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d (25 marks): The magnetic field of an EM wave is B = Bosin (kr -...
Question A2 [20 marks] Two plane waves are propagating in a linear dielectric material (ε-ε0G, μ-...
Question A2 [20 marks] Two plane waves are propagating in a linear dielectric material (ε-ε0G, μ-Ho) and are described by their respective complex electric field vectors as shown below: (a) [2 marks] Write down the direction of propagation of wave 1 and that of wave 2 (b) [2 marks] Write down the polarization-direction of wave 1 and that of wave 2. (c) [4 marks] What is the total (real) electric field Etot-Ei +E2? (d) [4 marks] What is the total...
4. (30) A linearly polarized electromagnetic wave has the following magnetic field component: B(x,t)-Bo sin(kr -ut)...
4. (30) A linearly polarized electromagnetic wave has the following magnetic field component: B(x,t)-Bo sin(kr -ut) Calculate the electric field of the electromagnetic wave by using the Maxwell term of the Ampere-Maxwell equation, evaluating the curl of the magnetic field, and then integrating to get the electric field.
a) The peak magnitude of the magnetic field in a particular electromagnetic wave in a vacuum...
a) The peak magnitude of the magnetic field in a particular electromagnetic wave in a vacuum is 1.0E-12 T. What is the peak electric field magnitude for the same wave? b) If at a given time t0 the Magnetic field vector for the wave pointed in the +z direction, what direction would the electric field point at that time? c) At time t0, which direction is the EM wave traveling? d) What is the speed of the wave? e) What...
kr ky (4) A plane EM wave with frequency o propagates in vacuum and approaches a...
kr ky (4) A plane EM wave with frequency o propagates in vacuum and approaches a dielectric interface (permittivity &, permeability u and refractive index n) at an angle of incidence Oi with its electric field parallel to the plane of incidence. If the incident E and B fields are of the form E(r, t) = Eel(k.r-wt) and B(r,t) = -K XE 'By (a) Write the boundary conditions satisfied by the fields at the interface (b) Derive the reflection and...
EM wavelength in water 1. At frequency w = 10 GHz, liquid water has a permittivity...
EM wavelength in water
1. At frequency w = 10 GHz, liquid water has a permittivity e = 1 i€2, With ei 80eo, 15€0, and a permeability u= Ho E2 (a) Starting from the Maxwell equations, show that the wave equation for EM waves in water, is given by VE(r, t) eHo2Er, t) (b) Show that the wave E(r, t) = żEg exp [i (kx - wt)] is a solution to the wave equation with k kR+ik, complex and w...
1. The electric field of an electromagnetic wave traveling through vacuum is the following: 5.90x1 :...
1. The electric field of an electromagnetic wave traveling through vacuum is the following: 5.90x1 : + a. Draw a qualitative sketch of this E function for t = 0. Add the B field as well to complete the EM wave. Be sure to label the axes. Don't worry about your drawing ability. b. What is the magnitude of the magnetic field B.? C. What is the wavelength of the EM wave? d. What is the frequency of the EM...
Find the magnetic field amplitude in an EM wave if the electric field amplitude is 681000.N/C....
Find the magnetic field amplitude in an EM wave if the electric field amplitude is 681000.N/C. 14. A B. C --/ 0.002381 T 0.00227.T 0.002565 T D. E F. 0.002733.T 0.002489.T 0.002649.T An electromagnetic wave with wavelength 0.0000286 m has what frequency? 15. A. B. C. 1.014E+13 Hz 1.049E-13 Hz 1.164E+13 Hz D. E F. 1.211E+13 Hz 1.132E+13 Hz 1.089E+13 Hz An electromagnetic wave with frequency 36400 Hz has what wavelength? 16. A. B. C. 8242 m 7589 m 6788...
[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...
