1
GATE ECE 2017 Set 1
+2
-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
A
does not represent a plane wave.
B
represents a circular polarized plane wave propagating normal to the z-axis.
C
represents an elliptically polarized plane wave propagating along x-y plane.
D
represents a linearly polarized plane wave
2
GATE ECE 2016 Set 1
+2
-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,

A
Linear, Circular (clockwise), $$−5dB$$
B
Circular (clockwise), Linear, $$−5dB$$
C
Circular (clockwise), Linear, $$−3dB$$
D
Circular (anti clockwise), Linear, $$−3dB$$
3
GATE ECE 2015 Set 2
+2
-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

A
Right hand circular
B
Left hand elliptical
C
Right hand elliptical
D
Linear
4
GATE ECE 2015 Set 1
Numerical
+2
-0
The electric field intensity of a plane wave traveling in free space is given by the following expression

$$E\left( {x,t} \right) = {\widehat a_{_y}}24\pi \,\,\cos \left( {\omega t - {k_0}x} \right)\,\,\,\left( {V/m} \right)$$. In this field, consider a square area $$10 cm$$ $$\times$$ $$10 cm$$ on a plane $$x + y = 1$$. The total time-averaged power $$(in mW)$$ passing through the square area is ________.