Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 12, Problem 12.7P
The semi-infinite regions z < 0 and z > 1m are free space. For 0
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The electric field component of a y-polarized plane wave is given as Ey(z)=Aexp(-az-jßz). This wave propagates with a frequency of 831MHZ in a homogeneous, linear medium with a relative magnetic permeability of 1, a relative dielectric permeability of 3.3 and a conductivity of 2.8. If the electric field amplitude is 90V in the z=0 plane, what happens at the z=1cm distance?
A wave is normally incident upon a surface with a layered lossless dielectric. Find the magnitude of effective reflection coefficient if medium 1 is free space, medium 2 has a relative permittiviy of 4
medium 3 has a permittivity of 9, and the thickness of medium 2 is 12/2.
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A plane wave of which the electric field vector, E0=10V/m, f=5GHz, is parallel to x-z plane, arrives on a dielectric medium of permittivity εr,=4 with an incident angle of 45∞. Find the reflection coefficient, Γ, transmission coefficients, T, and reflection, transmission angles.
Calculate the incident angles for zero reflection and full reflection.
Calculate the phase velocity and wavelenght in both media.
Chapter 12 Solutions
Engineering Electromagnetics
Ch. 12 - Prob. 12.1PCh. 12 - Prob. 12.2PCh. 12 - A uniform plane wave m region 1 is normally...Ch. 12 - Prob. 12.4PCh. 12 - Prob. 12.5PCh. 12 - In the beam-steering prism of Example 12.8,...Ch. 12 - The semi-infinite regions z 0 and z 1m are free...Ch. 12 - Prob. 12.8PCh. 12 - Prob. 12.9PCh. 12 - Prob. 12.10P
Ch. 12 - Prob. 12.11PCh. 12 - Prob. 12.12PCh. 12 - Prob. 12.13PCh. 12 - Prob. 12.14PCh. 12 - Prob. 12.15PCh. 12 - Prob. 12.16PCh. 12 - Prob. 12.17PCh. 12 - Prob. 12.18PCh. 12 - You are given Four slabs of lossless dielectric,...Ch. 12 - Prob. 12.20PCh. 12 - Prob. 12.21PCh. 12 - Prob. 12.22PCh. 12 - Prob. 12.23PCh. 12 - Prob. 12.24PCh. 12 - Prob. 12.25PCh. 12 - Show how a single block of glass can be used to...Ch. 12 - Prob. 12.27PCh. 12 - Over a small wavelength range, the refractive...Ch. 12 - Prob. 12.29PCh. 12 - Prob. 12.30P
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- Given is a linearly polarized uniform plane wave propagating in the +z-direction in seawater with E= 88cos(107πt)(V/m) at z= 0. Also εr= 72,μr= 1 and σ= 4(S/m). What is the phase constant? Also, what is skin depth? find the distancez1at which the amplitude of the wave decreasesto1%of its value at z= 0arrow_forwardIf a wave propagating in z-direction and incident on the air-glass interface at z= 0, plot the E field (amplitudes only) in the yz plane (plane of incidence) for :a. TE incidenceb. TM incidence Take -2lambda<y,z<2lambda for plotting. (Take lambda of your own choice. Amplitude = 1V/m.) If the angle of incidence is 30 degrees in the above case, what should be the E field distribution?arrow_forwardAt a frequency of 3 GHz and y-polarized, a plane wave travels in a magnetic medium with a dielectric constant of 2.5 and a loss tangent of 0.05 in the + x direction.a) Determine the distance at which the amplitude of the propagating wave will be halved.b) Find the impedance, wavelength and phase velocity of the wave in the medium.c) Assume E = ay50Sin (6pi (10 ^ 9) t + pi / 3) (V / m) at x = 0 and write the instantaneous expression of H for each t and x.arrow_forward
