Question

1. the diagram below shows two charged objects, a and b, that are placed 5 cm apart.

if the distance between the two objects is doubled, what happens to the electrical force between them?

the electrical force increases.
the electrical force decreases.
the electrical force stays the same.
the electrical force disappears completely.
clear all

Explanation:

To determine the change in electrical force when the distance between two charged objects is doubled, we use Coulomb's Law, which states that the electrical force \( F \) between two charged objects is inversely proportional to the square of the distance \( r \) between them, i.e., \( F \propto \frac{1}{r^2} \).

1. Let the initial distance be \( r_1 \) and the initial force be \( F_1 \). So, \( F_1 \propto \frac{1}{r_1^2} \).
2. When the distance is doubled, the new distance \( r_2 = 2r_1 \). The new force \( F_2 \propto \frac{1}{r_2^2} = \frac{1}{(2r_1)^2} = \frac{1}{4r_1^2} \).
3. Comparing \( F_2 \) and \( F_1 \), we see that \( F_2 = \frac{1}{4}F_1 \). This means the electrical force decreases when the distance is doubled.

Answer:

The electrical force decreases.