GATE ECE 2023 | Uniform Plane Waves Question 4 | Electromagnetics

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

GATE ECE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

The electric field of a uniform plane wave travelling along the negative $$z$$ direction is given by the following equation: $$$\overrightarrow E {}_w^i = \left( {{{\widehat a}_{_x}} + j{{\widehat a}_{_y}}} \right){E_0}{e^{jkz}}$$$

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:

$$${\overrightarrow E _{_a}} = \left( {{{\widehat a}_{_x}} + 2{{\widehat a}_{_y}}} \right){E_1}{1 \over r}{e^{ - jkr}}$$$

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

Linear, Circular (clockwise), $$−5dB$$

Circular (clockwise), Linear, $$−5dB$$

Circular (clockwise), Linear, $$−3dB$$

Circular (anti clockwise), Linear, $$−3dB$$

GATE ECE 2015 Set 2

MCQ (Single Correct Answer)

-0.6

The electric field intensity of a plane wave propagating in a lossless non-magnetic medium is given by the following expression
$$\overrightarrow E \left( {z,t} \right) = {\widehat a_x}5\cos \left( {2\pi \times {{10}^9}t + \beta z} \right)$$ $$$ + {\widehat a_y}3\cos \left( {2\pi \times {{10}^9}t + \beta z - {\pi \over 2}} \right)$$$

The type of the polarization is

Right hand circular

Left hand elliptical

Right hand elliptical

Linear

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