GATE EC Plane Waves and Properties questions

The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous medium is given by $$\vec{E}(z, t)=E_{0}[\hat{x} \cos (\omega t-k z)+\hat{y} \sin (\omega t-k z)]$$ in a right-handed orthogonal co-ordinate system. Which of the following is the correct polarization of the electromagnetic wave?

A uniform plane wave with electric field $\vec{E}(x)=A_{y} \hat{a}_{y} e^{-j \frac{2 \pi x}{3}} \mathrm{~V} / \mathrm{m}$ is travelling in the air (relative permittivity, $\epsilon_{r}=1$ and relative permeability, $\mu_{r}=1$ ) in the $+x$ direction ( $A_{y}$ is a positive constant, $\hat{a}_{y}$ is the unit vector along the $y$ axis). It is …

Consider a narrow band signal, propagating in a lossless dielectric medium $\left(\varepsilon_{r}=4, \mu_{r}=1\right)$, with phase velocity $v_{p}$ and group velocity $v_{g}$. Which of the following statement is true? ($c$ is the velocity of light in vacuum.)

The electric field of a plane electromagnetic wave is $\boldsymbol{E}=\boldsymbol{a}_{x} C_{1 x} \cos (\omega t-\beta z)+\boldsymbol{a}_{y} C_{1 y} \cos (\omega t-\beta z+\theta) \quad \mathrm{V} / \mathrm{m}$. Which of the following combination(s) will give rise to a left handed elliptically polarized $\text{(LHEP)}$ wave?

A transparent dielectric coating is applied to glass $\left(\varepsilon_r=4, \mu_r=1\right)$ to eliminate the reflection of red light $\left(\lambda_0=0.75 \; \mu \mathrm{m}\right)$. The minimum thickness of the dielectric coating, in $\mu \mathrm{m}$, that can be used is_____________(rounded off to two decimal places).

Consider a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x}\:a_{y}$ and $a_{z}$. A plane wave traveling in the region $z\geq 0$ with electric field vector $E=10\cos\left ( 2\times 10^{8}t\:+\:\beta z\right )a_{y}$ is incident normally on the plane at $z=0$, where $\beta$ is the phase constant. The region $z\geq 0$ is in free …

The magnetic field of a uniform plane wave in vacuum is given by $$\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+3x-y-z\right ).$$ The value of $b$ is ___________.

A Germanium sample of dimensions $1\: cm \times 1\: cm$ is illuminated with a $20\:mW,$ $600\: nm$ laser light source as shown in the figure. The illuminated sample surface has a $100\: nm$ of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon …

A uniform plane wave traveling in free space and having the electric field $$\overrightarrow{E} =\left ( \sqrt{2}\:\hat{a}_{x} -\hat{a}_{z}\right )cos\left [ 6\sqrt{3}\: \pi \times 10^{8}t-2\:\pi \left ( x+\sqrt{2} \:z\right )\right ]V/m$$ is incident on a dielectric medium (relative permittivity $>1$, relative permeability $=1$) as shown in the …

A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true?

The expression for an electric field in free space is , $\textbf{E}=E_{0}( \hat{x}+\hat{y}+j2 \hat{z} )e^{-j( \omega t-kx+ky)}$ where $x,y,z$ represent the special coordinates, $t$ represents time, and $\omega,k$ are constants.This electric field,

The permittivity of water at optical frequencies is $1.75 \varepsilon _0$. It is found that an isotropic light source at a distance $d$ under water forms an illuminated circular area of radius $5$ m, as shown in the figure. The critical angle is $\theta _c$. The value of $d$ (in meter) is _______________

The electric field of a uniform plane wave traveling along the negative $z$ direction is given by the following equation: $${\overrightarrow {E}^i_w= ( \hat {a}_x+ j\hat {a}_y)E_0e^{jkz}}$$ 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: …

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

The polar plot of the transfer function $G(s) = \frac{10(s+1)}{s+10}$ for $0 \leq \omega < \infty$ will be in the

The electric field component of a plane wave traveling in a lossless dielectric medium is given by $\overrightarrow{E}(z,t) = \hat{a}_y 2 \cos \bigg( 10^st-\frac{z}{\sqrt{2}} \bigg) \: V/m$. The wavelength (in m) for the wave is ___________.

All the logic gates shown in the figure have a propagation delay of $20$ ns. Let $A=C=0$ and $B=1$ until time $t=0$. At $t=0$, all the inputs flip (i.e., $A=C=1$ and $B=0$) and remain in that state. For $t>0$, output $Z=1$ for a duration (in ns) of ________.

The electric field of a uniform plane electromagnetic wave is $$\overrightarrow{E} = \left(\overrightarrow{a}_{x} + j 4 \overrightarrow{a}_{y}\right) \text{exp }[j(2\pi \times 10^{7}t – 0.2z)].$$ 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 $$\text{E}(z,t) = \textbf{a}_{x} 5 \cos(2\pi \times 10^{9}t + \beta z) + \textbf{a}_{y} 3 \cos\left(2\pi \times 10^{9} t + \beta z – \frac{\pi}{2}\right)$$ The type of the polarization is

Consider the periodic square wave in the figure shown. The ratio of the power in the $7^{th}$ harmonic to the power in the $5^{th}$ harmonic for this waveform is closest in value to ________.