Respuesta :
Answer:
Wavelength of the incident wave in air = 1 m
Wavelength of the incident wave in medium 2 = 0.33 m
Intrinsic impedance of media 1 = 377 ohms
Intrinsic impedance of media 2 = 125.68 ohms
Check the explanation section for a better understanding
Explanation:
a) Wavelength of the incident wave in air
The frequency of the electromagnetic wave in air, f = 300 MHz = 3 * 10⁸ Hz
Speed of light in air, c = 3 * 10⁸ Hz
Wavelength of the incident wave in air:
[tex]\lambda_{air} = \frac{c}{f} \\\lambda_{air} = \frac{3 * 10^{8} }{3 * 10^{8}} \\\lambda_{air} = 1 m[/tex]
Wavelength of the incident wave in medium 2
The refractive index of air in the lossless dielectric medium:
[tex]n = \sqrt{\epsilon_{r} } \\n = \sqrt{9 }\\n =3[/tex]
[tex]\lambda_{2} = \frac{c}{nf}\\\lambda_{2} = \frac{3 * 10^{6} }{3 * 3 * 10^{6}}\\\lambda_{2} = 1/3\\\lambda_{2} = 0.33 m[/tex]
b) Intrinsic impedances of media 1 and media 2
The intrinsic impedance of media 1 is given as:
[tex]n_1 = \sqrt{\frac{\mu_0}{\epsilon_{0} } }[/tex]
Permeability of free space, [tex]\mu_{0} = 4 \pi * 10^{-7} H/m[/tex]
Permittivity for air, [tex]\epsilon_{0} = 8.84 * 10^{-12} F/m[/tex]
[tex]n_1 = \sqrt{\frac{4\pi * 10^{-7} }{8.84 * 10^{-12} } }[/tex]
[tex]n_1 = 377 \Omega[/tex]
The intrinsic impedance of media 2 is given as:
[tex]n_2 = \sqrt{\frac{\mu_r \mu_0}{\epsilon_r \epsilon_{0} } }[/tex]
Permeability of free space, [tex]\mu_{0} = 4 \pi * 10^{-7} H/m[/tex]
Permittivity for air, [tex]\epsilon_{0} = 8.84 * 10^{-12} F/m[/tex]
ϵr = 9
[tex]n_2 = \sqrt{\frac{4\pi * 10^{-7} *1 }{8.84 * 10^{-12} *9 } }[/tex]
[tex]n_2 = 125.68 \Omega[/tex]
c) The reflection coefficient,r and the transmission coefficient,t at the boundary.
Reflection coefficient, [tex]r = \frac{n - n_{0} }{n + n_{0} }[/tex]
You didn't put the refractive index at the boundary in the question, you can substitute it into the formula above to find it.
[tex]r = \frac{3 - n_{0} }{3 + n_{0} }[/tex]
Transmission coefficient at the boundary, t = r -1
d) The amplitude of the incident electric field is [tex]E_{0} = 10 V/m[/tex]
Maximum amplitudes in the total field is given by:
[tex]E = tE_{0}[/tex] and [tex]E = r E_{0}[/tex]
E = 10r, E = 10t
