Final answer:
When the distance between two point charges is increased by a factor of three, the force between them becomes one ninth of the original force, which in this case is approximately 0.5556 N.
Step-by-step explanation:
Two point charges exert a 5.00 N force on each other. The force between two point charges is given by Coulomb's Law, which states that the force (F) between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance (r) between them. Mathematically, this is represented as F = k * q1 * q2 / r^2, where k is Coulomb's constant.
When the distance between the charges is increased by a factor of three, the new distance will be 3r. According to Coulomb's Law, the new force will be F' = k * q1 * q2 / (3r)^2 = F / 9, because the distance squared term in the denominator will increase by a factor of nine. So, the new force will be 5.00 N / 9, which is approximately 0.5556 N.