electric charge problem

[physicsuser]

two identical, equally charged balls are suspended from strings 0.25 in length from a single point. The mass of the ball is 8e-4kg. The strings spread 36 degrees. The problem asks to find the charges.

My question is what should the force be when moving the ball at 18 degrees?Is it F at full distance or 4*F at half the distance?

Diagram is attached below.

[Galileo]

The force you got is correct:
F=F_g\tan(18^{\circ})

You probably thought, because I`m using half the actual distance, the force must be 1/4th of the actual force, but that is not true.
You know the gravitational force and you know the angle. Since the ball is in equilibrium, the electrical force is just the gravitational force minus the tension.
Therefore, from your picture on the left: F=F_g\tan(18^{\circ})