1. Concept: Electrostatic force scales according to the inverse square law of the distance separating the two charges.
2. Formula: $$ F \propto \frac{1}{r^2} $$
3. Solution: - Decreasing the distance by 50 percent means the new distance is exactly half the original: \( r' = 0.5r = r/2 \).
- Substitute this new distance into the denominator: \( F' \propto \frac{1}{(r/2)^2} \).
- Square the term: \( F' \propto \frac{1}{r^2/4} \).
- Invert the fraction: \( F' = 4 \left( \frac{1}{r^2} \right) \).
- The final force is exactly 4 times the original force.
4. Why other options are incorrect: Option B (doubling) occurs if you forget to square the distance change. Options C and D are not mathematically possible via the inverse square law for a 50% change.
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