GATE ECE 2012 | Uniform Plane Waves Question 29 | Electromagnetics

GATE ECE 2012

MCQ (Single Correct Answer)

-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

$$\left( { - 8{{\widehat a}_x} - 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t + 3x + 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$

$$\left( { - 8{{\widehat a}_x} + 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t + 3x + 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$

$$\left( { - 8{{\widehat a}_x} - 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t - 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$

$$\left( { - 8{{\widehat a}_x} + 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t - 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$

GATE ECE 2012

MCQ (Single Correct Answer)

-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

$$1.2 GHz$$ and left circular

$$4 Hz$$ and left circular

$$1.2 GHz$$ and right circular

$$4 Hz$$ and right circular

GATE ECE 2007

MCQ (Single Correct Answer)

-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)

$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t - {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }x - {\pi \over \lambda }z} \right)}}$$

$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t - {\pi \over \lambda }x - {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }z} \right)}}$$

$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t + {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }x + {\pi \over \lambda }z} \right)}}$$

$$\vec E = \widehat y\,\,{\mkern 1mu} {E_0}{\mkern 1mu} {e^{j\left( {\omega t - {\pi \over \lambda }x + {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }z} \right)}}$$

GATE ECE 2006

MCQ (Single Correct Answer)

-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

linearly polarized in the z-direction

elliptically polarized

left-hand circularly polarized

right-hand circularly polarized

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