Final answer:
The new force between the two charges when the distance is reduced to one-ninth of its original value is 129.6 N, as calculated using Coulomb's Law and the inverse square law.
Step-by-step explanation:
The force between two charges is given by Coulomb's Law, which states that the force (F) is proportional to the product of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. Mathematically, it is expressed as:
F = k * (q1 * q2) / r²
Where k is the Coulomb's constant. If the original force is 1.6 N and the distance is reduced to one-ninth, according to the inverse square law, the new force is:
New force = 1.6 N * (1 / (1/9)²) = 1.6 N * 81 = 129.6 N