Final answer:
To change the force between two point charges by a factor of 10, the distance between them must be changed by a factor of 3.2, because the force is inversely proportional to the square of the distance according to Coulomb's law.
Step-by-step explanation:
To change the force between two point charges by a factor of 10, you must change the distance between the charges by a factor of 3.2. This is because the force between two point charges is given by Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
If the distance is increased by a factor of 3.2, the force will decrease by a factor of 10. Conversely, if the distance is decreased by a factor of 3.2, the force will increase by a factor of 10. This mathematically means that the distance changes by the square root of the change in force, hence the factor of 3.2, which is approximately the square root of 10.
In order 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. If the distance increases by 3.2, the force will decrease by a factor of 10. Similarly, if the distance decreases by 3.2, the force will increase by a factor of 10.