Solving Coulomb's Law: Using Mass, Length, and Charge

[Watsonb2]

Homework Statement

Given: Two similar tiny balls of mass M are hung from silk threads of length L and carry equal charges q. An angle is formed where the two threads meet which we'll call $$\phi$$ (This angle is actually divided in half and each half is called $$\theta$$)

Assume that $$\theta$$ is so small that tan $$\theta$$ can be replaced by its approximate equal, sin $$\theta$$.

I'm supposed to show that, for the following approximation, the distance between the two charges, x, in equilibrium, is equal to:

x = [((q^2)L) / 2 $$\pi$$ $$\epsilon$$sub 0 (m)(g)]^(1/3)

Homework Equations

Obviously, Coulomb's Law plays a major role in determining the outcome of this problem, but I'm yet unsure of where and how I actually apply it...

Since mass is given to us, I assume that I'll have to use F = ma or some derivation of it to find the force that will be used in Coulomb's Law...

The Attempt at a Solution

Since they give the length of the thread, I figure that 1/2 x is going to be equal to the tangent of $$\theta$$, but since tan is to be replaced with sin, I'm not exactly sure where this leaves me...

I really didn't know where to start with this one, so, even if you can offer direct advice, even a point in the right direction would be nice...

 

[rl.bhat]

In equilibrium position, the ratio of the forces to the sin of opposite angle are constant.
In the problem the forces are tension T, electrostatic force F and weight of the balls mg.
Identify the angles opposite to these forces and apply above rule.

 

[Watsonb2]

Thanks, I was able to get the right answer, I appreciate the helpful tip.

-B