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 [tex]\phi[/tex] (This angle is actually divided in half and each half is called [tex]\theta[/tex])
Assume that [tex]\theta[/tex] is so small that tan [tex]\theta[/tex] can be replaced by its approximate equal, sin [tex]\theta[/tex].
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 [tex]\pi[/tex] [tex]\epsilon[/tex]sub 0 (m)(g)]^(1/3)
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 [tex]\theta[/tex], 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...