Final answer:
Using Coulomb's law, we find that if the distance between two charges is halved, the electric force between them will increase by a factor of sixteen. So, the new force value when placed 5 m apart will be 256 N.
Step-by-step explanation:
If a 16 N electric force is exerted between two charges when they are separated by 10 m, and we want to determine the new force value when these charges are placed 5 m apart, we can use Coulomb's law, which states that the electric force (F) between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance (r) between them. Mathematically, this is expressed as F ∝ 1/r².
Since only the distance is changing and it is halving (from 10 m to 5 m), the relationship will become F ∝ 1/(5²), which is 1/25 of the original distance squared. Because the original force at 10 m was 16 N, at 5 m, the force will be 16 N multiplied by the inverse square of the change in distance, which is (10/5)² = 4² = 16. Therefore, the force at 5 m will be 16 N x 16 = 256 N.