The electric force between two charged particles is inversely proportional to the square of the distance between them. This means that if you double the distance, the force will be reduced to one-fourth of its original value.

Here's why:

* Coulomb's Law: This law describes the electric force between two charged objects. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

* Mathematical Representation:

* F = k * (q1 * q2) / r²

* Where:

* F is the electric force

* k is Coulomb's constant

* q1 and q2 are the magnitudes of the charges

* r is the distance between the charges

* Doubling the Distance: If you double the distance (r becomes 2r), the force becomes:

* F' = k * (q1 * q2) / (2r)²

* F' = k * (q1 * q2) / 4r²

* F' = (1/4) * (k * (q1 * q2) / r²)

* F' = (1/4) * F

Therefore, doubling the distance between two charged particles reduces the electric force to one-fourth of its original value.