What is the force at 18 degrees in a charged ball suspension 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: $F=F_g\tan(18^{\circ})$

 

[M98Ranger]

The force in this scenario would be 4 times the force at half the distance, since the strings are spread at 36 degrees. This means that the balls are at a distance of 0.125 inches from the center point, and the force acting on each ball would be half of what it would be at a distance of 0.25 inches. Therefore, the total force on both balls would be twice the force at 0.125 inches, or 4 times the force at 0.25 inches.

To find the force at 18 degrees, you would need to first calculate the distance from the center point to the balls at that angle. This can be done using trigonometry by finding the adjacent side of the right triangle formed by the strings and the center point. Once you have the distance, you can use Coulomb's Law to calculate the force between the balls. Keep in mind that the force will be repulsive since the balls have the same charge.

Hope this helps!