Chapter 22, Problem 45AP

Two small spheres of mass m are suspended from strings of length ℓ that are connected at a common point. One sphere has charge Q and the other charge 2Q. The strings make angles θ₁ and θ₂ with the vertical. (a) Explain how θ₁, and θ₂ are related. (b) Assume θ₁ and θ₂ are small. Show that the distance r between the spheres is approximately

$r={\left(\frac{4k_e{Q}^2\mathcal{l}}{mg}\right)}^{1/3}$