Final answer:
When the distance between two point charges is increased by a factor of three, the electrostatic force between them, originally 5.00 N, decreases to approximately 0.56 N based on Coulomb's Law, following an inverse square relationship.
Step-by-step explanation:
If two point charges exert a 5.00 N force on each other and the distance between them is increased by a factor of three, we can determine the new force using Coulomb's Law.
Coulomb's Law states that the electrostatic force (F) between two point charges is proportional to the product of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. Mathematically, F is proportional to (q1*q2)/r².
Therefore, if the distance is increased by a factor of three, the force will change according to the inverse square of this factor.
Calculating the new force, where the original force is 5.00 N and the distance is increased by 3, we can see that the new force will be F / (3²), or F / 9, since the square of 3 is 9. Consequently, the new force would be 5.00 N / 9, which equals approximately 0.56 N.