Electrostatics-- spheres leaking charge 1. The problem statement, all variables and given/known data Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length d. The distance between the spheres x << d. Find the rate dq / dt with which the charge leaks off each sphere if their approach velocity varies as v = a / √x, where a is a constant. 2. Relevant equations Coulomb's law, F = ma. 3. The attempt at a solution Approximating the gravity term since x << d, we can write k q^2 / x^2 - mg x / (2d) = m a. We could solve this for q and find dq / dt, etc. However, I only get the correct answer (from the back of the book) if I set a = 0, i.e. the spheres are in equilibrium as they fall toward each other. I also see the assumption of equilibrium made in other solutions of this problem on the web. Why is this assumption justified?