1
GATE ECE 2011
+2
-0.6
The electric and magnetic fields for a TEM wave of frequency $$14 GHz$$ in a homogeneous medium of relative permittivity $${\varepsilon _r}$$ and relative permeability $${\mu _r} = 1$$ are given by $$\overrightarrow E = {E_p}\,\,{e^{j\left( {\omega t - 280\pi y} \right)}}\,\,{\widehat u_z}\,\,V/m$$$$$\overrightarrow H = \,\,3\,\,{e^{j\left( {\omega \,t - 280\,\,\pi \,y} \right)}}\,\,\widehat u{\,_x}\,\,A/m$$$

Assuming the speed of light in free space to be $$3\,\, \times {10^8}\,\,\,m/s,$$ the intrinsic impedance of free space to be $$120\,\,\,\pi$$, the relative permittivity $${\varepsilon _r}$$ of the medium and the electric field amplitude $${E_p}$$ are

A
$${\varepsilon _r} = 3,\,\,{E_p} = 120\,\pi$$
B
$${\varepsilon _r} = 3,\,\,{E_p} = 360\,\pi$$
C
$${\varepsilon _r} = 9,\,\,{E_p} = 360\,\pi$$
D
$${\varepsilon _r} = 9,\,\,{E_p} = 120\,\pi$$
2
GATE ECE 2010
+2
-0.6
A plane wave having the electric field component $${\overrightarrow E _i} = 24\,\,\cos \,\,\left( {3 \times {{10}^8}\,t - \beta \,y} \right){\widehat a_z}\,\,V/m$$$and traveling in free space is incident normally on a lossless medium with $$\mu = {\mu _0}$$ and $$\varepsilon = 9\,\,{\varepsilon _0},$$ which occupies the region $$y \ge 0.$$ The reflected magnetic field component is given by A $${1 \over {10{\mkern 1mu} \pi }}\cos {\mkern 1mu} {\mkern 1mu} \left( {3 \times {{10}^8}{\mkern 1mu} t - y} \right)\hat a{\,_x}{\mkern 1mu} {\mkern 1mu} A/m$$ B $${1 \over {20{\mkern 1mu} \pi }}\cos {\mkern 1mu} {\mkern 1mu} \left( {3 \times {{10}^8}{\mkern 1mu} t - y} \right)\hat a{\,_x}{\mkern 1mu} {\mkern 1mu} A/m$$ C $$- {1 \over {20{\mkern 1mu} \pi }}\cos {\mkern 1mu} {\mkern 1mu} \left( {3 \times {{10}^8}{\mkern 1mu} t - y} \right)\hat a{\,_x}{\mkern 1mu} {\mkern 1mu} A/m$$ D $$- {1 \over {10{\mkern 1mu} \pi }}\cos {\mkern 1mu} {\mkern 1mu} \left( {3 \times {{10}^8}{\mkern 1mu} t - y} \right)\hat a{\,_x}{\mkern 1mu} {\mkern 1mu} A/m$$ 3 GATE ECE 2008 MCQ (Single Correct Answer) +2 -0.6 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant $${\varepsilon _r} = 9$$ ). The magnitude of the reflection coefficient is A $$0$$ B $$0.3$$ C $$0.5$$ D $$0.8$$ 4 GATE ECE 2007 MCQ (Single Correct Answer) +2 -0.6 The $$\overrightarrow H$$ field (in A/m) of a plane wave propagating in free space is given by $$\overrightarrow H = \widehat x{{5\sqrt 3 } \over {{\eta _0}}}\cos \left( {\omega \,t - \beta \,z} \right) + \widehat y{5 \over {{\eta _0}}}\sin \left( {\omega \,t - \beta \,z + {\pi \over 2}} \right)$$$

The time average power flow density in Watts is

A
$${{{\eta _0}} \over {100}}$$
B
$${{100} \over {{\eta _0}}}$$
C
$$50\,{\eta _0}^2$$
D
$${{50} \over {{\eta _0}}}$$
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