Final answer:
After doubling one charge and doubling the distance between the charges, the force becomes half the original force, or F/2.
Step-by-step explanation:
The question is related to Coulomb's Law, which states the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. When the charge on one of the particles is doubled, the force is also doubled. However, if the distance between the two charges is doubled, the force is reduced by a factor of 4 (since force is inversely proportional to the square of the distance). Combining these two changes, the overall effect is that the force becomes half as much, because the doubling of one charge doubles the force (2F), but then doubling the distance reduces it by a factor of 4, leading to F/2 (one half the original force).