To find the net electrostatic force on charge $q_2$ due to the other three charges in the system, we will use Coulomb's Law. Coulomb's Law describes the force between two point charges as:

$F = k_e \frac{|q_1 q_2|}{r^2}$

where:

• $F$ is the magnitude of the force,
• $k_e = 8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2$ is Coulomb’s constant,
• $q_1$ and $q_2$ are the charges,
• $r$ is the distance between the charges.

We are given:

• $q_1 = +q = +2.3 \, \mu \text{C} = 2.3 \times 10^{-6} \, \text{C}$,
• $q_2 = -2q = -4.6 \, \mu \text{C}$,
• $q_3 = -3q = -6.9 \, \mu \text{C}$,
• $q_4 = -4q = -9.2 \, \mu \text{C}$,
• $d = 31 \, \text{cm} = 0.31 \, \text{m}$.

Steps:

1. Calculate forces between $q_2$ and other charges:

   • The forces are calculated separately for each pair.
   • For the diagonal distances, we use $r_{\text{diagonal}} = \sqrt{2} d$ since the charges form a square.

2. Calculate the force from $q_3$ on $q_2$ (along the horizontal direction).

3. Calculate the force from $q_1$ on $q_2$ (along the diagonal).

4. Calculate the force from $q_4$ on $q_2$ (along the vertical).

5. Resolve the forces into components (horizontal and vertical) to determine the net force direction and magnitude.

Let me calculate each force now.The net electrostatic force exerted on charge $q_2$ has:

• Magnitude: $4.46 \, \text{N}$,
• Direction: $126^\circ$ counterclockwise from the $q_2$-$q_3$ direction.

Would you like further details on the steps, or do you have any questions?

Here are 5 related questions for deeper understanding:

1. How does the direction of the force change if the magnitude of one of the charges is increased?
2. What would happen to the net force if the charge at $q_3$ was positive instead of negative?
3. How would the force change if the distance $d$ was doubled?
4. How is the resultant angle affected by the diagonal component of the force from $q_1$?
5. How would the total force on $q_2$ change if $q_4$ was removed?

Tip: Always break forces into components when dealing with non-aligned forces to accurately find the net result.