a. Show that the skin depth in a poor conductor (sigma << WE) is (2/sigma) (E/mu)^1/2 when independent of frequency. Find the skin depth (in meters) for (pure) water.
b. Show that the skin depth in a good conductor (sigma >> WE) is lambda/2pi (where lambda is the wavelength in the conductor). Find the skin depth (in nanometers) for a typical meter (sigma= 10^7 omega meters ^-1) in the visible range (w = 10^15 /s), assuming E=Eo and mu=mu_o. 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).
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This solution contains step-by-step calculations to determine the skin depth in meters for pure water, skin depth for a good conductor, and it also shows the ratio of amplitudes of a lagged magnetic and electric field due to a good conductor. All workings and formulas are shown with brief explanations.