(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 ϵ, 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 wavelenght 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 ϵ≈ϵ0 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).