Final answer:
To increase the electrostatic force between two charges by 16 times, the distance between them must be decreased to a fourth. If initially the charges are 0.080 m apart, the new distance would be 0.020 m.
Step-by-step explanation:
The subject of this question is Physics, specifically relating to the topic of electrostatic forces between charged particles. Since the force between the charges becomes 16 times greater when they are moved, we can apply Coulomb's law which states that the electrostatic force F between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance r between them.
Initially, if the charges are separated by a distance r, Coulomb's law is given by F = k * Q1 * Q2 / r2, where k is Coulomb's constant, and Q1 and Q2 are the magnitudes of the two charges. To make the force 16 times stronger, and since F is inversely proportional to r2, the distance must be changed to r / 4. Therefore, if the particles were 0.080 m apart, to increase the force by 16 times, the new distance r' would be 0.080 m / 4 = 0.020 m.