Understanding the Problem
* Symmetry: The key is recognizing the symmetry of the situation. Since the charges are evenly distributed around the circle, the forces from each of the 450 charges will cancel out in pairs.
* Coulomb's Law: We'll use Coulomb's Law to calculate the force between any two charges.
Steps to Solve
1. Visualize: Imagine a circle with the 450 charges evenly distributed around it. Place the 45 C charge at the center of this circle.
2. Consider Pairs: Take any two charges on the circle that are diametrically opposite to each other. The forces they exert on the central charge will be equal in magnitude but opposite in direction, resulting in a net force of zero.
3. Total Cancellation: You can pair up all the charges on the circle in this way. Each pair will produce a net force of zero. Since all forces cancel out, the total force on the 45 C charge will be zero.
Conclusion
The force on the 45 C charge placed at the center of the circle is zero.
