The force acting on a spehere due to gravity that causes it to want to swing back to the center is

.

[ EDIT - I Originally had sin (theta) - should be tan (theta) ]

The combined electrostatic force from spheres B and C acting on A in the direction that A swings out is:

Where

The

factor comes from the fact that the force from sphere B acting on A has magntude in the outward direction of

times the electrosatic force between A and B , and 1/2 in the perpendicular direction. Same with sphere C. So the total of forces from both spere B and C is

times the electrostatic force.

Set these two forces equal.