Investigation of the steady equilibrium state of three charged body system in the gravitational field

In 2014 the following problem was proposed on the All-Ukrainian
physics Olympiad. Three equally charged bodies are hanged on three threads of equal
length. In equilibrium angles between the first two threads and the vertical line equals 20°,
angle between the third thread and the vertical line equals 14°, see Fig. 1. The question is to
describe the steady equilibrium state after the increasing of the charge of each particle in 2014
times. The author solution of the problem is an approximate one and it is based on the fact
that after such increasing the Coulomb forces become much greater than the gravity ones. In
this work we generalize this problem in the case where the charge of each particle increases in
n times in comparison with the initial value, n>1 is an arbitrary number.