The permittivity and permeability of medium 1 are εo and μo, while medium 2 has ε...
The permittivity and permeability of medium 1 are εo and μo, while medium 2 has ε and μo, where ε > εo. The Poynting vector S, given by S = E x H, represents the energy flow per unit cross-sectional area per unit time of an electromagnetic wave. Prove that if light normally incident from the medium 1 into the medium 2 is transmitted without any reflection, this violates the boundary conditions.
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The permittivity and permeability of medium 1 are εo
and μo, while medium 2 has ε...
19. A linearly polarized wave propagates in a perfect dielectric medium with relative permittivity of 2....
19. A linearly polarized wave propagates in a perfect dielectric medium with relative permittivity of 2. The wave reaches the interface between this medium and air at an angle of incidence 60°. The wave's electric field vector is parallel to the plane of incidence. What percentage of the incident power is transmitted in air? 20. A plane electromagnetic wave traveling in vacuum is normally incident onto a vacuum/dielectric boundary. 36% of the incident power is carried by the reflected wave....
2A uniform electromagnetic plane wave is normally incident norm the air region (medium #1 with intrinsic medium (medium #2 with intrinsic k,- and wavenumber k ) upon the planar interface separati...
2A uniform electromagnetic plane wave is normally incident norm the air region (medium #1 with intrinsic medium (medium #2 with intrinsic k,- and wavenumber k ) upon the planar interface separating air from a lossy dielectric impedance 'h-%(I + J) and wavenumber (1-)).The incident plane wave in air has a phasor electric field given by 2. Find (leave all answers in terms ofm: (a) value of the wavenumber in air, ko (b) attenuation constant α and phase constant β (c)...
A plane wave of angular frequency ω is incident on a plasma medium with permeability µ0...
A plane wave of angular frequency ω is incident on a plasma
medium with permeability µ0 and permittivity ε = ε0 (1 −
ωp2 /ω2) where ωp is
the plasma frequency and ω = 2ωp.
a) Calculate the critical angle θc such that the incident wave
is totally reflected
b) Calculate the Brewster angle θB such that TM waves
are totally transmitted
c) In general for any two isotropic media, can you find an
incident angle θ such that θ...
3. A uniform plane electromagnetic wave with the time harmonic electric field intensity vector E' =ǐ10cos(cr-6m) (volts/meter) 46.μ.-Ha ) upon the is incident from the lossless medium I ( Ei 수x...
3. A uniform plane electromagnetic wave with the time harmonic electric field intensity vector E' =ǐ10cos(cr-6m) (volts/meter) 46.μ.-Ha ) upon the is incident from the lossless medium I ( Ei 수x lossless half-space medium 2 (629 Find: 4o) (a) the wave numbers and intrinsic impedances of each medium expressed in terms of air parameters ko and巩; give formulas for these air parameters. (b) the phasor reflected and transmitted electric field intensities Leave answers (c) the phasor reflected and transmitted magnetic...
A plane electromagnetic wave with a time-averaged Poynting vector 〈S!〉 is incident on a long prism made from a conduc...
A plane electromagnetic wave with a time-averaged Poynting vector 〈S!〉 is incident on a long prism made from a conducting material which has a cross-section in the shape of an equilateral triangle, with side length a (see figure below). Assume that the prism is large compared to the wavelength of the electromagnetic wave and that scattering from the corners can be neglected. In other words, it can be assumed that the outgoing waves are produced by specular reflection from the...
A5-MHz wave propagates in a lossy medium characterized with g = 32 S/m, ε = 36.4=1....
A5-MHz wave propagates in a lossy medium characterized with g = 32 S/m, ε = 36.4=1. a) Compute the loss tangent of the medium and determine whether this medium is a low-loss dielectric, a good conductor, or neither. b) Compute the wavelength of the wave in the medium. c) After traveling a distance equal to 3 penetration depths into the medium, the wave's E-field amplitude has decreased to 0.25 V/m. What is the initial E-field amplitude just after the wave...
Please answer all parts of the question (a,b,c,d,e) Consider the case of oblique incidence of electromagnetic plane waves going from medium 1 to a. Draw a diagram showing the wavevectors and the direc...
Please answer all parts of the
question (a,b,c,d,e)
Consider the case of oblique incidence of electromagnetic plane waves going from medium 1 to a. Draw a diagram showing the wavevectors and the directions of the electric and magnetic b. Using the appropriate boundary conditions, obtain the Fresnel equations for the reflected 1. medium 2 with the polarization perpendicular to the plane of incidence. fields of the incident, reflected, and transmitted waves for an angle of incidence θ| and transmitted complex...
Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in...
Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields, respectively, and also makes a useful connection between the energy density of a plane electromagnetic wave and the Poynting vector. In this problem, we explore the properties of a plane electromagnetic wave traveling at the speed of light c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: E = E, sin (kx...
