1
GATE ECE 2012
MCQ (Single Correct Answer)
+1
-0.3
The electric field of a uniform plane electromagnetic wave in free spce, along the positive x direction, is given by $$\vec E = 10\left( {{{\widehat a}_y} + j{{\widehat a}_z}} \right){e^{ - j25x}}.$$ The frequency and polarization of the wave respectively are
A
$$1.2 GHz$$ and left circular
B
$$4 Hz$$ and left circular
C
$$1.2 GHz$$ and right circular
D
$$4 Hz$$ and right circular
2
GATE ECE 2012
MCQ (Single Correct Answer)
+1
-0.3
A plane wave propagating in air with $$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \right){\mkern 1mu} {\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$ is incident on a perfectly conducting slab positioned at $$x \le 0$$. The $$\overrightarrow E $$ field of the reflected wave is
A
$$\left( { - 8{{\widehat a}_x} - 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t + 3x + 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$
B
$$\left( { - 8{{\widehat a}_x} + 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t + 3x + 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$
C
$$\left( { - 8{{\widehat a}_x} - 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t - 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$
D
$$\left( { - 8{{\widehat a}_x} + 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t - 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$
3
GATE ECE 2007
MCQ (Single Correct Answer)
+1
-0.3
A plane wave of wavelength $$\lambda $$ is traveling in a direction making an angle $${{{30}^ \circ }}$$ with positive $$x$$-axis and $${{{90}^ \circ }}$$ with positiv $$y$$-axis. The $$\overrightarrow E $$ field of the plane wave can be represented as ($${E_0}$$ is a constant)
A
$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t - {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }x - {\pi \over \lambda }z} \right)}}$$
B
$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t - {\pi \over \lambda }x - {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }z} \right)}}$$
C
$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t + {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }x + {\pi \over \lambda }z} \right)}}$$
D
$$\vec E = \widehat y\,\,{\mkern 1mu} {E_0}{\mkern 1mu} {e^{j\left( {\omega t - {\pi \over \lambda }x + {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }z} \right)}}$$
4
GATE ECE 2006
MCQ (Single Correct Answer)
+1
-0.3
The electric field of an electromagnetic wave propagating in the positive z-direction is given by $$$E = {\widehat a_x}\sin \left( {\omega t - \beta z} \right) + {\widehat a_y}\sin \left( {\omega t - \beta z + \pi /2} \right)$$$

The wave is

A
linearly polarized in the z-direction
B
elliptically polarized
C
left-hand circularly polarized
D
right-hand circularly polarized
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