Question

A uniform plane wave is propagating +z direction in a medium of (εr=36, μr=1, σ =2 (S/m)). If the operating frequency, f=500MHz and its magnetic field intensity at z =0 and t=0 is ∣H∣=10μA/m and directed toward the y - axis, determine and calculate the following:

i) The attenuation constant, α and phase constant, β also the wave parameters: phase velocity, vp, wavelength, λ, intrinsic impedance, η and skin depth δs.
ii) Write the expressions for the electric and magnetic field intensities E and H in phasor and time forms.

Answer 1

The attenuation constant, α, and phase constant, β, can be calculated for the given wave in the medium. the wave parameters, such as phase velocity, wavelength, intrinsic impedance and skin depth can also be determined. the electric and magnetic field intensities can be described in phasor and time forms.

Step-by-step explanation:

The attenuation constant, α, and phase constant, β, can be determined using the following equations:

α = sqrt((σ/2) * (ω * με - jω * μσ))

β = sqrt((ω * με) - jω * μσ)

Where ω is the angular frequency, σ is the conductivity, με is the relative permeability, and μσ is the relative electrical impedance.

The wave parameters can be calculated as follows:

Phase velocity, vp = ω / β

Wavelength, λ = 2π / β

Intrinsic impedance, η = sqrt(με / μσ)

Skin depth, δs = 1 / α

The electric and magnetic field intensities, E and H, can be described in phasor and time forms as follows:

E = E0 * e^(j(ωt - βz))

H = H0 * e^(j(ωt - βz))