a. Show that the skin depth in a poor conductor (σ << ωε) is (2/σ)√ε/μ when independent of frequency. Find the skin depth (in meters) for (pure) water.
b. Show that the skin depth in a good conductor (σ >> ωε) is λ/2Π (whereλ is the wavelength in the conductor). Find the skin depth (in nanometers) for a typical meter (σ ≈ 10^7Ωm^-1) in the visible range (ω = 10^15 /s), assuming ε=εo and μ≈ μo. Why are metals opaque?
c. Show that in a good conductor the magnetic field lags the electric field by 45 degrees and the find the ratio of their amplitudes. For a numerical example use the 'typical metal' in part (b).