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

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.

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.