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Question 3 (20 Marks) The plane z 0 forms the boundary between free space (z> 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...
Question 3 a) Two perfect dielectrics sit side by side in free space. Describe the boundary...
Question 3 a) Two perfect dielectrics sit side by side in free space. Describe the boundary conditions for E and the dielectric boundary. fields across 4 marks b) The boundary is parallel to the j direction. Material 1 has parameters &r-5 and 1. Material 2 has parameters Er-12 and 0.95. In material 1, there is a uniform E-field and H-field, with strengths: 10 20 Assuming no loss, what are the E and H field strengths in material 2? 6 marks...
Q2(a) A uniform plane wave propagating in a z in free space ( 0)is normally incident...
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...
12.2 The plane z = 0 is the boundary between the air and a magnetic material...
12.2 The plane z = 0 is the boundary between the air and a magnetic material with relative perameability of 100. In the air, H = (Hx, Hy, Hz) = (1, 1, 1) (A/m). Find the B (T) in the magnetic material.
The solid where z ≤ 9−x 2−y 2 is a perfect conductor. Outside this conductor is free space, where...
The solid where z ≤ 9−x 2−y 2 is a perfect conductor. Outside
this conductor is free space, where some distribution of charges
establishes this electric potential:
Question 4 [15 marks: The solid where 39-2-is a perfect conductor. Outside this conductor is free space, where some distribution of charges establishes this electric potential: V=xy(x2 + y2 + z-9) Volts. Find the total charge on the part of the conductor surface defined by >0, >0. Hint: Finding the partial derivatives of...
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3)...
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3) 0 Find the solution u using the expansion with the normalization conditions vn (0)-1, wn(0) 1 a. (3/10) Find the functionsw with index n1 b. (3/10) Find the functions vn with index n1 Un c. (4/10) Find the coefficients cn, with index n 1
Let u be...
3. An electric dipole with p -Qd a (C-m) is placed in free space at a distance h from a perfect c...
3. An electric dipole with p -Qd a (C-m) is placed in free space at a distance h from a perfect conducting plane of infinite extent. Determine the electrie potential at point P (0,) in region (15 marks) >0. Assume the distance between the dipole and the point P is much larger thand P (r, 0, 2) -0
3. An electric dipole with p -Qd a (C-m) is placed in free space at a distance h from a perfect conducting...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z) 28?u(t,z), te (0,00), z (0,3); with initial condition u(0, z)fx), where f(0) 0 and f (3) 0 and with boundary...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z) 28?u(t,z), te (0,00), z (0,3); with initial condition u(0, z)fx), where f(0) 0 and f (3) 0 and with boundary conditions u(t,0)-0, r 30 Using separation of variables, the solution of this problem is 4X with the normalization conditions un(m3ī)-. n@) : ї, a. (5/10) Find the functions wn with index n1. Wnlz) b. (5/10) Find the functions vn with index n 1. n(t)...
0 plane forms a chargeless interface between twe regions of space having different dielectric constants. coastant...
0 plane forms a chargeless interface between twe regions of space having different dielectric constants. coastant of 1 where the elds E, and D, are unknown Region 2 (ro) has a dielectric constant of 3 where also E- ?+21 vm is given. For 10 points each, find, with units, the folowing three ields: D, , Ei and by
A uniform plane wave propagating in free space reaches a planar dielectric boundary at normal incidence,...
A uniform plane wave propagating in free space reaches a planar dielectric boundary at normal incidence, as shown below. The dielectric medium is characterized by (mu_0, 4epsilon_0), and the incident power flux density is 10 watt/m^2. Find the (a) transmitted power flux density and (b) reflected power flux density. (c) If the dielectric medium is replaced by a perfect conducting medium, find the (a) transmitted power flux density and (b) reflected power flux density.
[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...
Question 3 a) Two perfect dielectrics sit side by side in free space. Describe the boundary conditions for E and the dielectric boundary. fields across 4 marks b) The boundary is parallel to the j direction. Material 1 has parameters &r-5 and 1. Material 2 has parameters Er-12 and 0.95. In material 1, there is a uniform E-field and H-field, with strengths: 10 20 Assuming no loss, what are the E and H field strengths in material 2? 6 marks...
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...
The solid where z ≤ 9−x 2−y 2 is a perfect conductor. Outside
this conductor is free space, where some distribution of charges
establishes this electric potential:
Question 4 [15 marks: The solid where 39-2-is a perfect conductor. Outside this conductor is free space, where some distribution of charges establishes this electric potential: V=xy(x2 + y2 + z-9) Volts. Find the total charge on the part of the conductor surface defined by >0, >0. Hint: Finding the partial derivatives of...
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3) 0 Find the solution u using the expansion with the normalization conditions vn (0)-1, wn(0) 1 a. (3/10) Find the functionsw with index n1 b. (3/10) Find the functions vn with index n1 Un c. (4/10) Find the coefficients cn, with index n 1
Let u be...
3. An electric dipole with p -Qd a (C-m) is placed in free space at a distance h from a perfect conducting plane of infinite extent. Determine the electrie potential at point P (0,) in region (15 marks) >0. Assume the distance between the dipole and the point P is much larger thand P (r, 0, 2) -0
3. An electric dipole with p -Qd a (C-m) is placed in free space at a distance h from a perfect conducting...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z) 28?u(t,z), te (0,00), z (0,3); with initial condition u(0, z)fx), where f(0) 0 and f (3) 0 and with boundary conditions u(t,0)-0, r 30 Using separation of variables, the solution of this problem is 4X with the normalization conditions un(m3ī)-. n@) : ї, a. (5/10) Find the functions wn with index n1. Wnlz) b. (5/10) Find the functions vn with index n 1. n(t)...
0 plane forms a chargeless interface between twe regions of space having different dielectric constants. coastant of 1 where the elds E, and D, are unknown Region 2 (ro) has a dielectric constant of 3 where also E- ?+21 vm is given. For 10 points each, find, with units, the folowing three ields: D, , Ei and by
A uniform plane wave propagating in free space reaches a planar dielectric boundary at normal incidence, as shown below. The dielectric medium is characterized by (mu_0, 4epsilon_0), and the incident power flux density is 10 watt/m^2. Find the (a) transmitted power flux density and (b) reflected power flux density. (c) If the dielectric medium is replaced by a perfect conducting medium, find the (a) transmitted power flux density and (b) reflected power flux density.
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