Utilising B = ₀ H , determine the ratio E₀ / H₀ for a plane electromagnetic wave propagating through a vacuum. Note that this ratio, known as the impedance of free space, has the dimensions of electric resistance.

Step-by-step solution

For a plane electromagnetic wave in vacuum, the ratio of the electric field amplitude to the magnetic field amplitude is E₀ / B₀ = c . Given B₀ = ₀ H₀ , substituting this yields E₀ / ( ₀ H₀) = c . Rearranging for the ratio E₀ / H₀ , we get: E₀ H₀ = ₀ c Substituting the standard values ₀ = 4 10⁻⁷ T m A ⁻¹ and c = 3 10^8 m s ⁻¹ : E₀ H₀ = (4 10⁻⁷) (3 10^8) = 120 Using 3.1416 , we get: E₀ H₀ 120 3.1416 377