GATE ECE 2024 | Uniform Plane Waves Question 1 | Electromagnetics

GATE ECE 2024

MCQ (Single Correct Answer)

-1.33

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, $\dot{o}_r=1$ 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 incident normally on an ideal electric conductor (conductivity, $\sigma=\infty$ ) at $x=0$. The position of the first null of the total magnetic field in the air (measured from $x=0$, in metres) is ________.

$\frac{3}{4}$

$\frac{3}{2}$

$-6$

$-3$

GATE ECE 2023

MCQ (More than One Correct Answer)

-0.67

The electric field of a plane electromagnetic wave is

$$E = {a_x}{C_{1x}}\cos (\omega t - \beta z) + {a_y}{C_{1y}}\cos (\omega t - \beta z + \theta )$$ V/m.

Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

$${C_{1x}} = 1,{C_{1y}} = 1,\theta = \pi /4$$

$${C_{1x}} = 2,{C_{1y}} = 1,\theta = \pi /2$$

$${C_{1x}} = 1,{C_{1y}} = 2,\theta = 3\pi /2$$

$${C_{1x}} = 2,{C_{1y}} = 1,\theta = 3\pi /4$$

GATE ECE 2023

Numerical

-0.67

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

Your input ____

GATE ECE 2017 Set 1

MCQ (Single Correct Answer)

-0.6

The expression for an electric field in free space is $$E = {E_0}\left( {\widehat x + \widehat y + j2\widehat z} \right){e^{ - j\left( {\omega t - kx + ky} \right)}},$$ where $$x,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} y,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} z\,\,\,\,\,\,\,$$ represent the spatial coordinates, $$t$$ represents time, and $$\omega ,\,\,k$$ are contants. This electric field

does not represent a plane wave.

represents a circular polarized plane wave propagating normal to the z-axis.

represents an elliptically polarized plane wave propagating along x-y plane.

represents a linearly polarized plane wave