Final answer:
To increase the force between two point charges by a factor of 5, the distance between them must be changed by a factor of 1/sqrt(5), according to Coulomb's law.
Step-by-step explanation:
The force between two point charges is described by Coulomb's law, which states that the force (F) between two charges is directly proportional to the product of the magnitudes of the charges (q1 and q2), and inversely proportional to the square of the distance (r) between them. Coulomb's law is mathematically represented as F = k * (q1*q2) / r^2, where k is Coulomb's constant.
To increase the force between two point charges by a factor of 5, you must alter the distance so that the new force (F') equals 5 times the original force (F). Since F' is proportional to 1/r'^2, if you want to increase F by a factor of 5, you need to decrease the distance r by a factor that, when squared, equals 5. This requires the new distance r' to be inversely proportional to the square root of 5. Therefore, the distance must be changed by a factor of 1/sqrt(5).