F = k * (q1 * q2) / r²
Where:
* F is the electric force
* k is Coulomb's constant
* q1 and q2 are the charges of the particles
* r is the distance between the particles
If the distance is decreased by a factor of 3, the new distance becomes r/3. Let's see how this affects the force:
* New force (F') = k * (q1 * q2) / (r/3)²
* F' = k * (q1 * q2) / (r²/9)
* F' = 9 * [k * (q1 * q2) / r²]
* F' = 9 * F
Therefore, if the distance between the two charged particles is decreased by a factor of 3, the electric force between them increases by a factor of 9.
