1
GATE ECE 1998
Subjective
+5
-0
The electric field vector of a wave is given as $$$\vec E = {E_0}{\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {{8{{\vec a}_x} + 6{{\vec a}_y} + 5{{\vec a}_z}} \over {\sqrt {125} }}\,\,V/m$$$

Its frequency is 10 GHz.

(i) Investigate if this wave is a plane wave.
(ii) Determine its propagation constant, and
(iii) Calculate the phase velocity in $$y$$-direction.

2
GATE ECE 1998
MCQ (Single Correct Answer)
+1
-0.3
An antenna in free space receives 2$$\mu $$ W of power when the incident electric field is 20 m V/m rms. The effective aperture of the antenna is
A
0.005 $${m^2}$$
B
0.05 $${m^2}$$
C
1.885 $${m^2}$$
D
3.77 $${m^2}$$
3
GATE ECE 1998
MCQ (Single Correct Answer)
+1
-0.3
The radiation resistance of a circular loop of one turn is 0.01 $$\Omega $$. The radiation resistance of five turns of such a loop will be
A
0.002 $$\Omega $$
B
0.01 $$\Omega $$
C
0.05 $$\Omega $$
D
0.25 $$\Omega $$
4
GATE ECE 1998
MCQ (Single Correct Answer)
+1
-0.3
The far field of an antenna varies with distance r as
A
1/r
B
1 / $${r^2}$$
C
1 / $${r^3}$$
D
$${1 \over {\sqrt r }}$$
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