Solution:

To find \(\sum \overrightarrow{F_i}\), the vector sum of forces acting on each charge in the system, we can apply Newton's third law:

1. Newton's Third Law:
- For any pair of charges, the force exerted by one charge on another is equal in magnitude and opposite in direction to the force exerted by the second charge on the first.

2. Net Force on System:
- Since each pair of charges in the system exerts equal and opposite forces on each other, all internal forces cancel out in pairs.

3. Resultant Force:
- As a result, the net force on the entire system of charges is zero.

Conclusion:

The total force \(\sum \overrightarrow{F_i} = 0\).