Question

how does increasing the distance between charged objects affect the electric force between them?
the electric force increases because the distance has an indirect relationship to the force.
the electric force increases because the distance has a direct relationship to the force.
the electric force decreases because the distance has a direct relationship to the force.
the electric force decreases because the distance has an indirect relationship to the force.

Explanation:

To solve this, we use Coulomb's Law, which states the electric force \( F \) between two charged objects is given by \( F = k\frac{q_1q_2}{r^2} \), where \( r \) is the distance between them. From the formula, we see that force \( F \) is inversely proportional to the square of the distance \( r \) (an indirect relationship). So as distance \( r \) increases, the electric force \( F \) decreases. Now let's analyze each option:

• First option: Says force increases with indirect relationship, but force decreases with indirect (inverse) relationship, so wrong.
• Second option: Says force increases with direct relationship, but relation is inverse, so wrong.
• Third option: Says force decreases with indirect (inverse) relationship, which matches Coulomb's Law.
• Fourth option: Says force decreases with direct relationship, but the relationship is inverse, so wrong.

Answer:

The electric force decreases because the distance has an indirect relationship to the force.