To practice Tactics Box 18.1 Analyzing refraction. If a ray refracts between medium 1 and medium 2, having indices of...
To practice Tactics Box 18.1 Analyzing refraction. If a ray refracts between medium 1 and medium 2, having indices of refraction n1 and n2, the ray angles θ1 and θ2 in the two media are related by Snell's law, n1sinθ1=n2sinθ2. This law becomes a central idea in a procedure for analyzing refraction problems, as explained in the following Tactics Box. Draw a ray diagram. Represent the light beam with one ray. Draw a line normal to the boundary. Do this...
[132 2 2 3 4 17 marks] Question 4 A plane wave is travelling in a...
[132 2 2 3 4 17 marks] Question 4 A plane wave is travelling in a vacuum in the +z-direction with wavenumber k and angular frequency . It is linearly polarised in the x-direction, and has electric field given by E(t, z) Eo Cos(kz - wt)f This wave is normally incident on a perfectly electrically conducting, semi-infinite slab in the region z > 0 and the resulting field in vacuum (z < 0) is a superposition of the incident and...
19. A linearly polarized wave propagates in a perfect dielectric medium with relative permittivity of 2. The wave reaches the interface between this medium and air at an angle of incidence 60°. The wave's electric field vector is parallel to the plane of incidence. What percentage of the incident power is transmitted in air? 20. A plane electromagnetic wave traveling in vacuum is normally incident onto a vacuum/dielectric boundary. 36% of the incident power is carried by the reflected wave....
2A uniform electromagnetic plane wave is normally incident norm the air region (medium #1 with intrinsic medium (medium #2 with intrinsic k,- and wavenumber k ) upon the planar interface separating air from a lossy dielectric impedance 'h-%(I + J) and wavenumber (1-)).The incident plane wave in air has a phasor electric field given by 2. Find (leave all answers in terms ofm: (a) value of the wavenumber in air, ko (b) attenuation constant α and phase constant β (c)...
A plane wave of angular frequency ω is incident on a plasma
medium with permeability µ0 and permittivity ε = ε0 (1 −
ωp2 /ω2) where ωp is
the plasma frequency and ω = 2ωp.
a) Calculate the critical angle θc such that the incident wave
is totally reflected
b) Calculate the Brewster angle θB such that TM waves
are totally transmitted
c) In general for any two isotropic media, can you find an
incident angle θ such that θ...
3. A uniform plane electromagnetic wave with the time harmonic electric field intensity vector E' =ǐ10cos(cr-6m) (volts/meter) 46.μ.-Ha ) upon the is incident from the lossless medium I ( Ei 수x lossless half-space medium 2 (629 Find: 4o) (a) the wave numbers and intrinsic impedances of each medium expressed in terms of air parameters ko and巩; give formulas for these air parameters. (b) the phasor reflected and transmitted electric field intensities Leave answers (c) the phasor reflected and transmitted magnetic...
A plane electromagnetic wave with a time-averaged Poynting vector 〈S!〉 is incident on a long prism made from a conducting material which has a cross-section in the shape of an equilateral triangle, with side length a (see figure below). Assume that the prism is large compared to the wavelength of the electromagnetic wave and that scattering from the corners can be neglected. In other words, it can be assumed that the outgoing waves are produced by specular reflection from the...
A5-MHz wave propagates in a lossy medium characterized with g = 32 S/m, ε = 36.4=1. a) Compute the loss tangent of the medium and determine whether this medium is a low-loss dielectric, a good conductor, or neither. b) Compute the wavelength of the wave in the medium. c) After traveling a distance equal to 3 penetration depths into the medium, the wave's E-field amplitude has decreased to 0.25 V/m. What is the initial E-field amplitude just after the wave...
Please answer all parts of the
question (a,b,c,d,e)
Consider the case of oblique incidence of electromagnetic plane waves going from medium 1 to a. Draw a diagram showing the wavevectors and the directions of the electric and magnetic b. Using the appropriate boundary conditions, obtain the Fresnel equations for the reflected 1. medium 2 with the polarization perpendicular to the plane of incidence. fields of the incident, reflected, and transmitted waves for an angle of incidence θ| and transmitted complex...
Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields, respectively, and also makes a useful connection between the energy density of a plane electromagnetic wave and the Poynting vector. In this problem, we explore the properties of a plane electromagnetic wave traveling at the speed of light c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: E = E, sin (kx...
[132 2 2 3 4 17 marks] Question 4 A plane wave is travelling in a vacuum in the +z-direction with wavenumber k and angular frequency . It is linearly polarised in the x-direction, and has electric field given by E(t, z) Eo Cos(kz - wt)f This wave is normally incident on a perfectly electrically conducting, semi-infinite slab in the region z > 0 and the resulting field in vacuum (z < 0) is a superposition of the incident and...
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