Final answer:
The distance between the charged foam cup and the charged metal sphere is approximately 0.64 meters, found using Coulomb's law with the given forces and charges. Therefore correct option is B
Step-by-step explanation:
The question asked requires us to use Coulomb's law to determine the distance between a charged foam cup and a charged metal sphere.
According to Coulomb's law, the electric force (F) between two charges (q1 and q2) is given by F = k * (q1 * q2) / r^2, where k is Coulomb's constant, and r is the distance between the charges.
In this case, the electric force is given as 2.12 newtons, the charges on the cup and the sphere are 2.0 × 10^-6 coulombs and 2.5 × 10^-6 coulombs respectively, and the Coulomb's constant (k) is 9.0 × 10^9 newton·meter^2/coulombs^2.
Using this information, we can rearrange Coulomb's law to solve for the distance r: r = √(k * (q1 * q2) / F).
Plugging in the values, we get r = √((9.0 × 10^9 N·m^2/C^2) * (2.0 × 10^-6 C) * (2.5 × 10^-6 C) / 2.12 N).
After calculating, we find that the distance r is approximately 0.64 meters, which corresponds to option B: 6.4 × 10^-1 meters.