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To solve this problem, we’ll use Coulomb’s law to find the net force on charge \( Q_4 \) due to the other three charges \( Q_1 \), \( Q_2 \), and \( Q_3 \). The force on \( Q_4 \) due to each of these charges will be calculated based on their distance and relative directions.

### Given Data
- Side length of the square, \( \ell = 0.80 \, \text{m} \).
- Charges:
  - \( Q_1 = -3 \, \text{nC} \)
  - \( Q_2 = -4 \, \text{nC} \)
  - \( Q_3 = +5 \, \text{nC} \)
  - \( Q_4 = +4 \, \text{nC} \)
  
### Steps
1. **Determine distances between charges**:
   - Since the charges are at the corners of a square, each side is \( \ell = 0.80 \, \text{m} \).
   - The diagonal distance between opposite corners (e.g., between \( Q_1 \) and \( Q_4 \)) is \( d = \sqrt{2} \, \ell \).

2. **Calculate forces on \( Q_4 \) due to each charge** using Coulomb’s law:
   - \( F = \frac{k |Q_4 \cdot Q_i|}{r^2} \), where \( k = 8.99 \times 10^9 \, \text{N} \, \text{m}^2/\text{C}^2 \).

3. **Find force components** in the x- and y-directions for each force.

4. **Calculate the net force** by adding up the x- and y-components of the forces.

5. **Determine the angle \( \theta \) of the net force** with respect to the positive x-axis using:
   \[
   \theta = \arctan\left(\frac{F_y}{F_x}\right)
   \]

Would you like me to go through each step with detailed calculations? 

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### Additional Questions
1. What would be the force on \( Q_4 \) if it were positioned halfway along the diagonal?
2. How would the net force on \( Q_4 \) change if \( Q_3 \) were negative?
3. What would happen to the angle if \( Q_4 \) had a negative charge?
4. How does the force direction change if the square's side length doubles?
5. How would this problem differ if it were set in three-dimensional space?

### Tip
Always resolve vector components carefully when dealing with forces in multiple directions.

Determine the angle made by the direction of the net force acting on the charge Q4 with respect to the positive x-axis, given three fixed point charges Q1 = -3 nC, Q2 = -4 nC, and Q3 = +5 nC arranged at three corners of a square with side length ℓ = 0.80 m, and a free charge Q4 = +4 nC at the fourth corner.

Calculate the angle of the net force acting on charge Q4 in a square configuration of charges. Given charges Q1 = -3 nC, Q2 = -4 nC, Q3 = +5 nC, and Q4 = +4 nC with a square side length of 0.80 m, apply Coulomb's law and vector addition to find the force angle with respect to the x-axis.

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