Problem 9.20 (a) Show that the skin depth in a poor conductor (σ << we) is (2/0)√√√ε/μ (inde- pendent 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 » we) is λ/2л (where λ is the wavelength in the conductor). Find the skin depth (in nanometers) for a typical metal (σ 107 (2 m)¯¹) in the visible range (w≈ 10¹5/s), assuming € ≈ €0 and μ≈μo. 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).
Problem 9.20 (a) Show that the skin depth in a poor conductor (σ << we) is (2/0)√√√ε/μ (inde- pendent 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 » we) is λ/2л (where λ is the wavelength in the conductor). Find the skin depth (in nanometers) for a typical metal (σ 107 (2 m)¯¹) in the visible range (w≈ 10¹5/s), assuming € ≈ €0 and μ≈μo. 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).
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter7: Tunneling Phenomena
Section7.1: The Square Barrier
Problem 2E
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Transcribed Image Text:Problem 9.20
(a) Show that the skin depth in a poor conductor (σ << we) is (2/0)√√√ε/μ (inde-
pendent 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 » we) is λ/2л (where λ is the
wavelength in the conductor). Find the skin depth (in nanometers) for a typical
metal (σ 107 (2 m)¯¹) in the visible range (w≈ 10¹5/s), assuming € ≈ €0 and
μ≈μo. 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).
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