = 10.0 microC is at x = 1.00 m, and the negative charge q2 = -2.00 microC is at the origin. Where must a positive charge q3 be placed on the x-axis so that the resultant force on it is zero?

Answer: x = - 0.809 m

Homework Equations

Columb's Law
F= k q1 q2
- - - - - -
r^2

k = 8.9875 x 10^9

The Attempt at a Solution

Force of 1 acting on 3 = - k q1 q3 / (1 - x)^2
Force of 2 acting on 3 = k q2 q3 / x^2

k q2 q3 / x^2 - k q1 q3 / (1 - x)^2 = 0

k's and q3's cancel out and I get

q2(1 - x^2) = q1(x^2)
-2(1 - 2x + x^2) = 10x^2
-2 + 4x - 2x^2 = 10x^2
12x^2 - 4x +2 = 0

x = .167 m

Needing a bit of help in setting this one up perhaps. No solutions guide is available. Can someone have a more conceptual explanation on how to solve this one?

 

[johnnyies]

the problem seems to be a negative sign but I can't see where.

 

[rl.bhat]

Since q1 and q2 are having opposite signs, There cannot be a zero field in between them. Bur you can have a zero field out side the two charges and the point is closer to the smaller charge. So rewrite your equation by taking (1 + x) rather than (1 - x).