Solution Found!
(a) Show that the skin depth in a poor conductor
Chapter 9, Problem 20P(choose chapter or problem)
Problem 20P
(a) Show that the skin depth in a poor conductor (independent of frequency). Find the skin depth (in meters) for (pure) water. (Use the static values of ? , μ, and σ; your answers will be valid, then, only at relatively low frequencies.)
(b) Show that the skin depth in a good conductor(where λ is the wavelength 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 ? ≈ ? 0 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).
Questions & Answers
QUESTION:
Problem 20P
(a) Show that the skin depth in a poor conductor (independent of frequency). Find the skin depth (in meters) for (pure) water. (Use the static values of ? , μ, and σ; your answers will be valid, then, only at relatively low frequencies.)
(b) Show that the skin depth in a good conductor(where λ is the wavelength 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 ? ≈ ? 0 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).
ANSWER:
Solution 20P
(a)
Step 1: To find the skin depth in a poor conductor for pure water.
Given that
And we know that, skin depth is given by the equation;
…..(1)
From eq(1) we can approximate;
So,
And …..(2)