- A y-polarized smooth plane wave at a frequency of 3 GHz is propagating in the + x direction in a magnetic medium with a dielectric constant of 2.5 and a loss tangent of 0.05,a) Determine the distance at which the amplitude of the propagating wave will be halved.b) Find the impedance, wavelength and phase velocity of the wave in the medium.c) Assume E = ay 50sin (6π 10 9 t + π / 3) (V / m) at x = 0 and write your instantaneous expression of H for each t and x. (please show all steps one by one)arrow_forwardThe relative magnetic permeability (μr) of a lossless medium is given as 16 and the relative dielectric constant (r) as 25. The electric field component of a planar electromagnetic wave with a frequency of 1 MHz oscillates only along the x-axis and the wave travels in the + z direction. The electric field component of the wave takes a value of 500 V / m at the point z = 0.7 m at t = 70 ns. According to this; a) Find the phase constant (β), wavelength (λ), propagation velocity (up), and the impedance of the medium (η). b) Find the expressions ?⃗ (0.7, t) and ?⃗⃗ (0.7, t).arrow_forwardPlease answer both. 1. The electric field associated with a uniform plane wave propagating in the +z-direction in a nonmagnetic (u = uo.) material medium is given by Ē = Eo.e-2z cos(6(3)1/2 pi x 107 – 3z)x^ (V/m), a. Find the conductivity (sigma) of the medium. b. Find the permittivity ε of the medium. 2. For the circuit shown below: Determine R, if V(t = 3.8 us, l = 50m) = 62 (V). For the plane wave in free space, the electric field is defined as follows Ē = Eo. cos(6pi x 108t + 2pix)z^ Compute velocity and wavelength of the wave.arrow_forward
- Can you solve this problem step by steps A uniform plane wave propagating through a medium has E = 2 e-αz sin (106 t –βz) ay V/m.If the medium is characterized by εr = 1, μr = 10, and σ = 3 mhos/m, find(a) Check whether the medium is conductive or not(b) The attenuation constant and phase constant (c) Skin depth(d) H fieldarrow_forwardIn a uniform electromagnetic wave which is at a significant distance from the source of energy if the wave is falling from medium 1(z<0,σ=0,µr = 2,ɛr =9) to a second medium where the values are (z>0,σ=0,µr = 16,ɛr =4) . Find the values of reflection and transmission coefficient in this scenarioarrow_forwardA circularly polarized uniform plane wave of phasor electric field intensity Ei = (Aaz + j.sqrt{5}ay - Baz){e}^{-jkir} where A and B are real constants, and f = 3 GHz is obliquely incident from a dielectric medium with (3ε0, μ0) onto another dielectric with (2ε0, μ0) planar boundry z = 0 on xz plane. a) Find angle of incidence (so that reflected field is linearly polarized), numerical values of A and B, propagation vectors and the expression of the reflected electric field. b) Comment on the polarization of the transmitted wave without actually computing fields.c) Find the range of Incidence angles, so that incident field is totally reflected.arrow_forward
- Assuming that the amplitude of the electric intensity of a plane wave propagating in a certain lossy medium is 1 (mV/m) at P1 and 0,8 (mV/m) at P2 50(m) away, finda) the total attenuation between points P1 and P2 both in nepers and in decibels.b) α in (Np/m).arrow_forwardType your question here n an anisotropic medium, permittivity varies with electric field direction, and is a property seen in most crystals. Consider a uniform plane wave propagating in the z direction in such a medium, and which enters the material with equal field components along the x and y axes. The field phasor will take the form: ?? (?) = ?0(?? + ??? ?∆?? )? −??? Where ∆? = ?? − ?? is the difference in phase constants for waves that are linearly polarized in the x and y directions. Find distances into the material (in terms of ∆?) at which the field is (a) linearly polarized and (b) circularly polarized. (c) Assume intrinsic impedance ? that is approximately constant with field orientation and find ??and < S >.arrow_forwardDesign a dielectric-filled rectangular waveguide for transmission of electromagnetic power at 2.45 GHz. Find the maximum power the waveguide can transmit. Use an electric field safety factor of 10. Neglect conduction losses. The material filling the waveguide is nonmagnetic with zero conductivity, and has r = 2.1; its breakdown electric field is 6x107 V/m.arrow_forward
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What Is a Plane Wave? — Lesson 2; Author: EMViso;https://www.youtube.com/watch?v=ES2WFevGM0g;License: Standard Youtube License