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?

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.