(a) Show that the skin depth in a poor conductor (independent of frequency). Find the sk...

(a) Show that the skin depth in a poor conductor (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(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 ≈ 10¹⁵/s), assuming ? ≈ ? 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).