A. Show that the skin depth in a poor conductor (σ << ωε) is (2/σ ) √ε/μ (independent of frequency). Find the skin depth (in meters) for (pure) water. (Use the static values of , μ, and σ; your answers will be valid, then, only at relatively low frequencies.) b. Show that the skin depth in a good conductor (σ >> ωε ) is λ/2π (where λ is the wavelength in the conductor). Find the skin depth (in nanometers) for a typical metal (σ ≈ 107(Ω m)^−1) in the visible range (ω ≈ 10^15/s), assuming ε≈ 0 and μ ≈ μ0. Why are metals opaque?
c. Show that in a good conductor the magnetic field lags the electric field by 45◦, and find the ratio of their amplitudes. For a numerical example, use the "typical metal" in part (b).