# GATE Questions & Answers of Plane waves and properties: reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth

## What is the Weightage of Plane waves and properties: reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth in GATE Exam?

Total 23 Questions have been asked from Plane waves and properties: reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth topic of Electromagnetics subject in previous GATE papers. Average marks 1.57.

The expression for an electric field in free space is , where x, y, z represent the special coordinates, t represent time, and ω, k are constant. This electric field

The electric field of a uniform plane wave travelling along the negative z direction is given by the following equation:

${\stackrel{\to }{E}}_{w}^{i}=\left({\stackrel{^}{a}}_{x}+j{\stackrel{^}{a}}_{y}\right){E}_{0}{e}^{jkz}$

This wave is incident upon a receiving antenna placed at the origin and whose radiated electric field towards the incident wave is given by the following equation:

${\stackrel{\to }{E}}_{a}=\left({\stackrel{^}{a}}_{x}+2{\stackrel{^}{a}}_{y}\right){E}_{I}\frac{1}{r}{e}^{-jkr}$

The polarization of the incident wave, the polarization of the antenna and losses due to the polarization mismatch are, respectively,

Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $\mathrm{E}=\stackrel{^}{x}{E}_{x}{e}^{-j\left(\omega t-\beta z\right)}$, where the propagation constant $\beta$ is a function of the angular frequency $\omega$. Assume that $\beta \left(\omega \right)$ and Ex are known and are real. From the information available, which one of the following CANNOT be determined?

A positive charge q is placed at x=0 between two infinite metal plates placed at x=-d and at x=+d respectively. The metal plates lie in the yz plane The charge is at rest at t=0, when a voltage +V is applied to the plate at -d and voltage -V is applied to the plate at x=+d. Assume that the quantity of the charge q is small enough that it does not perturb the field set up by the metal plates. The time that the charge q takes to reach the right plate is proportional to

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

The electric field component of a plane wave traveling in a lossless dielectric medium is given by $\stackrel{\to }{E}\left(z,t\right)={\stackrel{^}{a}}_{y}2\mathrm{cos}\left({10}^{8}t-\frac{z}{\sqrt{2}}\right)\mathrm{V}/\mathrm{m}$. Thewavelength (in m) for the wave is_______.

The electric field intensity of a plane wave traveling in free space is given by the following expression

$\boldsymbol E(x,t)={\boldsymbol a}_y\;24\mathrm\pi\;\cos(\mathrm{ωt}-{\mathrm k}_0\mathrm x)(\mathrm V/\mathrm m).$

In this field, consider a square area 10 cm X 10 cm on a plane $\mathrm x+\mathrm y=1.$ The total time-averaged power (in mW) passing through the square area is _______.

Consider a uniform plane wave with amplitude (E0) of 10 V/m and 1.1 GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity (${\mathrm{\epsilon }}_{\mathrm{r}}$) and permeability (${\mathrm{\mu }}_{\mathrm{r}}$) as shown in the figure. The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of 10 cm inside the dielectric region is_______.

The electric field of a uniform plane electromagnetic wave is

$\stackrel{\to }{E}=\left({\stackrel{\to }{a}}_{x}+j4{\stackrel{\to }{a}}_{y}\right)\mathrm{exp}\left[j\left(2\mathrm{\pi }×{10}^{7}t-0.2z\right)\right]$

The polarization of the wave is

The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expression

The type of the polarization is

If the electric field of a plane wave is

$\overrightarrow{\mathrm E}\left(z,t\right)=\widehat x3\cos\left(\omega t-kz+30^\circ\right)-\widehat y4\sin\left(\omega t-kz+45^\circ\right)\left(mV/m\right)$

the polarization state of the plane wave is

Assume that a plane wave in air with an electric field $\overrightarrow E=10\cos\left(\omega t-3x-\sqrt3z\right){\overset\frown a}_y\;V/m$ is incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z > 0. The angle of transmission in the dielectric slab is ________ degrees.

A plane wave propagating in air with is incident on a perfectly conducting slab positioned at $x\le 0$.The $\stackrel{\to }{E}$ field of the reflected wave is

The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\stackrel{\to }{E}=10\left({\stackrel{^}{a}}_{y}+j{\stackrel{^}{a}}_{z}\right){e}^{-j25x}$.The frequency and polarization of the wave, respectively, are

A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given , the characteristic impedance of the cable is

Consider the following statements regarding the complex Poynting vector $\stackrel{\to }{P}$ for the power radiated by a point source in an infinite homogeneous and lossless medium. Re$\left(\stackrel{\to }{P}\right)$ denotes the real part of $\stackrel{\to }{P}$, S denotes a spherical surface whose centre is at the point source, and $\stackrel{^}{n}$ denotes the unit surface normal on S. Which of the following statements is TRUE?

 (A)  $\mathbf{Re}\mathbf{\left(}\stackrel{\mathbf{\to }}{\mathbf{P}}\mathbf{\right)}$ remains constant at any radial distance from the source (B)  $\mathbf{Re}\mathbf{\left(}\stackrel{\mathbf{\to }}{\mathbf{P}}\mathbf{\right)}$ increases with increasing radial distance from the source (C) (D) A current sheet  $\stackrel{\to }{j}=10{\stackrel{^}{u}}_{y}$ A/m lies on the dielectric interface x=0 between two dielectric media with  ${\epsilon }_{r1}$ = 5, μr1 = 1 in Region -1 (x<0) and ${\epsilon }_{r2}$= 2   μr2 = 2 in Region -2 (x>0). If the magnetic field in Region-1 at x=0- is $\stackrel{\to }{{H}_{1}}=3{\stackrel{^}{u}}_{x}+30{\stackrel{^}{u}}_{y}$ A /m the magnetic field in Region-2 at x=0+ is The electric field component of a time harmonic plane EM wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector (in W/m2) is

A plane wave having the electric field component $\stackrel{\to }{{E}_{i}}=24\mathrm{cos}\left(3×{10}^{8}t-\beta y\right)\stackrel{^}{{a}_{z}}v}{m}$ and traveling in free space is incident normally on a lossless medium with µ= µ0 and $\epsilon$=9${\epsilon }_{0}$ which occupies the region y≥0. The reflected magnetic field component is given by

A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant $\epsilon$r = 9). The magnitude of the reflection coefficient is

A plane wave of wavelength $\lambda$ is traveling in a direction making an angle 30° with positive x-axis and 90° with positive y-axis. The $\stackrel{\to }{E}$ field of the plane wave can be represented as (E0 is constant)

The $\stackrel{\to }{H}$ field (in A/m) of a plane wave propagating in free space is given by $\stackrel{\to }{H}=\stackrel{^}{x}\frac{5\sqrt{3}}{{\eta }_{0}}\mathrm{cos}\left(\omega t-\beta z\right)+\stackrel{^}{y}\frac{5}{{\eta }_{0}}\mathrm{sin}\left(\omega t-\beta z+\frac{\pi }{2}\right)$.

The time average power flow density in watts is

A right circularly polarized (RCP) plane wave is incident at an angle of 60° to the normal, on an air-dielectric interface. If the reflected wave is linearly polarized, the relative dielectric constant ${\epsilon }_{r2}$ is 