Which expression correctly relates the speed of light to the vacuum permeability μ0 and the vacuum permittivity ε0?

• A. c = μ0 ε0
• B. c = √(μ0 ε0)
• C. c = 1/√(μ0 ε0)
• D. c = μ0/ε0

Answer: (C)

In vacuum, the speed of light is set by the electromagnetic properties of empty space, μ0 and ε0. From Maxwell’s equations, the electric field in free space satisfies the wave equation ∇^2E = μ0 ε0 ∂^2E/∂t^2, which describes waves with speed v = 1/√(μ0 ε0). Since all electromagnetic waves in vacuum travel at the same speed, that speed is c = 1/√(μ0 ε0). This also means μ0 ε0 = 1/c^2, so plugging in the constants gives c ≈ 3.00×10^8 m/s.

The other expressions don’t yield a velocity with the correct units or magnitude: μ0 ε0 by itself isn’t a speed, √(μ0 ε0) has the wrong units, and μ0/ε0 also has incompatible dimensions.