Understanding Coulomb's Law
The electric force between two charged particles is described by Coulomb's Law:
* F = k * (q1 * q2) / r²
Where:
* F is the electric force
* k is Coulomb's constant (a proportionality constant)
* q1 and q2 are the magnitudes of the charges
* r is the distance between the charges
The Key Relationship
Notice that the force (F) is inversely proportional to the square of the distance (r²). This means if you increase the distance, the force decreases, and vice versa.
Finding the Solution
To increase the electric force by a factor of 25, you need to find the distance that results in a force 25 times greater. Since the force is inversely proportional to the square of the distance, you need to find the distance that's the square root of 1/25:
* √(1/25) = 1/5
This means you need to reduce the distance between the charges by a factor of 5.
Example:
If the original distance was 10 cm, you would need to decrease it to 2 cm (10 cm / 5 = 2 cm) to increase the electric force by a factor of 25.
