Explanation Given data: The height of the rectangular block is h = 30 cm along the z direction. The current induced in the block in the positive x − direction. Calculation: The required diagram is drawn as shown in Figure 1. Write the standard expression for the resistance in dc. R dc = l σ A (1) Here, R dc is the dc resistance. l is the length of the conductor. σ is the conductivity of the material. A is the area of the cross section of the conductor. Write the standard expression for the resistance in ac. R ac = R s l w (2) Here, R s is the surface resistance. w is the width of the conductor. The standard relation for surface resistance is, R s = 1 σ δ s Here, δ s is the skin depth. Substitute 1 σ δ s for R s in the equation (2). R ac = l σ δ s w (3) The conversion from 1 cm into m is done as, 1 cm = 1 × 10 − 2 m So the conversion from 30 cm into m is given as, 30 cm = 30 × 10 − 2 m = 0 .3 m From the figure, the length l of the rectangular block is equal to height of the block that is, l = h Substitute 0.3 m for h in the above equation. l = 0.3 m Write the standard expression for the area of the rectangular surface. A = l × w Here, w is the width of the conductor. Substitute 0.3 m for l in the above expression. A = ( 0.3 × w ) m 2 = ( 0.3 w ) m 2 Substitute ( 0.3 w ) m 2 for A in the equation (1). R dc = l σ × 0.3 × w (4) Divide equation (3) by equation (4) to calculate the ratio of resistance in the dc and ac. R ac R dc = l σ δ s w l σ × 0.3 × w Simplify the above expression. R ac R dc = 0.3 δ s (5) Write the standard relation for skin depth and attenuation constant. δ s = 1 α (6) Here, α is the attenuation constant. Write the standard expression for attenuation constant in good conductor. α = π f μ σ Np / m Substitute π f μ σ Np / m for α in the equation (6)

7th Edition

ISBN: 8220100663659

Author: ULABY

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Chapter 7, Problem 30P

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The ratio of ac resistance of the block to its dc resistance at 10 MHz.

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Chapter 7, Problem 29P

Chapter 7, Problem 31P

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Chapter 7 Solutions

EBK FUNDAMENTALS OF APPLIED ELECTROMAGN

Ch. 7.2 - What is a uniform plane wave? Describe its...Ch. 7.2 - Since E and H are governed by wave equations of...Ch. 7.2 - If a TEM wave is traveling in the y direction, can...Ch. 7.2 - Prob. 1E Ch. 7.2 - Prob. 2E Ch. 7.2 - If the magnetic field phasor of a plane wave...Ch. 7.2 - Repeat Exercise 7-3 for a magnetic field given by...Ch. 7.3 - An elliptically polarized wave is characterized by...Ch. 7.3 - Prob. 5CQ Ch. 7.3 - The electric field of a plane wave is given by...

Ch. 7.4 - If the electric field phasor of a TEM wave is...Ch. 7.4 - The constitutive parameters of copper are = 0 = 4...Ch. 7.4 - Prob. 8E Ch. 7.4 - For a wave traveling in a medium with a skin depth...Ch. 7.5 - Prob. 6CQ Ch. 7.5 - In a good conductor, does the phase of H lead or...Ch. 7.5 - Prob. 8CQ Ch. 7.5 - Is a conducting medium dispersive or...Ch. 7.5 - Compare the flow of current through a wire in the...Ch. 7.6 - Convert the following values of the power ratio G...Ch. 7.6 - Find the voltage ratio g corresponding to the...Ch. 7 - The magnetic field of a wave propagating through a...Ch. 7 - Prob. 2P Ch. 7 - The electric field phasor of a uniform plane wave...Ch. 7 - The electric field of a plane wave propagating in...Ch. 7 - A wave radiated by a source in air is incident...Ch. 7 - The electric field of a planewave propagating in a...Ch. 7 - The magnetic field of a plane wave propagating in...Ch. 7 - A 60 MHz plane wave traveling in the x direction...Ch. 7 - Prob. 9P Ch. 7 - For a wave characterized by the electric field...Ch. 7 - Prob. 11P Ch. 7 - The magnetic field of a uniform plane wave...Ch. 7 - A linearly polarized plane wave of the form...Ch. 7 - The electric field of an elliptically polarized...Ch. 7 - Compare the polarization states of each of the...Ch. 7 - Plot the locus of E(0, t) for a plane wave with...Ch. 7 - Prob. 17P Ch. 7 - Prob. 18P Ch. 7 - In a medium characterized by r = 9, r = 1, and =...Ch. 7 - Prob. 20P Ch. 7 - Prob. 21P Ch. 7 - Prob. 22P Ch. 7 - The skin depth of a certain nonmagnetic conducting...Ch. 7 - Prob. 24P Ch. 7 - The electric field of a plane wave propagating in...Ch. 7 - The magnetic field of a plane wave propagating in...Ch. 7 - At 2 GHz, the conductivity of meat is on the order...Ch. 7 - In a nonmagnetic, lossy, dielectric medium, a 300...Ch. 7 - A rectangular copper block is 30 cm in height...Ch. 7 - Prob. 30P Ch. 7 - The inner and outer conductors of a coaxial cable...Ch. 7 - Prob. 32P Ch. 7 - The magnetic field of a plane wave traveling in...Ch. 7 - A wave traveling in a nonmagnetic medium with r =...Ch. 7 - The electric-field phasor of a uniform plane wave...Ch. 7 - Prob. 36P Ch. 7 - A wave traveling in a lossless, nonmagnetic medium...Ch. 7 - At microwave frequencies, the power density...Ch. 7 - Consider the imaginary rectangular box shown in...Ch. 7 - Repeat Problem 7.39 for a wave traveling in a...Ch. 7 - Given a wave with E=x E0 cos(t kz): (a) Calculate...Ch. 7 - Prob. 42P

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