Understanding Coulomb's Law

The force between two charged particles is described by Coulomb's Law:

F = k * (q1 * q2) / r²

where:

* F is the electrostatic force

* k is Coulomb's constant (approximately 8.98755 × 10⁹ N⋅m²/C²)

* q1 and q2 are the magnitudes of the charges

* r is the distance between the charges

Solving the Problem

1. Identify the change in distance: The distance is reduced to one-seventh of the original distance. This means the new distance (r') is (1/7)r.

2. Apply Coulomb's Law: We know the original force (F) and the new distance (r'). We want to find the new force (F'). Let's set up a ratio:

F / F' = (r')² / r²

3. Substitute values:

* F = 5.2 x 10⁻² N

* r' = (1/7)r

(5.2 x 10⁻² N) / F' = ((1/7)r)² / r²

4. Simplify and solve for F':

* (5.2 x 10⁻² N) / F' = 1/49

* F' = 49 * (5.2 x 10⁻² N)

* F' = 2.548 N

Answer: If the charged particles are moved so they are only one-seventh as far apart, the force between them will increase to 2.548 N.