# Finding the charge when three charges are in equilibrium

1. Sep 2, 2014

### johnsch3

q1___________Q___________q2
10cm 10cm

In the figure above the charge in the middle is Q=-3.1nC. For what charge q1 will charge q2 be in static equilibrium?

Relevant equations
I think that F=kq1q2/r^2 is relevant

my attempt at a solution
Since the ions are in equilibrium I assumed that F=0. so F2onQ=F1onQ=0
thus kQq2/r^2=kQq1/r^2
so [(9x10^9)(3.1x10^-9C)(q2)]/.1^2=[(9x10^9)(3.1x10^-9C)(q1)]/.1^2

but I'm not quite sure where to go from here or if I'm even going in the right direction. Please help!

2. Sep 3, 2014

### jackarms

You're close with setting the two forces equal, but they aren't quite the correct forces to use. You want q2 to be in equilibrium, which means the forces you're going to be dealing with are those that act on q2. So that will be the force between Q and q2 and between q1 and q2. If you set up the force equations for those two pairs and then equate them, you should be able to solve for q1.

3. Sep 3, 2014

### johnsch3

okay, I re-set up the equations to look like
[(9x10^9)(3.1x10^-9)(q2)]/.1^2=(9x10^9)(q1)(q2)/.2^2

And I know that I have to solve for q1, but I dont understand how I am supposed to do that without the value for q2. How do I solve for q2 or is there something I'm not seeing where I don't have to know it?

4. Sep 3, 2014

### BiGyElLoWhAt

1) symbols man, they make things look so much prettier =]

2) whenever I have 2 unknowns I have to solve for, I always like to have 2 linearly independent equations. Makes things much easier, I've found.

5. Sep 3, 2014

### BiGyElLoWhAt

Let me try to summarize what I think you've said so far, and maybe you'll see what's going on with this.

$F = K \frac{q_1q_2}{r^2}$ is a relevant equation.

The charges are in equilibrium so we can say $\Sigma F = 0$

That being in mind $\Sigma F_{\text{ net on Q!!!!!}} = K \frac{Qq_1}{r^2} + K \frac{Qq_2}{r^2}$

[See anything yet?]

Now for some questions. How many forces act on each charge?
Therefore, how many forces should you have in the summation for each charge?

I'm trying to drop some hints without giving it away

P.S.
Can someone msg me and let me know why putting color tags in the middle of an equation makes the itex crap it's pants? I want to highlight certain elements i.e. subscripts but I can't... WTF ITEX

6. Sep 3, 2014

### ChiralWaltz

Try drawing and labeling the forces on q2.

Then set up your equation based on those forces, charges and distances.