A plane wave propagating through a medium with er 5 8, mr 5 2 has E 5 0.5e2z/3 sin1108t 2 bz2ax V/m. Determine(a) b (d) Wave velocity(b) The loss tangent (e) H field(c) Intrinsic impedance

To determine the values requested, we will follow these steps:

(a) To find the value of b, we need to compare the given electric field equation with the general form of a plane wave in a medium. The general form is E = E0e^(j(kz - ωt)), where E0 is the amplitude, k is the wave number, z is the distance, ω is the angular frequency, and t is the time. By comparing the given equation with the general form, we can see that b = 2.

(b) The wave velocity (v) can be calculated using the formula v = ω/k. From the given equation, we can determine that ω = 1108 rad/s. The wave number (k) can be found using the formula k = 2π/λ, where λ is the wavelength. Since the wavelength is not given, we cannot directly calculate the wave velocity.

(c) The intrinsic impedance (η) of the medium can be calculated using the formula η = √(μr/εr), where μr is the relative permeability and εr is the relative permittivity. From the given values, μr = 2 and εr = 8. Plugging these values into the formula, we get η = √(2/8) = √(1/4) = 1/2.

(d) The loss tangent (tan δ) can be calculated using the formula tan δ = (1/2) * (1/εr). From the given value, εr = 8. Plugging this value into the formula, we get tan δ = (1/2) * (1/8) = 1/16.

(e) The H field can be determined using the relationship H = E/η. From the given values, E = 0.5e^(2z/3)sin(1108t - 2bz)ax V/m and η = 1/2. Plugging these values into the formula, we get H = (0.5e^(2z/3)sin(1108t - 2bz)ax)/(1/2) = e^(2z/3)sin(1108t - 2bz)ax.

In summary: (a) b = 2 (b) The wave velocity cannot be determined without the wavelength. (c) The intrinsic impedance (η) = 1/2 (d) The loss tangent (tan δ) = 1/16 (e) The H field = e^(2z/3)sin(1108t - 2bz)ax