We draw a free-body diagram for one of the charged balls, say left. This is shown in the figure below.
All the forces acting on the charged ball are in equilibrium.
One force is tension
Equating the magnitude of vertical component of tension with weight of the ball we get
and equating the magnitude of horizontal component of tension with the magnitude of electrostatic force we get
Dividing (2) by (1) we get
It is given that the angle between the silk threads is small (
From the geometry of the figure we see that
Using (4) and (5) equation (3) reduces to
Substituting the value of Coulomb's constant