1
GATE ECE 2006
+2
-0.6
A medium of relative permittivityb $${\varepsilon _r} = 2$$ forms an interface with free-space. A point source of electromagnetic energy is located in the medium at a depth of $$1$$ meter from the interface. Due to the total internal reflection, the transmitted beam has a circular cross-section over the interface. The area of the beam cross-section at the interface is given by
A
$$2\pi \,{m^2}$$
B
$${\pi ^2}\,{m^2}$$
C
$$\pi /2\,{m^2}$$
D
$$\pi \,{m^2}$$
2
GATE ECE 2006
+2
-0.6
A medium is divided into regions $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ about $$x = 0$$ plane, as shown in the Fig. below. An electromagnetic wave with electric field $${\overrightarrow E _1} = 4{\widehat a_x} + 3{\widehat a_y} + 5{\widehat a_z}$$ is incident normally on the interface form region-$${\rm I}$$ . The electric field $${E_2}$$ in region-$${\rm I}$$$${\rm I}$$ at the interface is A
$${E_2} = {E_1}$$
B
$$4\,\,{\widehat a_x} + 0.75\,\,{\widehat a_y} - 1.25\,\,{\widehat a_z}$$
C
$$3\,{\widehat a_x} + 3\,{\widehat a_y} + 5\,{\widehat a_z}$$
D
$$\, - 3\,{\widehat a_x} + 3\,{\widehat a_y} + 5\,{\widehat a_z}$$
3
GATE ECE 2006
+2
-0.6
When a plane wave traveling in free-space is incident normally on a medium having $${\varepsilon _r} = 4.0,$$ the fraction of power transmitted into the medium is given by
A
8/9
B
1/2
C
1/3
D
5/6
4
GATE ECE 2004
+2
-0.6
A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non-magnetic, dielectric material with $$\varepsilon > {\varepsilon _0}$$. Maxima and minima are observed when the electric field is measured in front of the slab. The maximum electric field is found to be $$5$$ times the minimum field. The intrinsic impedance of the medium should be
A
$$120\,\pi \,\Omega$$
B
$$60\,\pi \,\Omega$$
C
$$600\,\pi \,\Omega$$
D
$$24\,\pi \,\Omega$$
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Communications
Electromagnetics
General Aptitude
Engineering Mathematics
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