1
GATE ECE 2007
+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
$$\vec E = \widehat y\,\,{\mkern 1mu} {E_0}{\mkern 1mu} {e^{j\left( {\omega t - {\pi \over \lambda }x + {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }z} \right)}}$$
2
GATE ECE 2006
+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
3
GATE ECE 2005
+1
-0.3
The magnetic field intensity vector of a plane wave is given by
$$\overline H \left( {x,y,z,t} \right) = 10\,\sin \left( {50000t + 0.004x + 30} \right){\mathop a\limits^ \cap _y}$$
Where $${\mathop a\limits^ \cap _y}$$ denotes the unit vector in $$y$$ direction. The wave is propagating with a phase velocity
A
$$5 \times {10^4}\,\,m/s$$
B
$$-3 \times {10^8}\,\,m/s$$
C
$$-1.25 \times {10^7}\,\,m/s$$
D
$$3 \times {10^8}\,\,m/s$$
4
GATE ECE 2003
+1
-0.3
The depth of penetration of electromagnetic wave in a medium having conductivity $$\sigma$$ at a frequency of 1 KHz is 25 cm. The depth of penetration at a frequency of 4 KHz will be
A
6.25 cm
B
12.50 cm
C
50.00 cm
D
100.00 cm
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
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