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Q7. You are presented the derivation of equation of velocity of electromagnetic wave as follows. Fill...
In a medium characterised by a = 0,4 = Ho,€, an electromagnetic wave is described by;...
In a medium characterised by a = 0,4 = Ho,€, an electromagnetic wave is described by; E = Em sin(wt -ky) a, V/m a) find an expression for; (1 marks) ii. B (5 marks) b) Sketch E and Hatt=0. (3 marks) c) The electromagnetic wave enters a region and propagates such that; i. D Em = 50 V /m, do = 2mx10? rad/s, k = 5 i. State the direction of wave propagation ii. Compute the period T, velocity v...
5. (Hints: This derivation is presented in your textbook briefly. I also discussed that in the cl...
plz if you could make it clear.
will thumb up
5. (Hints: This derivation is presented in your textbook briefly. I also discussed that in the class. I would like you to provide step-by-step process for this mathematical derivation. You need to use the continuity equation (Eq. 6-21) for the derivation process) Starting from the first law of Thermodynamics for a differential control volume, derive the general governing equation for temperature (6-35) for a 2D flow over flat plate. Using...
2. 24 pts. Boundary conditions for EM wave reflection and transmission. The boundary conditions i...
2. 24 pts. Boundary conditions for EM wave reflection and transmission. The boundary conditions incident on a boundary can be written as: conditions on electromagnetic waves (ii) E- E0 (ii) B-B: =0 (a) 10 pts. Corresponding Maxwell Equations. For each equation (i, ii, iii, iv) above write the corresponding Maxwell equation in BOTH operator form AND in integral form from which the boundary condition can be derived. What terms in Maxwell's equations are assumed to be zero in the above?...
d1=8 d2=9 lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero in...
d1=8
d2=9
lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
d1= 3 & d2= 2 Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram bel...
d1= 3 & d2= 2
Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and 1, somewhat similar to fex) on page 8s of the Notes Part 2. 2 d2+5 r-0 di+10 di+15 di+20 3...
Question 1: As you work through the parts of this question you are going to show...
Question 1: As you work through the parts of this question you are going to show that the Maxwell equations naturally contain electromagnetic waves. In a region of space that is void of all charges and currents, p=0 and J = 0 the Maxwell equations come out to be: Y E = 0 7.B=0 7 x Ē = -1 1 x B = Poco a) Using the same idea as I did in the lecture, derive the Wave Equation for...
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy...
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy dy +y?, y(0) = 1, y'(0) = -1, "(0) = 2 dt3 dt (a) [5pts. Transform the above initial value problem into an equivalent first order differential system, including initial conditions. (b) [2pts.] Express the system and the initial condition in (a) in vector form. (c) [4pts.] Using the second order Runge Kutta method as follows Ū* = Ūi + hĚ(ti, Ūi) h =...
Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular...
Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular displacement (angle of twist) along the shaft, z is the distance from the end of the shaft and t is time. For a shaft of length that is supported by frictionless bearings at each end, boundary conditions are 0(0,t) 0(4x,t) 0, t> 0. Suppose that the initial angular displacement and angular velocity are e(z,0) 3cos(2r), 0(z,0)= 4+cos(2r), 0<z< 4m, respectively You may use the...
Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular...
Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular displacement (angle of twist) along the shaft, z is the distance from the end of the shaft and t is time. For a shaft of length that is supported by frictionless bearings at each end, boundary conditions are 0(0,t) 0(4x,t) 0, t> 0. Suppose that the initial angular displacement and angular velocity are e(z,0) 3cos(2r), 0(z,0)= 4+cos(2r), 0<z< 4m, respectively You may use the...
2. The electric field in a plane wave is described by the equation (k > 0):...
2. The electric field in a plane wave is described by the equation (k > 0): Ē(x,y,z,1)= E, sin(kz – mt)ị Answer the following questions about the wave. i. What direction is the wave traveling? Explain how you can tell from the equation for the electric field. ii. Write an expression for the magnitude of the magnetic field of the wave. iii. Calculate the average intensity of the wave if Eo = 3000 V/m. The MKS units of intensity are...
In a medium characterised by a = 0,4 = Ho,€, an electromagnetic wave is described by; E = Em sin(wt -ky) a, V/m a) find an expression for; (1 marks) ii. B (5 marks) b) Sketch E and Hatt=0. (3 marks) c) The electromagnetic wave enters a region and propagates such that; i. D Em = 50 V /m, do = 2mx10? rad/s, k = 5 i. State the direction of wave propagation ii. Compute the period T, velocity v...
plz if you could make it clear.
will thumb up
5. (Hints: This derivation is presented in your textbook briefly. I also discussed that in the class. I would like you to provide step-by-step process for this mathematical derivation. You need to use the continuity equation (Eq. 6-21) for the derivation process) Starting from the first law of Thermodynamics for a differential control volume, derive the general governing equation for temperature (6-35) for a 2D flow over flat plate. Using...
2. 24 pts. Boundary conditions for EM wave reflection and transmission. The boundary conditions incident on a boundary can be written as: conditions on electromagnetic waves (ii) E- E0 (ii) B-B: =0 (a) 10 pts. Corresponding Maxwell Equations. For each equation (i, ii, iii, iv) above write the corresponding Maxwell equation in BOTH operator form AND in integral form from which the boundary condition can be derived. What terms in Maxwell's equations are assumed to be zero in the above?...
d1=8
d2=9
lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
d1= 3 & d2= 2
Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and 1, somewhat similar to fex) on page 8s of the Notes Part 2. 2 d2+5 r-0 di+10 di+15 di+20 3...
Question 1: As you work through the parts of this question you are going to show that the Maxwell equations naturally contain electromagnetic waves. In a region of space that is void of all charges and currents, p=0 and J = 0 the Maxwell equations come out to be: Y E = 0 7.B=0 7 x Ē = -1 1 x B = Poco a) Using the same idea as I did in the lecture, derive the Wave Equation for...
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy dy +y?, y(0) = 1, y'(0) = -1, "(0) = 2 dt3 dt (a) [5pts. Transform the above initial value problem into an equivalent first order differential system, including initial conditions. (b) [2pts.] Express the system and the initial condition in (a) in vector form. (c) [4pts.] Using the second order Runge Kutta method as follows Ū* = Ūi + hĚ(ti, Ūi) h =...
Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular displacement (angle of twist) along the shaft, z is the distance from the end of the shaft and t is time. For a shaft of length that is supported by frictionless bearings at each end, boundary conditions are 0(0,t) 0(4x,t) 0, t> 0. Suppose that the initial angular displacement and angular velocity are e(z,0) 3cos(2r), 0(z,0)= 4+cos(2r), 0<z< 4m, respectively You may use the...
Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular displacement (angle of twist) along the shaft, z is the distance from the end of the shaft and t is time. For a shaft of length that is supported by frictionless bearings at each end, boundary conditions are 0(0,t) 0(4x,t) 0, t> 0. Suppose that the initial angular displacement and angular velocity are e(z,0) 3cos(2r), 0(z,0)= 4+cos(2r), 0<z< 4m, respectively You may use the...
2. The electric field in a plane wave is described by the equation (k > 0): Ē(x,y,z,1)= E, sin(kz – mt)ị Answer the following questions about the wave. i. What direction is the wave traveling? Explain how you can tell from the equation for the electric field. ii. Write an expression for the magnitude of the magnetic field of the wave. iii. Calculate the average intensity of the wave if Eo = 3000 V/m. The MKS units of intensity are...
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