Question

select the correct answer.
which statement best explains the relationship between the electric force between two charged objects and the distance between them?
a. as the distance increases by a factor, the electric force increases by the square of that factor.
b. as the distance increases by a factor, the electric force increases by twice that factor.
c. as the distance increases by a factor, the electric force decreases by twice that factor.
d. as the distance increases by a factor, the electric force decreases by the same factor.
e. as the distance increases by a factor, the electric force decreases by the square of that factor.

Explanation:

The electric force between two charged objects is governed by Coulomb's Law, which states that the electric force \( F \) is inversely proportional to the square of the distance \( r \) between the charges (\( F \propto \frac{1}{r^2} \)). This means if the distance increases by a factor (e.g., if \( r \) becomes \( kr \) where \( k \) is the factor), the force becomes \( \frac{1}{(kr)^2}=\frac{1}{k^2}\times\frac{1}{r^2} \), so the force decreases by the square of that factor. Option A and B are incorrect as force should decrease with increasing distance. Option C and D are incorrect as the relationship is inverse - square, not inverse - linear or related to twice the factor. Option E correctly describes the inverse - square relationship.

Answer:

E. As the distance increases by a factor, the electric force decreases by the square of that factor.