Final answer:
The distance between two point charges must be changed by a factor of 3.2 to alter the force between them by a factor of 10, showing that force is inversely proportional to the square of the distance.
Step-by-step explanation:
To change the force between two point charges by a factor of 10, you must change the distance between them by a factor of 3.2. According to Coulomb's Law, which states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them, if you increase the distance by a factor of 3.2, the force will decrease by a factor of 10. Conversely, if you decrease the distance by a factor of 3.2, the force will increase by a factor of 10. This relationship demonstrates that force is inversely proportional to the square of the distance when it comes to point charges.
An example of this is evident in the context of a simple machine, where increasing the distance over which the same force is applied can result in the same amount of work done while reducing the effort. Similarly, when you increase the length of a rope in a circular orbit, more force is required to maintain the same speed, highlighting the inversely proportional relationship between force and radius.