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5. Electromagnetic wave in a conductor (10 points) Assume that there is an electromagnetic wave in...
The electric field of a plane electromagnetic wave in vacuum is Ē = Ēo cos(kz –...
The electric field of a plane electromagnetic wave in vacuum is Ē = Ēo cos(kz – wt), [1] where Ēo = (3î + 4ỹ) Vm-1 (a) Write down the expression for the magnetic field of this wave. (b) Compute the Maxwell tensor of the wave and provide a physical interpretation of your results. (c) If the frequency of the waves is f = 2.5 x 10Hz what is the energy density in the waves at t= 0 and z= 2.0...
[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...
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...
2. (a) Consider the propagation of a plane electromagnetic wave in a conductor. Show that the wav...
2. (a) Consider the propagation of a plane electromagnetic wave in a conductor. Show that the wavenumber, k, as a function of a, is given by the dispersion relationship ex ωε ωε where σ is the conductivity, μ is the permeability and ε is the permittivity of the conducting medium. (Hint: start with Maxwell's equations, and develop an equation of the form, V" E -k 2 E ). (3 marks) (b) Write down an expression for the physical electrical field...
Question 2: For an electromagnetic plane wave, the electric field is given by: Ē= E, cos(kz...
Question 2: For an electromagnetic plane wave, the electric field is given by: Ē= E, cos(kz +wt) ĉ +0 ġ+02 a) Determine the direction of propagation of the electromagnetic wave. b) Find the magnitude and direction of the magnetic field for the given electromagnetic wave B. c) Calculate the Poynting vector associated with this electromagnetic wave. What direction does this vector point? Does this makes sense? d) If the amplitude of the magnetic field was measured to be 2.5 *...
Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum...
Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. The wave is incident on a conductor which is placed at z > 0 region of the space. The conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) Find the characteristic time for the free charge density which dissipates at the conductor. (b) Write the Maxwell equations and derive the wave equation for a plane wave propagating in...
4. Consider the cylindrical waveguide below, which has an electromagnetic wave propagating in the space between...
4. Consider the cylindrical waveguide below, which has an
electromagnetic wave propagating in the space between the inner and
outer conductors, which is a gap where air exists. The radius of
the inner conductor is a, while the inner radius of the outer
conductor is b (as shown). The fields in the air-gap have the form
E = E0r cos (kz z ωt) B = B0r cos (kz z ωt) where E0 and B0 are
constants, r is the radial...
2. A plane electromagnetic wave, with wavelength 3.0 m, travels in vacuum in the positive x...
2. A plane electromagnetic wave, with wavelength 3.0 m, travels in vacuum in the positive x direction with its electric field Ē, of amplitude 300 V/m, directed along the y axis. (a) What is the frequency of the wave? (b) What are the direction and amplitude of the magnetic field associated with the wave? (c) What are the values of "k" and "o" if E = Eo sing (kx-ot)? (d) What is the time-averaged rate of energy flow in watts...
Electromagnetic plane waves in a lossy medium field of an electromagnetic plane wave traveling in a lossy medium can be written as 6. The where z is the distance, t is time, and f the frequency....
Electromagnetic plane waves in a lossy medium field of an electromagnetic plane wave traveling in a lossy medium can be written as 6. The where z is the distance, t is time, and f the frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (ie, to 130f the amplitude at z = 0 when it arrives at z-100 m)....
1. An electromagnetic plane wave is propagating through space. Its electric field vector is given by...
1. An electromagnetic plane wave is propagating through space. Its electric field vector is given by E i Eo cos(kz- ot). Its magnetic field vector is: a) B=jBo cos(kz-t) b) B- kBo cos(ky-at) c) B-iB, cos(ky-) d) B- kBo cos(kz-o) 1 2. The velocity of an electromagnetic plane wave is: a) In the electric field direction b) In the magnetic field direction c) In a direction parallel to the electric and magnetic fields d) In a direction perpendicular to the...
The electric field of a plane electromagnetic wave in vacuum is Ē = Ēo cos(kz – wt), [1] where Ēo = (3î + 4ỹ) Vm-1 (a) Write down the expression for the magnetic field of this wave. (b) Compute the Maxwell tensor of the wave and provide a physical interpretation of your results. (c) If the frequency of the waves is f = 2.5 x 10Hz what is the energy density in the waves at t= 0 and z= 2.0...
[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...
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...
2. (a) Consider the propagation of a plane electromagnetic wave in a conductor. Show that the wavenumber, k, as a function of a, is given by the dispersion relationship ex ωε ωε where σ is the conductivity, μ is the permeability and ε is the permittivity of the conducting medium. (Hint: start with Maxwell's equations, and develop an equation of the form, V" E -k 2 E ). (3 marks) (b) Write down an expression for the physical electrical field...
Question 2: For an electromagnetic plane wave, the electric field is given by: Ē= E, cos(kz +wt) ĉ +0 ġ+02 a) Determine the direction of propagation of the electromagnetic wave. b) Find the magnitude and direction of the magnetic field for the given electromagnetic wave B. c) Calculate the Poynting vector associated with this electromagnetic wave. What direction does this vector point? Does this makes sense? d) If the amplitude of the magnetic field was measured to be 2.5 *...
4. Consider the cylindrical waveguide below, which has an
electromagnetic wave propagating in the space between the inner and
outer conductors, which is a gap where air exists. The radius of
the inner conductor is a, while the inner radius of the outer
conductor is b (as shown). The fields in the air-gap have the form
E = E0r cos (kz z ωt) B = B0r cos (kz z ωt) where E0 and B0 are
constants, r is the radial...
2. A plane electromagnetic wave, with wavelength 3.0 m, travels in vacuum in the positive x direction with its electric field Ē, of amplitude 300 V/m, directed along the y axis. (a) What is the frequency of the wave? (b) What are the direction and amplitude of the magnetic field associated with the wave? (c) What are the values of "k" and "o" if E = Eo sing (kx-ot)? (d) What is the time-averaged rate of energy flow in watts...
Electromagnetic plane waves in a lossy medium field of an electromagnetic plane wave traveling in a lossy medium can be written as 6. The where z is the distance, t is time, and f the frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (ie, to 130f the amplitude at z = 0 when it arrives at z-100 m)....
1. An electromagnetic plane wave is propagating through space. Its electric field vector is given by E i Eo cos(kz- ot). Its magnetic field vector is: a) B=jBo cos(kz-t) b) B- kBo cos(ky-at) c) B-iB, cos(ky-) d) B- kBo cos(kz-o) 1 2. The velocity of an electromagnetic plane wave is: a) In the electric field direction b) In the magnetic field direction c) In a direction parallel to the electric and magnetic fields d) In a direction perpendicular to the...
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