Help with Coulomb's Law problem needed.

1. May 13, 2007

frankfjf

1. The problem statement, all variables and given/known data

In Fig. 21-26, particle 1 of charge +1.0 microCoulombs and particle 2 of charge -3.0 microCoulombs are held at separation L = 10.0cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3?

Fig 21-26 (Sorry, couldn't format the L right, but it's basically the distance between particles q1 and q2.)

-Oq1-------Oq2- X
<----L--->

2. Relevant equations

F31x + F32x = 0.

3. The attempt at a solution

Since this is only on the x axis, I already know that the answer to b is zero because otherwise equilibrium would be impossible, so really I'm concerned with a. I've eliminated common factors and converted units and end up with an equation looking like 1E-6/x^2 = 3E-6/(L-x)^2. After taking the square roots of both sides to further simplify, I've got something like .001/x = .002/(L-x).

At this point I should be able to solve for x and then plug in L to get my answer, but how can I isolate x here? Did I do something wrong?

Last edited: May 13, 2007
2. May 13, 2007

Mentz114

.001/x = .002/(L-x).

Multiply both sides by x

.001 = x*.002/(L-x)

multiply both sides by (L-x)

.001*(L-x) = .002*x

Can you get x now ?

3. May 13, 2007

frankfjf

Ah, yes I can. Thanks!