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An electric field propagating in a lossless nonmagnetic medium is characterized by
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Chapter 4 Solutions
Fundamentals of Electromagnetics with Engineering Applications
- A y-polarized smooth plane wave at a frequency of 3 GHz is propagating in the + x direction in a magnetic medium with a dielectric constant of 2.5 and a loss tangent of 0.05,a) Determine the distance at which the amplitude of the propagating wave will be halved.b) Find the impedance, wavelength and phase velocity of the wave in the medium.c) Assume E = ay 50sin (6π 10 9 t + π / 3) (V / m) at x = 0 and write your instantaneous expression of H for each t and x. (please show all steps one by one)arrow_forwardA plane electromagnetic wave of frequency f = 1 GHz propagates in a non-magnetic medium with relative dielectric permittivity er = 9 and conductivity s = 0.1 S/m. Find the constants a, b, and h for this medium. Write the time-domain expression of the electric field E, assuming that its magnitude is 10 volts/m, its only component is along x , and the propagation is along the z Write the time-domain equation for the correspondent magnetic field H.arrow_forwardWhich is correct for the reflection and transmission coefficients of the electromagnetic wave perpendicular to the plane surface separating the two dielectric mediums. The impedance of the medium with the incoming wave is 100 ohms, and the impedance of the medium with the transmitted wave is 200 ohms. a-Reflection coefficient 3, transmission coefficient 4b-Reflection coefficient 1/3, transmission coefficient 4/3c-Reflection coefficient -1, transmission coefficient 0d-Reflection coefficient 1, transmission coefficient 2arrow_forward
- A nonmagnetic medium has an intrinsic impedance of 250∠30 Ω. Find a) Loss tangent b) Dielectric constant c) Complex permittivity d) Attenuation constant at 1 MHz?arrow_forwardIf the electric field intensity associated with a uniform plane electromagnetic wave traveling in a perfect dielectric medium is given by E(z, t) = 10 cos (2π10^7t- 0.1πz)V/m, then find the velocity of the traveling wave.arrow_forwardPlease answer both. 1. The electric field associated with a uniform plane wave propagating in the +z-direction in a nonmagnetic (u = uo.) material medium is given by Ē = Eo.e-2z cos(6(3)1/2 pi x 107 – 3z)x^ (V/m), a. Find the conductivity (sigma) of the medium. b. Find the permittivity ε of the medium. 2. For the circuit shown below: Determine R, if V(t = 3.8 us, l = 50m) = 62 (V). For the plane wave in free space, the electric field is defined as follows Ē = Eo. cos(6pi x 108t + 2pix)z^ Compute velocity and wavelength of the wave.arrow_forward
- At a frequency of 3 GHz and y-polarized, a plane wave travels in a magnetic medium with a dielectric constant of 2.5 and a loss tangent of 0.05 in the + x direction.a) Determine the distance at which the amplitude of the propagating wave will be halved.b) Find the impedance, wavelength and phase velocity of the wave in the medium.c) Assume E = ay50Sin (6pi (10 ^ 9) t + pi / 3) (V / m) at x = 0 and write the instantaneous expression of H for each t and x.arrow_forwardA rectangular waveguide with dimensions a = 5cm, b = 4.2cm will operate below 4.5Ghz. if it is filled with a medium characterized by o = 0 e = 3E0 Ur = 2 How many TE and TM modes can I transmit? Calculate the cutoff frequency of the nodesarrow_forwardThe axis of a circular cylinder coincides with the z-axis and it rotates with an angular velocity of (3i−5j +9k) rad/s. Determine the tangential velocity at a point P on the cylinder, whose co-ordinates are ( j +5k) metres, the magnitude of the tangential velocity iii. Derive the electromagnetic wave equation considering a region with no charges and currents, such as in a vacuum.arrow_forward
- A slab of dielectric material has a relative dielectric constant of 3.8 and contains a uniform electric flux density of 8nC/m^2. If the material is lossless; find (a) E, which is the amplitude of the electric field. (b) The polarization P.arrow_forwardIf the electric field strength phasor of the electromagnetic wave propagating in the z-direction in a lossless medium (r=1 and r=9) is ax12.57e-jz V/m, a) Angular frequency, b) Instantaneous expression of the magnetic field strength, and c) Find the time average power density vector.arrow_forwardIn a uniform electromagnetic wave which is at a significant distance from the source of energy if the wave is falling from medium 1(z<0,σ=0,µr = 2,ɛr =9) to a second medium where the values are (z>0,σ=0,µr = 16,ɛr =4) . Find the values of reflection and transmission coefficient in this scenarioarrow_forward
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