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In a lossless, nonmagnetic media, the magnetic field at some point distant from a source at the origin is given by
Find the relative permittivity of the medium, the frequency and phase constant of the wave, and
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Fundamentals of Electromagnetics with Engineering Applications
- 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_forwardThe relative magnetic permeability (μr) of a lossless medium is given as 16 and the relative dielectric constant (r) as 25. The electric field component of a planar electromagnetic wave with a frequency of 1 MHz oscillates only along the x-axis and the wave travels in the + z direction. The electric field component of the wave takes a value of 500 V / m at the point z = 0.7 m at t = 70 ns. According to this; a) Find the phase constant (β), wavelength (λ), propagation velocity (up), and the impedance of the medium (η). b) Find the expressions ?⃗ (0.7, t) and ?⃗⃗ (0.7, t).arrow_forwardFor a non-magnetic material having E,= 2.25,0 = 10-4 S/m. Find (a) loss tangent attenuation constant, phase constant, and intrinsic impedance for a wave having a frequency of 2.5 MHz. Assume mate a good dielectric.arrow_forward
- Two homogeneous lossless dielectric mediums with dielectric constants ϵr1=3 and ϵr2=5 are separated by the xz plane (y=0). In case of E1→=20x^+30y^−50z^V/m uniform dielectric field in the y<0 region; Find E2→ in the region y>0?arrow_forwardIn a medium characterized by σ = 0, µ = µ0, ε = 4ε0, and ?? = 20 sin((10^8) ? − ?z)?? V/m. Calculate k and H.arrow_forwardA good sheet-shaped conductor transmits a planar electromagnetic wave with a wavelength of 0.5 mm and traveling at a speed of 5 × 105 m / sec. Assuming that the conductor is non-magnetic, determine the frequency of the wave and the conductivity of the conductor?arrow_forward
- A plane wave of which the electric field vector, E0=10V/m, f=5GHz, is parallel to x-z plane, arrives on a dielectric medium of permittivity εr,=4 with an incident angle of 45∞. Find the reflection coefficient, Γ, transmission coefficients, T, and reflection, transmission angles. Calculate the incident angles for zero reflection and full reflection. Calculate the phase velocity and wavelenght in both media.arrow_forwardFor a non-magnetic material having ?? = 2.25, ? = 10−4 S/m. Find (i) loss tangent, (ii)attenuation constant, (iii) phase constant and (iv) intrinsic impedance for a wave having afrequency of 2.5 MHz. Assume material to be a good dielectric.arrow_forwardAn electric field propagates along the z-direction and has only one component along the x -axis. It can be generally described by the equation (phasor form): Ex = E+ exp (-jbz) + E- exp (+jbz) At z=0, there is a mirror (perfect conductor); using the boundary condition Ex =0 at z=0, find: The relation between E- and E+ , also known as the “reflection coefficient”. The time expression of the total electric field for z < 0, assuming an angular frequency w. The distance between the maxima and minima of the electric field. (THIS PROBLEM IS ENTIRELY EQUIVALENT OF AN IDEAL TRANSMISSION LINE SHORT-CIRCUITED AT Z= 0).arrow_forward
- a medium is characterized by σ= 0, μ= 2μ0,, and ε= 5ε0. if H = 2 cos (wt — 3y) az, a/m, calculate E.arrow_forwardA 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_forwardCalculating the skin thickness of any metal with characteristics σ = 3.5x107 S\m, є = єo and μ = μo at 60 Hz and 60 MHz, a hollow metal with a length of 100 m and an outer diameter of 2.54 cm and a thickness of 5 mm ( Find the surface resistance of the conductor at each frequencyarrow_forward
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