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Skin Depth in Conductors

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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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Solution Summary

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.

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See Also This Related BrainMass Solution

Electric Field in Matter

See the attached file.

An electromagnetic wave with frequency f = 10^6 Hz ravels along the z-axis in aluminum. In this medium
sigma=38*10^6 (Ohm*m)^(-1) , e = e0 and mu=mu0
At the surface of the aluminum the electric field amplitude/polarization is E in the x direction.

Write an expression for the electric field inside the conductor in terms of k, kappa, w and delta (the phase shift). for the waveform use the cosine form rather than exponential form.

If the real part of the wave number is (see attached file for formula)
Find the skin depth, wave velocity and the wavelength.

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