Fall2023 ECE3120 Homework6 Solutions

A plane wave in air with an electric field amplitude of 10 V/m is incident normally upon the surface of a lossless, nonmagnetic medium with = 25. Determine the following: a) The reflection and transmission coefficients b) The standing-wave ratio c) The average power densities of the incident, reflected, and transmitted waves

A 60 MHz plane wave travels from a lossless dielectric medium with a relative electrical value of 1.96 and a magnetic permeability of 1 at an angle of 30 degrees to the air.what is the angle of transmission? which of the options is correct? a)44.42 b)45 c)43.36 d)48.59

2. (1) How do you define the skin depth of an electromagnetic wave in a conductor? (2) Compare the skin depths for a microwave with a frequency of ~1 GHz and an infrared wave with a wavelength of~1 µm.

Find the velocity of a plane wave in a lossless medium having a relative permittivity 4 and relative permeability of 3.55.

A plane wave of unknown frequency is normally incident in air upon the surface of a perfect conductor. Using an electric-field meter, it is determined that the total electric field in the air medium is always zero when measured at a distance of 2.5m from the conductor surface. Moreover, no such nulls were observed at distances closer to the conductor. What is the frequency of the incident wave?

A single mode fibre is to be dimensioned. The normalised frequency is 80 % of the maximum allowed for single mode condition. The relative refractive index difference is 0.005 and the refractive index of the core is 1.5. The wavelength is 1.5 µm. A. Determine the radius of the core. B. If the number of modes supported by this fiber is 5. Determine the radius of the core.

The magnetic field component of a plane wave in a lossless dielectric is H = 30 sin (2nx 10°t – 5z) a, mA/m a. If u=1 find b. Determine the direction of wave propagation c. Determine the polarization of the wave. d. Calculate the wavelength and wave velocity. e. Determine the wave impedance. f. Find the corresponding electric field component. g. Find the displacement current density. Er.

1. A 50 MHz uniform plane wave is propagating in a material with relative permeability and relative permittivity as 2.25 and 1 respectively. The material is assumed to be loss less. Find the phase constant of the wave propagation. A TU rad/m rad/m Brad/m D 2π rad/m

Electomagnetism

A sinusoidal wave on a transmission line is specified by voltage and current in phasor form: Vs(z) = Voeaz ejßz and Is(z) = 1,eaz ejßzejp where Vo and I, are both real. a) In which direction does this wave propagate and why? b) Consider that a = 0, Zo 500, and the wave velocity is v, = 2.5 × 108 m/s, with w = 108 s-1. S Find the resistance (R), the admittance (G), the inductance (L), the capacitance (C), the wavelength (1) and the current phase ().

This question is about Wave propagation and I want to answer in 20 minutes

Hi can you please make a sketch of the wave . I am struggling on how to sketch these problems thank you ?

A uniform plane wave has a wavelength of 2 cm in free space and 1 cm in a perfect dielectric. What is tbe relative permittivity of the of the dielectric ?

2. The electric field phasor of a uniform plane wave is given by E 5 ell.6y âz (V/m). If the phase velocity of the wave is 2.25 x 10 (m/s), and the relative permittivity of the medium is 3, a. What is the type of the medium? b. Find the direction of propagation, c. Find the wavelength and the frequency of the wave, d. Find a and B if possible, e. Find the relative permeability of the medium, f. Find the wave impedance, g. Find the magnetic field in time domain H(z, t), h. Find the wave polarization.

The skin depth at 10 MHz for a conductor is 1cm. Find the phase velocity of an electromagnetic wave in the conductor at 1,000 MHz.