Which statement about μ0, ε0, and the relation c = 1/√(μ0 ε0) is correct?

Which statement about μ0, ε0, and the relation c = 1/√(μ0 ε0) is correct?

• A. μ0 = 1.0×10^−7 N/A^2; ε0 ≈ 8.854×10^−12 F/m; c ≈ 3.00×10^8 m/s.
• B. μ0 = 4π×10^−7 N/A^2; ε0 ≈ 8.854×10^−12 F/m; c ≈ 2.5×10^8 m/s.
• C. c = 1/√(μ0 ε0)
• D. μ0 = 4π×10^−7 N/A^2; ε0 ≈ 8.854×10^−12 F/m; c ≈ 3.00×10^8 m/s.

Answer: (C)

The main idea is how the vacuum’s electromagnetic properties set the speed of light. From Maxwell’s equations, an electromagnetic wave in empty space propagates with speed c = 1/√(μ0 ε0). This ties together the magnetic permeability μ0 and the electric permittivity ε0 of vacuum to the universal constant c. In SI units, μ0 is defined exactly as 4π×10^−7 N/A^2, and c is defined exactly as 299,792,458 m/s, which makes ε0 the derived value ε0 = 1/(μ0 c^2) ≈ 8.854×10^−12 F/m. So the statement c = 1/√(μ0 ε0) is the correct one because it expresses the fundamental link between these vacuum constants and the speed of light. The numerical options either give approximations that don’t reflect the exact definitions (like μ0 or c values) or mix in numbers without stating the underlying relationship.

The main idea is how the vacuum’s electromagnetic properties set the speed of light. From Maxwell’s equations, an electromagnetic wave in empty space propagates with speed c = 1/√(μ0 ε0). This ties together the magnetic permeability μ0 and the electric permittivity ε0 of vacuum to the universal constant c. In SI units, μ0 is defined exactly as 4π×10^−7 N/A^2, and c is defined exactly as 299,792,458 m/s, which makes ε0 the derived value ε0 = 1/(μ0 c^2) ≈ 8.854×10^−12 F/m. So the statement c = 1/√(μ0 ε0) is the correct one because it expresses the fundamental link between these vacuum constants and the speed of light. The numerical options either give approximations that don’t reflect the exact definitions (like μ0 or c values) or mix in numbers without stating the underlying relationship.