Which expression correctly relates ε0 to Coulomb's constant k?

Which expression correctly relates ε0 to Coulomb's constant k?

• A. ε0 = k
• B. ε0 = 1/4πk
• C. ε0 = 4πk
• D. ε0 = π/k

Answer: (B)

Coulomb's law in SI uses k = 1/(4π ε0), so the force is F = (1/(4π ε0)) q1 q2 / r^2. Rearranging this relation to solve for ε0 gives ε0 = 1/(4π k). This is the correct connection because it directly comes from how the electric force is expressed in vacuum. Numerically, k ≈ 8.99×10^9 N·m^2/C^2 and ε0 ≈ 8.85×10^-12 F/m, and their product ε0 k ≈ 1/(4π) confirms the relationship. The other forms would misplace ε0 or omit the 4π factor, which would contradict the standard Coulomb’s law constant.

Coulomb's law in SI uses k = 1/(4π ε0), so the force is F = (1/(4π ε0)) q1 q2 / r^2. Rearranging this relation to solve for ε0 gives ε0 = 1/(4π k). This is the correct connection because it directly comes from how the electric force is expressed in vacuum. Numerically, k ≈ 8.99×10^9 N·m^2/C^2 and ε0 ≈ 8.85×10^-12 F/m, and their product ε0 k ≈ 1/(4π) confirms the relationship. The other forms would misplace ε0 or omit the 4π factor, which would contradict the standard Coulomb’s law constant.