1. If the electric field in an EM wave in free space has a peak magnitude...
1. If the electric field in an EM wave in free space has a peak magnitude of 8.7×10−5V/m, what is the peak magnitude of the magnetic field strength? B0 = _________ T 2. A 1500-nF capacitor with circular parallel plates2.0 cm in diameter is accumulating charge at the rate of 39.0 mC/s at some instant in time. a) What will be the induced magnetic field strength 12.5 cm radially outward from the center of the plates? B1 = _______ T...
(a) What are the wavelength and frequency of the EM wave? (b) Write an equation for...
(a) What are the wavelength and
frequency of the EM wave?
(b) Write an equation for the magnetic field vector of the EM
field.
(c) What is the average Poynting vector?
. The y-component of the electric field of an electromagnetic(EM) field traveling in the x-direction through vacuum obeys the equation Ēy(1,t) = (325 N/C) cos[(4500 m-1)– (1.35 x 1012 rad/s)t +0.6]j (a) What are the wavelength and frequency of the EM wave?
Question A2 [20 marks] Two plane waves are propagating in a linear dielectric material (ε-ε0G, μ-Ho) and are described by their respective complex electric field vectors as shown below: (a) [2 marks] Write down the direction of propagation of wave 1 and that of wave 2 (b) [2 marks] Write down the polarization-direction of wave 1 and that of wave 2. (c) [4 marks] What is the total (real) electric field Etot-Ei +E2? (d) [4 marks] What is the total...
4. (30) A linearly polarized electromagnetic wave has the following magnetic field component: B(x,t)-Bo sin(kr -ut) Calculate the electric field of the electromagnetic wave by using the Maxwell term of the Ampere-Maxwell equation, evaluating the curl of the magnetic field, and then integrating to get the electric field.
kr ky (4) A plane EM wave with frequency o propagates in vacuum and approaches a dielectric interface (permittivity &, permeability u and refractive index n) at an angle of incidence Oi with its electric field parallel to the plane of incidence. If the incident E and B fields are of the form E(r, t) = Eel(k.r-wt) and B(r,t) = -K XE 'By (a) Write the boundary conditions satisfied by the fields at the interface (b) Derive the reflection and...
EM wavelength in water
1. At frequency w = 10 GHz, liquid water has a permittivity e = 1 i€2, With ei 80eo, 15€0, and a permeability u= Ho E2 (a) Starting from the Maxwell equations, show that the wave equation for EM waves in water, is given by VE(r, t) eHo2Er, t) (b) Show that the wave E(r, t) = żEg exp [i (kx - wt)] is a solution to the wave equation with k kR+ik, complex and w...
1. The electric field of an electromagnetic wave traveling through vacuum is the following: 5.90x1 : + a. Draw a qualitative sketch of this E function for t = 0. Add the B field as well to complete the EM wave. Be sure to label the axes. Don't worry about your drawing ability. b. What is the magnitude of the magnetic field B.? C. What is the wavelength of the EM wave? d. What is the frequency of the EM...
Find the magnetic field amplitude in an EM wave if the electric field amplitude is 681000.N/C. 14. A B. C --/ 0.002381 T 0.00227.T 0.002565 T D. E F. 0.002733.T 0.002489.T 0.002649.T An electromagnetic wave with wavelength 0.0000286 m has what frequency? 15. A. B. C. 1.014E+13 Hz 1.049E-13 Hz 1.164E+13 Hz D. E F. 1.211E+13 Hz 1.132E+13 Hz 1.089E+13 Hz An electromagnetic wave with frequency 36400 Hz has what wavelength? 16. A. B. C. 8242 m 7589 m 6788...
[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...
(a) What are the wavelength and
frequency of the EM wave?
(b) Write an equation for the magnetic field vector of the EM
field.
(c) What is the average Poynting vector?
. The y-component of the electric field of an electromagnetic(EM) field traveling in the x-direction through vacuum obeys the equation Ēy(1,t) = (325 N/C) cos[(4500 m-1)– (1.35 x 1012 rad/s)t +0.6]j (a) What are the wavelength and frequency of the EM wave?
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