Final answer:
The product of Coulomb's constant and the electric constant in free space is 1/(4π). Coulomb's constant and the electric constant in free space are key values in Coulomb's law, with the former being 8.99 × 109 Nm2/C2 and the latter being 8.85 × 10-12 F/m.
Step-by-step explanation:
The product of Coulomb's constant (k) and the electric constant in free space (also known as the permittivity of free space, ε0), when multiplied together, gives a result that is mathematically interesting. Coulomb's constant is approximately 8.99 × 109 Nm2/C2, and the permittivity of free space is approximately 8.85 × 10-12 F/m. When these constants are multiplied together (k × ε0), they yield a dimensionless number that is exactly 1/(4π). Therefore, the correct answer to the given question is a. 1/4π.