Consider electromagnetic waves in free space of the form Ē(x,y,z,t)= Ē. (x, y )e i kz-ot)...
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...
A wave defined by the expression E (z,t) = A cos(ot-kz) fills all space directions perpendicular to the z-axis in 3-dimensional space. A wave confined in the directions transverse to the direction of propagation can be constructed by superimposing such waves propagating in different directions. This problem is an illustration on how it can be done (a) Consider the space defined by the Cartesian coordinates x-y-z. Rotate the coordinates about the y-axis by an angle A to form a new...
7.12 The electric field of an elliptically polarized plane wave is given by [-k 10 sin(cot-kz-60°) E(z, t) y 30 cos(ot - kz)] (V/m). Determine the following: (a) The polarization angles (y, x). (b) The direction of rotation. 7.12 The electric field of an elliptically polarized plane wave is given by [-k 10 sin(cot-kz-60°) E(z, t) y 30 cos(ot - kz)] (V/m). Determine the following: (a) The polarization angles (y, x). (b) The direction of rotation.
Electromagnetic Waves 1 2 3 468 The magnetic field in a plane monochromatic electromagnetic wave with wavelength 1 = 674 nm, propagating in a vacuum in the z-direction is described by B= (Bộ sin(kz - t) (+3) where B, = 4.8 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. 1) What is k, the wavenumber of this wave? m1 Submit 2) What is Zmax, the distance along the positive Z-axis...
Electromagnetic Waves 2 1 2 3 4 A plane monochromatic electromagnetic wave with wavelength 1 = 2.6 cm, propagates through a vacuum. Its magnetic field is described by B = (B,i+Byj) cos(kx + wt) where B, = 2.7 x 10-6 T, B, - 5.9 X 106T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. 1) What is f, the frequency of this wave? 0 GHz Submit 2) What is I, the intensity of...
Pretest: Electromagnetic waves Name Pretests 159 1. Shown below are pictorial and mathematical representations of an electromagnetic plane wave space. The electric field is parailel to the z-axis. The magnetic field propagating through empty is parallel to the y-axis. The E(x, y, z, t) E, sin(kx + 0x)2 The points P. Q. R, and S in the diagram above lie in thex-y plane. i. For the instant shown, rank points P. Q. R, and S according to the magnitude of...
Light, radiant heat (infrared radiation), X rays, and radio waves are all examples of traveling electromagnetic waves. Electromagnetic waves comprise combinations of electric and magnetic fields that are mutually compatible in the sense that the changes in one generate the other. The simplest form of a traveling electromagnetic wave is a plane wave. For a wave traveling in the x direction whose electric field is in the y direction, the electric and magnetic fields are given by Ē = E,...
8. In a lossless Eq, λ and H. dielectric for which η,:20π, μ.-1,and E(z,t) 94πcos(wt +2z) a/m. Calculate 9. A plane wave in a lossless medium has H(z,t) 0.2 cos(ot-62)-y 2 sin(ot -6z) AV/m. Find a) The direction of wave propagating. b) εr and a. c) E(z,t). 10. The electric field component of an electromagnetic wave in free-space is given by E.z,t)Eocos(ay)sin wt -kx) V/rm (Hint: Use the identity 2 sin a cos b (sina+ b) +sin(a -b)) a) Find...
NUMBER 2 only explain clearly step by step thanks I. Representations of electromagnetic waves A. Shown below are mathematical and pictorial representations of an electromagnetic plane wave propagating through empty space. The electric field is parallel to the z-axis; the magnetic field is parallel to the y-axis. .y, and are unit vectors along the x, ty, and +z directions.) 1. In which direction is the wave propagating? Explain how you can tell from the expressions for the electric field and...
5. Consider the system of differential equations regarding x = c(t), y = y(t), and z = z(t): x' = 211 x + 212 y + 213 2 y = 221 x + 222 y + 223 2 z' = 231 2 + 232 y + 233 z where 211, 212,..., 233 are all real constants. Which of the following options could be a general solution of this system? (a) C C[-] é 2t + C2 eft (b) C-1 137...