select the correct answer. which statement best explains the relationship between the electric force between…

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.

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.

Answer

Answer:

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

Explanation:

Step1: Recall Coulomb's law

The electric - force formula between two charged objects is $F = k\frac{q_1q_2}{r^{2}}$, where $F$ is the electric force, $k$ is the electrostatic constant, $q_1$ and $q_2$ are the charges of the two objects, and $r$ is the distance between them.

Step2: Analyze the relationship

If we consider the distance $r$ changing by a factor $n$ (new distance $r'=nr$), the new force $F'=k\frac{q_1q_2}{(nr)^{2}}=\frac{1}{n^{2}}k\frac{q_1q_2}{r^{2}}=\frac{1}{n^{2}}F$. So, as the distance increases by a factor $n$, the electric force decreases by the square of that factor.