Homework Answers
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(i) Consider the wave Ē(7,t) = Ło cos(wt – k ), where Ē, is a fixed...
4. Plot the locus of E(0,t) for a plane wave with Ē (z,t) = î cos(wt+kz)...
4. Plot the locus of E(0,t) for a plane wave with Ē (z,t) = î cos(wt+kz) +ŷ 1.3 sin(wt + kz) (V/m) Determine the polarization state from your plot. Determine the direction of propagation of the wave.
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 *...
For the electromagnetic wave represented by the equations E_y(x, t) = E_max cos(kx + Wt), B_z(x,...
For the electromagnetic wave represented by the equations E_y(x, t) = E_max cos(kx + Wt), B_z(x, t) = -B_max cos(kx + omega t), find the direction of the Poynting vector. in the - y -direction in the +x -direction in the +y -direction in the -x -direction Part B Find the average magnitude of the Poynting vector. Express your answer in terms of the variables E_max, B_max, and appropriate constants (mu 0 or epsilon_0). submit
Question 2: For an electromagnetic plane wave, the electric field is given by: Ē = E,...
Question 2: For an electromagnetic plane wave, the electric field is given by:$$ \vec{E}=E_{0} \cos (k z+\omega t) \hat{x}+0 \hat{y}+0 \hat{z} $$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 \(\vec{B}\).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 \(2.5 * 10^{-7} \mathrm{~T}\),...
[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...
5. In a lossless nonmagnetic medium with er = 4, E(y,t) = 20 cos(108nt +By+)a, V/m...
5. In a lossless nonmagnetic medium with er = 4, E(y,t) = 20 cos(108nt +By+)a, V/m Find the following: (a) Direction of propagation and the wave length , Speed of propagation of the wave and propagation constant, B, attenuation constant, (b) using the Maxwell's equation, find the magnetic field intensity H(y,t) (c) phase angle between the E and H fields.
An electromagnetic wave traveling in the -x direction in vacuum has a frequency 2x1014Hz. The electric...
An electromagnetic wave traveling in the -x direction in vacuum
has a frequency 2x1014Hz. The electric field in the wave has
maximum value of 2 V/m. If we define the time and position such
that the electric field has maximum value at position x=0 at
time=0, a possible equation describing the electric field is:
"⃗
a. ?=(2V/m)sin[(4.2x106 /m)x-(1.3x1015Hz)t]?̂
"⃗ ' b. ?=(2V/m)cos[(4.2x106 /m)x+(1.3x1015Hz)t]?
"⃗ ' c. ?=(1V/m)sin[(1.3x1015 /m)x-(4.2x106Hz)t]?
"⃗
d. ?=(4V/m)cos[(4.2x106 /m)x+(1.3x1015Hz)t]?̂
2. An electromagnetic wave traveling in the -x...
E (t) = Eo cos (kz-wt) Where k is the wave-number and w is the angular...
E (t) = Eo cos (kz-wt) Where k is the wave-number and w is the angular frequency of the wave. Now some scientist tells you that a distant star has been observed to be green in color, with an observed frequency of fobserved 550 THz (terahertz, 1012). She also says that from other factors, it is known that the star should be emitting light with wavelength factual-1800 THz somewhere in the UV spectrum. They ask you to find two things...
Problem 3 Consider a possible solution to Maxwell's equations in vacuum given by A(x, t) =...
Problem 3 Consider a possible solution to Maxwell's equations in vacuum given by A(x, t) = Ao exp(i(kx - wt)), V(x, t) = 0 where A is the vector potential and V is the scalar potential. Suppose Ao, k and w are constants in space and time. a) Compute the time-dependent electric and magnetic fields from the given potentials. Show your work. b) Give the contraints, if any, on Ao, k and w imposed by the following two Maxwell's equations...
Problem 4: Time harmonic waves in lossy dielectric Start with Maxwell's equations and show that t...
Problem 4: Time harmonic waves in lossy dielectric Start with Maxwell's equations and show that the electric field E(x, y, z, t) in a conductive material with conductivity σ satisfies the following wave equation a. 72 _ με.at? _ μσαί)F-0 b. Show that the following is a solution E(F, t)-(8 + 9) Eo e-kız cos(at-kez) where Eo is a constant and kR and k, are given by 0.5 w22 c. Obtain the direction of propagation for the wave in part...
4. Plot the locus of E(0,t) for a plane wave with Ē (z,t) = î cos(wt+kz) +ŷ 1.3 sin(wt + kz) (V/m) Determine the polarization state from your plot. Determine the direction of propagation of the wave.
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 *...
For the electromagnetic wave represented by the equations E_y(x, t) = E_max cos(kx + Wt), B_z(x, t) = -B_max cos(kx + omega t), find the direction of the Poynting vector. in the - y -direction in the +x -direction in the +y -direction in the -x -direction Part B Find the average magnitude of the Poynting vector. Express your answer in terms of the variables E_max, B_max, and appropriate constants (mu 0 or epsilon_0). submit
Question 2: For an electromagnetic plane wave, the electric field is given by:$$ \vec{E}=E_{0} \cos (k z+\omega t) \hat{x}+0 \hat{y}+0 \hat{z} $$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 \(\vec{B}\).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 \(2.5 * 10^{-7} \mathrm{~T}\),...
[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...
5. In a lossless nonmagnetic medium with er = 4, E(y,t) = 20 cos(108nt +By+)a, V/m Find the following: (a) Direction of propagation and the wave length , Speed of propagation of the wave and propagation constant, B, attenuation constant, (b) using the Maxwell's equation, find the magnetic field intensity H(y,t) (c) phase angle between the E and H fields.
An electromagnetic wave traveling in the -x direction in vacuum
has a frequency 2x1014Hz. The electric field in the wave has
maximum value of 2 V/m. If we define the time and position such
that the electric field has maximum value at position x=0 at
time=0, a possible equation describing the electric field is:
"⃗
a. ?=(2V/m)sin[(4.2x106 /m)x-(1.3x1015Hz)t]?̂
"⃗ ' b. ?=(2V/m)cos[(4.2x106 /m)x+(1.3x1015Hz)t]?
"⃗ ' c. ?=(1V/m)sin[(1.3x1015 /m)x-(4.2x106Hz)t]?
"⃗
d. ?=(4V/m)cos[(4.2x106 /m)x+(1.3x1015Hz)t]?̂
2. An electromagnetic wave traveling in the -x...
E (t) = Eo cos (kz-wt) Where k is the wave-number and w is the angular frequency of the wave. Now some scientist tells you that a distant star has been observed to be green in color, with an observed frequency of fobserved 550 THz (terahertz, 1012). She also says that from other factors, it is known that the star should be emitting light with wavelength factual-1800 THz somewhere in the UV spectrum. They ask you to find two things...
Problem 3 Consider a possible solution to Maxwell's equations in vacuum given by A(x, t) = Ao exp(i(kx - wt)), V(x, t) = 0 where A is the vector potential and V is the scalar potential. Suppose Ao, k and w are constants in space and time. a) Compute the time-dependent electric and magnetic fields from the given potentials. Show your work. b) Give the contraints, if any, on Ao, k and w imposed by the following two Maxwell's equations...
Problem 4: Time harmonic waves in lossy dielectric Start with Maxwell's equations and show that the electric field E(x, y, z, t) in a conductive material with conductivity σ satisfies the following wave equation a. 72 _ με.at? _ μσαί)F-0 b. Show that the following is a solution E(F, t)-(8 + 9) Eo e-kız cos(at-kez) where Eo is a constant and kR and k, are given by 0.5 w22 c. Obtain the direction of propagation for the wave in part...
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