To find the direction and magnitude of the net electrostatic force on charge $q_2$ in the given square arrangement of charges, we can use Coulomb's Law. The charges are arranged in a square, and we need to find the individual forces between $q_2$ and the other charges $q_1, q_3, q_4$, and then sum them vectorially.

Given:

• $q = +2.3 \, \mu C$
• $d = 31 \, cm = 0.31 \, m$
• The charges at the corners:
  • $q_1 = +q = +2.3 \, \mu C$
  • $q_2 = -2q = -4.6 \, \mu C$
  • $q_3 = -3q = -6.9 \, \mu C$
  • $q_4 = -4q = -9.2 \, \mu C$

Steps:

1. Coulomb's Law: The magnitude of the force between two charges is given by Coulomb's Law: $F = k \frac{|q_1 q_2|}{r^2}$ where:

   • $k = 8.99 \times 10^9 \, N \cdot m^2/C^2$ (Coulomb constant),
   • $q_1$ and $q_2$ are the magnitudes of the charges,
   • $r$ is the distance between the charges.

2. Force between $q_2$ and $q_3$: The distance between $q_2$ and $q_3$ is $d = 0.31 \, m$. The force is attractive since they have opposite charges. The direction will be along the line connecting $q_2$ and $q_3$.

3. Force between $q_2$ and $q_1$: The distance between $q_2$ and $q_1$ is also $d = 0.31 \, m$. The force is repulsive since they have opposite signs, and the force direction will be along the line connecting $q_2$ and $q_1$.

4. Force between $q_2$ and $q_4$: The diagonal distance between $q_2$ and $q_4$ is $\sqrt{2}d$. Again, they have opposite charges, so the force will be attractive along the diagonal.

5. Vector components: Once the magnitudes are calculated, we can decompose the forces into their components along the x and y axes and sum them to find the resultant net force. The angle $\theta$ counterclockwise from the $q_2$-$q_3$ axis can then be determined using trigonometry.

I'll calculate the forces next.The magnitude of the net electrostatic force exerted on charge $q_2$ is approximately $4.39 \, N$.

The direction of this net force is $\theta \approx 5.36^\circ$ counterclockwise from the $q_2$-$q_3$ direction (horizontal axis).

Would you like further details or explanations on how the forces were calculated or how the components were handled?

Here are 5 related questions that expand on this:

1. How would the forces change if the distances between the charges were doubled?
2. What would happen to the net force direction if charge $q_1$ were negative instead of positive?
3. How can you generalize this method for charges arranged in a different geometric shape, such as a triangle?
4. How do electric field lines behave in the vicinity of multiple charges like these?
5. How does the principle of superposition help in calculating forces in systems with multiple charges?

Tip: Always break forces into components when dealing with non-aligned vectors to simplify vector addition.