plane waue proy dc atoslnd E=0,s eplasA in a medicam uwih relrE8,Mr e2sen (10*t-62)a V ind6 Loss taugent) impedanco oF the wave12

Answered: A plane waue prop agatos and E=0;s e in…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

plane waue proy dc atos
lnd E=0,s e
plas
A in a medicam uwih relrE8,Mr e2
sen (10*t-62)a V ind
6 Loss taugent
) impedanco oF the wave
12

Expert Solution

Step 1

Given that,

$E = 0.5 e^{- \frac{z}{3}} \sin (10^{8} t - β z) a_{x} V / m ε_{r} = 8 μ_{r} = 2 ω = 10^{8} r a d / s e c$

In the given wave propagation $α = \frac{1}{3}$

The formula for $α$ is given by

$α = ω \sqrt{\frac{μ ε}{2} (\sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} - 1)} plugging values \frac{1}{3} = 10^{8} \sqrt{\frac{4 π \times 10^{- 7} \times 2 \times 8.85 \times 10^{- 12} \times 8}{2} (\sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} - 1)} \frac{1}{3 \times 10^{8}} = \sqrt{\frac{4 π \times 10^{- 7} \times 2 \times 8.85 \times 10^{- 12} \times 8}{2} (\sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} - 1)} \frac{1}{9 \times 10^{16}} = \frac{4 π \times 10^{- 7} \times 2 \times 8.85 \times 10^{- 12} \times 8}{2} (\sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} - 1) \frac{1}{9 \times 10^{16}} = 8.901 \times 10^{- 17} (\sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} - 1) \frac{1}{9 \times 10^{16} \times 8.901 \times 10^{- 17}} = (\sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} - 1) \frac{1}{8.010} = (\sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} - 1) \frac{1}{8.010} + 1 = \sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} 1.124 = \sqrt{1 + \frac{σ^{2}}{ω^{2} ε^{2}}} 1.2633 = 1 + \frac{σ^{2}}{ω^{2} ε^{2}} 0.2633 = \frac{σ^{2}}{ω^{2} ε^{2}} σ^{2} = 0.2633 \times ω^{2} ε^{2} σ = \sqrt{0.2633} \times 10^{8} \times 8.85 \times 10^{- 12} \times 8 σ = 0.0036$