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 \epsilonsub 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