1. Concept: The electric field of a point charge obeys the inverse square law. Halving the distance from the source dramatically magnifies the field strength.
2. Formula: $$ E \propto \frac{1}{r^2} $$
3. Solution: - Original state: \( E_1 = 200 \text{ N/C} \) at \( r_1 = 4 \text{ m} \).
- New state: \( r_2 = 2 \text{ m} \), which means the distance is halved (\( r_2 = r_1 / 2 \)).
- Because \( E \) varies inversely with the square of the distance, replacing \( r \) with \( r/2 \) introduces a factor of \( 1 / (1/2)^2 = 1 / (1/4) = 4 \).
- The new field is 4 times stronger: \( 200 \times 4 = 800 \text{ N/C} \).
4. Why other options are incorrect: Option A incorrectly assumes a linear relationship (distance halved = field doubled). Options C and D are mathematically unrelated to the inverse-square geometric scaling.
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