Official PYQ · 2012Set 1 · Q4Plane Waves and PropertiesMCQ1 mark

GATE EC 2012 Set 1 Q4 — Plane Waves and Properties

A plane wave propagating in air with $\overrightarrow{E}=(8\hat{a}_x+6\hat{a}_y+5\hat{a}_z)e^{j(\omega t+3x-4y)}\:V/m$ is incident on a perfectly conducting slab positioned at $x\le0$ . The $\overrightarrow{E}$ field of the reflected wave is

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Published 10 Oct 2026

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GATE EC · 2026Plane Waves and Properties
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?
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GATE EC · 2024Plane Waves and Properties
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 …
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GATE EC · 2023Plane Waves and Properties
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.)
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GATE EC · 2023Plane Waves and Properties
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?
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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).
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GATE EC · 2021Plane Waves and Properties
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 …
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GATE EC 2012 Set 1 Q4 — Plane Waves and Properties

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