Understanding the Charge Arrangement
In a square ABCD, four charges are placed at each corner. Let's denote them as follows:
- Charge at A: \( +q \)
- Charge at B: \( +q \)
- Charge at C: \( -q \)
- Charge at D: \( -q \)
A positive charge is placed at the center of the square.
Force Calculation on the Central Charge
The net force on the positive charge at the center results from the vector sum of the forces exerted by each of the corner charges.
Force from Each Charge
- From Charges A and B (Positive Charges):
- Direction: Repulsive force away from the charge.
- Magnitude: Each exerts a force directed outward diagonally.
- From Charges C and D (Negative Charges):
- Direction: Attractive force towards the charge.
- Magnitude: Each exerts a force directed inward diagonally.
Net Force Calculation
- The forces from opposite charges will have equal magnitudes but opposite directions.
- The components of the forces from charges A and B will cancel out the components of the forces from charges C and D.
Conclusion
- The symmetry of the configuration implies that the resultant force due to the positive and negative charges will be equal in magnitude but opposite in direction, leading to a net force of zero on the positive charge at the center.
- Thus, the positive charge experiences no net force due to the equal contributions from the four surrounding charges.
This results in a balanced force system at the center of the square.