What is the general expression for the speed of an electromagnetic wave in a medium with permittivity ε and permeability μ?

What is the general expression for the speed of an electromagnetic wave in a medium with permittivity ε and permeability μ?

• A. v = √(μ ε)
• B. v = 1/√(μ ε)
• C. v = √(μ/ε)
• D. v = √(ε/μ)

Answer: (B)

The speed of an electromagnetic wave in a medium is determined by the medium’s electric permittivity ε and magnetic permeability μ. For a lossless, isotropic medium, Maxwell’s equations lead to the wave equation ∇^2E = μ ε ∂^2E/∂t^2. If you try a plane-wave solution E ∝ e^{i(k·r − ωt)}, you get k^2 = μ ε ω^2, so the wave’s phase speed is v = ω/k = 1/√(μ ε). This matches the familiar vacuum result, where ε = ε0 and μ = μ0 giving v = c = 1/√(μ0 ε0). In general, with ε = ε_r ε0 and μ = μ_r μ0, the speed is v = c/√(ε_r μ_r). So the correct expression is v = 1/√(μ ε). The other forms do not come from the wave equation for a non-conducting medium.

The speed of an electromagnetic wave in a medium is determined by the medium’s electric permittivity ε and magnetic permeability μ. For a lossless, isotropic medium, Maxwell’s equations lead to the wave equation ∇^2E = μ ε ∂^2E/∂t^2. If you try a plane-wave solution E ∝ e^{i(k·r − ωt)}, you get k^2 = μ ε ω^2, so the wave’s phase speed is v = ω/k = 1/√(μ ε).

This matches the familiar vacuum result, where ε = ε0 and μ = μ0 giving v = c = 1/√(μ0 ε0). In general, with ε = ε_r ε0 and μ = μ_r μ0, the speed is v = c/√(ε_r μ_r).

So the correct expression is v = 1/√(μ ε). The other forms do not come from the wave equation for a non-conducting medium.