As shown in the figure on the back, the region x < 0 is free space,...
A uniform TEM plane wave in free-space (z < 0) is incident normally on a semi- infinite non-magnetic dielectric region (z > 0). The total frequency-domain magnetic field intensity in free-space is given by: Ħ, = (4e-j242 + 2ej2nz)ây [A/m] The standing wave ratio in the dielectric region is: O 1.0 None of them 3.0 O 0.0 O 0.5
In free space (x ≤ 0), a plane wave with ? ⃗ = 100 sin(3x108t - βx)? y V/m is incident normally on a lossless medium (ε= 6ε0, ?= 8μ0) in region x ≥ 0. Determine the reflected and the transmitted wave electric and magnetic field equations.
1. In the region x<0 (air), an electromagnetic uniform plane wave with phasorelectric fieldAIR 1 PEC E (x)-iSe is incident upon a perfect electric conductor (PEC) at x -0 Leave answers in terms of free space (air) parameters k,70 Find the (a) phasor reflected electric field E b) total phasor magnetic field H(x) in the air region xco () phasor surface electric current density Js on the perfect electric conductor (PEC)
1. In the region x
Electromagnetic Wave Theory
Kong Problem 3-35
In a parallel-plate waveguide, the region z < 0 is free space
and the region z > 0 is filled with a dielectric medium having
permittivity
. How would you write the modes for both regions? For a TM mode
incident upon the dielectric from the z < 0 region, show that
there is no reflected wave when
. Compare this result with the case of a wave incident upon a
half-space medium at...
2) Compute the field in region 2 (inside the solid dielectric cylinder). For this problem, assume that the region around the cylinder is free space with μ,-Ho and that the dielectric cylinder has μ2-Spio. Also, the magnetic field in region 1 is Hi-coso, +p4 + sind, and assume that a surface current exists in the z-direction denoted as J, Jo,. Write H2 in cylindrical coordinates. region 1 free space region 2 Figure 2. Diagram for problem 2
2) Compute the...
Q2(a) A uniform plane wave propagating in a z in free space ( 0)is normally incident at z-0 on a conductor (z>0) for which ?-61.7 MS/m, r 1 The free-space E wave has a frequency s-1.SMHz and an amplitude of 1.0 V/m; at the interface it is given by Develop He,t fo0 (10 marks) (b) In free space, Generate the: Phase constant p (2 marks) (ii) Wavelength (2 marks) (ii) Phase velocity v, (2 marks) (iv) Intrinsic impedance of the...
Q3) An incident wave travels in free-space along the z-direction and impinges upon a cube of dielectric material with a constant permittivity of ε. The faces of the dielectric cube are parallel to the x-y. y-z, x-z planes. The length of each side of the cube is d. The polarization of the incident electric field is along the x-axis. Use the Born approximation to calculate the scattered electric and magnetic fields in the far-field zone along the ks-R, =+x and...
3.A uniform electromagnetic plane wave is normally incident from the air region ( medium #1 with+ η = η。= 120π ) upon the planar interface separating air from a lossy dielectric medium (medium #2 with intrinsic impedance 20π + jlOr ). The incident plane wave in air has a phasor electric field given by E(x)-le, x<0 Find: (a) the frequency f (Hertz) (b) the magnitude and the phase of the reflected phasor electric field E as a function of coordinates...
Equipotential lines for some region of space are shown in the figure. o v +1 V B. 0 m 1 m ITm What is the approximate magnitude of the electric field Es at point A? EA 15 What is the approximate magnitude of the electric field En at point En 3.5 V/m V/m
424· The complex electric field of a uniform 4.26. In a source-free, free-space region, the plane wave is given by complex magnetic field of a time-harmonic field is represented by (a) Find the polarization of the wave (lin- ear, circular, or elliptical) (b) Determine the sense of rotation (clock wise or counterclockwise). (c) Sketch the figure the electric field where EO is a constant and Po is the intrin- sic impedance of free space. Determine the: (a) Polarization of the...