Electric field problem — Changing the charge on two spheres

[KingAlexander211B]

Homework Statement

Two identical conducting spheres A and B carry equal charge. They are separated by a distance much larger than their diameters. A third identical conducting sphere C is uncharged. Sphere C isfirst touched to A, then to B, and finally removed. As a result, the electrostatic force between A and B, which was originally F, becomes:

A. F/2
B. F/4
C. 3F/8
D. F/16
E. 0

Relevant Equations

F=(Ke*Q*q)/r**2

Two identical conducting spheres A and B carry equal charge. They are separated by a distance much larger than their diameters. A third identical conducting sphere C is uncharged. Sphere C isfirst touched to A, then to B, and finally removed. As a result, the electrostatic force between A and B, which was originally F, becomes:

A. F/2 B. F/4 C. 3F/8 D. F/16 E. 0

 

[berkeman]

You are required to post your work toward a solution. What do you think the answer is and why?

 

[KingAlexander211B]

The answer is C). However, I really don't know how to work it out.

 

[berkeman]

What happens when you touch an isolated neutral object to an isolated charged object? How does the charge divide up and re-distribute?