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Charles Augustin de Coulomb found that doubling the distance between two charged spheres cut the force between them to one quarter, and tripling the distance cut it to one ninth. What relationship between force and distance does this describe?
AThe force is directly proportional to the square of the distance
BThe force is inversely proportional to the distance itself
CThe force does not depend on the distance at all
DThe force is inversely proportional to the square of the distance
Answer & Solution
Correct answer: D. The force is inversely proportional to the square of the distance
1. Doubling the distance cutting the force to one quarter (1/2 squared) is the signature of an inverse-square relationship.
2. Tripling the distance cutting the force to one ninth (1/3 squared) confirms the same pattern.
3. This means the force is inversely proportional to the square of the distance, which is exactly Coulomb's law.
_Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.2 Coulomb's law_
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