A Show The Skin Depth In Poor Conductor

(a) Show that the skin depth in a poor conductor (σ << wε) is (2/σ)√ε/µ (independent of frequency). Find the skin depth (in meters) for (pure) water.

(b) Show that the skin depth in a good conductor (σ >> wε) 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–l) in the visible range (w ≈ 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 45o, and find the ratio of their amplitudes. For a numerical example, use the “typical metal” in part (b).

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