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Find the direction and magnitude of the net electrostatic force exerted on the point charge q2 in the figure. Let q=+2.3μ, and d=31cm. what is the direction (θ) in ∘ counterclockwise from q2-q3 direction

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.

Find the direction and magnitude of the net electrostatic force exerted on the point charge q2 in the figure. Let q = +2.3μC, and d = 31cm. What is the direction (θ) in degrees counterclockwise from the q2-q3 direction?

Find the direction and magnitude of the net electrostatic force exerted on q2 in a square arrangement of charges. Includes detailed calculations using Coulomb's Law and vector decomposition for undergraduate physics students.

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