Two tiny conducting balls of identical mass m and identical charge q hang from non-conducting threads of length L. Assume that $\displaystyle \theta$ is so small that $\displaystyle \tan{\theta}$ can be replaced by its approximate equal, $\displaystyle \sin{\theta}$.

(a) Show that

$\displaystyle x = \left(\frac{q^2L}{2\pi\epsilon_0 mg}\right)^{\frac{1}{3}}$

gives the equilibrium separation x of the balls.

(b) If L = 120cm, m = 10g, and x =5.0, what is |q|?