1. Concept: The magnitude of an electric field produced by a single point charge falls off with the square of the distance.
2. Formula: $$ E = \frac{k q}{r^2} $$
3. Solution: - Given field: \( E = 2 \text{ N/C} \). Distance \( r = 60 \text{ cm} = 0.6 \text{ m} \).
- Rearrange for charge: \( q = \frac{E r^2}{k} \).
- Substitute: \( q = \frac{2 \times (0.6)^2}{9 \times 10^9} \).
- Square \( r \): \( (0.6)^2 = 0.36 \). So numerator is \( 2 \times 0.36 = 0.72 \).
- Calculate: \( q = \frac{0.72}{9 \times 10^9} = 0.08 \times 10^{-9} \text{ C} \).
- Convert to scientific notation: \( 0.08 \times 10^{-9} = 8 \times 10^{-11} \text{ C} \).
4. Why other options are incorrect: Failing to square the 0.6 meters or failing to convert cm to meters correctly leads to the incorrect exponent powers seen in the other options.
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