1. Concept: The magnitude of the electrostatic force between two point charges can be found using Coulomb's Law.
2. Formula: $$ F = \frac{k q_1 q_2}{r^2} $$
3. Solution: - Given force: \( F = 2 \text{ N} \), charge \( q_1 = 2 \text{ C} \), distance \( r = 3 \text{ m} \).
- Coulomb's constant is \( k = 9 \times 10^9 \text{ Nm}^2/\text{C}^2 \).
- Rearrange the formula to solve for \( q_2 \): \( q_2 = \frac{F \cdot r^2}{k \cdot q_1} \)
- Substitute values: \( q_2 = \frac{2 \times 3^2}{(9 \times 10^9) \times 2} \)
- Cancel out the 2s and calculate the numerator: \( q_2 = \frac{9}{9 \times 10^9} = 1 \times 10^{-9} \text{ C} \)
4. Why other options are incorrect: Option A forgets the negative sign in the exponent. Options C and D result from failing to properly square the distance \( r \) or from arithmetic errors.
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