The problem you’ve provided involves three charges arranged in different configurations, and you're asked to determine the net force on charge 2 for each arrangement. The charge magnitude is given as $|q| = 8.9 \, \mu C$, and the distance between charges is $d = 3.8 \, \text{mm}$.

We will use Coulomb's Law to calculate the forces between charges. Coulomb's Law states that the electrostatic force between two charges is given by:

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

Where:

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

To solve the question for each part:

• (a), (b), and (c) correspond to different charge arrangements, and we need to calculate the net force on charge 2 by considering the forces due to charge 1 and charge 3 in each case.

Let me break down the steps and start the calculations. I will first calculate the force for each case.

I will start by asking for clarification: can you confirm the signs of the charges in each configuration? This will help determine the direction of the forces involved. For example:

• In case (a), what are the charges on 1, 2, and 3?
• In case (b), what are the charges on 1, 2, and 3?
• In case (c), what are the charges on 1, 2, and 3?

Feel free to let me know!