GATE ECE
Electromagnetics
Uniform Plane Waves
Previous Years Questions

## Marks 1

Consider the following wave equation, $${{{\partial ^2}f(x,t)} \over {\partial {t^2}}} = 10000{{{\partial ^2}f(x,t)} \over {\partial {x^2}}}$$ Which o...
If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be
Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $$E = \widehat x{E_x}\,{e^{ - j\left... The electric field of a uniform plane electromagnetic wave is$$$\vec E = \left( {{{\overrightarrow a }_x} + j4{{\overrightarrow a }_y}} \right)\exp ... The electric field component of a plane wave traveling in a lossless dielectric medium is given by $$\overrightarrow E \left( {z,t} \right) = {\wide... Which one of the following field patterns represents a TEM wave traveling in the positive$$x$$direction? A two - port network has scattering parameters given by$$[S] = \left[ {\matrix{ {{s_{11}}} & {{s_{12}}} \cr {{s_{21}}} & {{s_{2... The electric field of a uniform plane electromagnetic wave in free spce, along the positive x direction, is given by $$\vec E = 10\left( {{{\widehat... A plane wave propagating in air with$$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \right){\mkern 1mu} {\mkern 1mu} {e... A plane wave of wavelength $$\lambda$$ is traveling in a direction making an angle $${{{30}^ \circ }}$$ with positive $$x$$-axis and $${{{90}^ \circ ... The electric field of an electromagnetic wave propagating in the positive z-direction is given by$$$E = {\widehat a_x}\sin \left( {\omega t - \beta ...
The magnetic field intensity vector of a plane wave is given by $$\overline H \left( {x,y,z,t} \right) = 10\,\sin \left( {5... The depth of penetration of electromagnetic wave in a medium having conductivity$$\sigma $$at a frequency of 1 KHz is 25 cm. The depth of penetratio... If a plane electromagnetic wave satisfies the equation$${{{\partial ^2}\,{E_x}} \over {\partial \,{z^2}}} = \,{c^2}{{{\partial ^2}\,{E_x}} \over {\pa...
A TEM wave is incident normally upon a perfect conductor. The E and H fields at the boundary will be respectively
The depth of penetration of a wave in a lossy dielectric increases with increasing
The intrinsic impedance of copper at high frequencies is
The wavelength of a wave with propagation constant $$\left( {0.1\,\pi + j\,0.2\pi } \right){m^{ - 1}}$$ is
The polarization of a wave with electric field vector $$\overrightarrow E = {E_0}\,{e^{j\left( {\omega t - \beta z} \right)}}\left( {\overrightarrow ... The intrinsic impedance of a lossy dielectric medium is given by Copper behaves as a A plane electromagnetic wave traveling along the +z-direction, has its electric field given by Ex = 2 cos$$\left( {\omega t} \right)$$and Ey = 2 cos... ## Marks 2 The expression for an electric field in free space is$$E = {E_0}\left( {\widehat x + \widehat y + j2\widehat z} \right){e^{ - j\left( {\omega t - kx ...
The electric field of a uniform plane wave travelling along the negative $$z$$ direction is given by the following equation: $$\overrightarrow E {}_w... The electric field intensity of a plane wave propagating in a lossless non-magnetic medium is given by the following expression$$\overrightarrow E \...
The electric field intensity of a plane wave traveling in free space is given by the following expression $$E\left( {x,t} \right) = {\widehat a_{_y}}... Consider a uniform plane wave with amplitude$$\left( {{E_0}} \right)$$of$$10\,\,\,V/m$$and$$1.1 GHz$$frequency travelling in air, and incident n... A region shown below contains a perfect conducting half-space and air. The surface current$${\overrightarrow K _{_s}}$$on the surface of the perfect... Assume that a plane wave in air with an electric field$$\overrightarrow E = 10\cos \left( {\omega t - 3x - \sqrt {3z} } \right){\widehat a_{_y}}\,\...
If the electric field of a plane wave is $$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t - kz + {{30}^ \circ }} \right) ... In spherical coordinates, let$${{{\widehat a}_{_0}},\,{{\widehat a}_{_\phi }}}$$denote unit vectors along the$$\theta ,\,\,\phi $$directions.$$$E... A monochromatic plane wave of wavelength $$\lambda = 600$$ is propagating in the direction as shown in the figure below. $${\overrightarrow E _i},\,{... A monochromatic plane wave of wavelength$$\lambda = 600$$is propagating in the direction as shown in the figure below.$${\overrightarrow E _i},\,{... The electric and magnetic fields for a TEM wave of frequency $$14 GHz$$ in a homogeneous medium of relative permittivity $${\varepsilon _r}$$ and rela... A plane wave having the electric field component $${\overrightarrow E _i} = 24\,\,\cos \,\,\left( {3 \times {{10}^8}\,t - \beta \,y} \right){\wideha... A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant$${\varepsilon _r} = 9$$). Th... The$$\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...
A medium of relative permittivityb $${\varepsilon _r} = 2$$ forms an interface with free-space. A point source of electromagnetic energy is located in...
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 wit...
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 t...
A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non-magnetic, dielectric material with $$\va... A uniform plane wave traveling in air is incident on the plane boundary between air and another dielectric medium with$${\varepsilon _r} = 4$$. The r... Medium$$1$$has the electrical permittivity$${\varepsilon _1} = 1.5\,\,{\varepsilon _0}\,\,\,F/m$$and occupies the region to left of$$x = 0$$pl... If the electric field intensity associated with a uniform plane electromagnetic wave traveling in a perfect dielectric medium is given by$$E\left( {z...
A plane wave is characterized by $$\overrightarrow E = \left( {0.5\mathop x\limits^ \cap + \mathop y\limits^ \cap \,{e^{j\pi /2}}} \right){e^{j\... Distilled water at$${25^ \circ }C$$is characterized by$$\sigma = 1.7 \times {10^{ - 4}}$$mho/m and$$ \in = 78{ \in _0}$$at a frequency of$$3 ...
A uniform plane electromagnetic wave incident normally on a plane surface of a dielectric material is reflected with a VSWR of 3. What is the percenta...
A uniform plane wave in air impinges at 45° angle on a lossless dielectric material with dielectric constant $${\varepsilon _r}$$. The transmitted wav...
A uniform plane wave in air is normally incident on an infinitely thick slab. If the reflective index of the glass slab is 1.5, then the percentage of...
Some unknown material has a conductivity of $${10^{ 6}}$$ $$mho/m$$ and a permeability of $$4\pi \times {10^{ - 7}}\,\,\,\,\,H/m.$$ The skin depth...
A material is described by the following electrical parameters at a frequency of $$10$$ GHz is $$\sigma = {10^6}$$ mho/m, $$\mu = {\mu _0},$$ and $$... A plane wave is incident normally on a perfect conductor as shown in Fig. Here$$E_x^i,\,\,H_y^i$$and$$\overrightarrow P {}^i$$are electric field, ... The electric field component of a uniform plane electromagnetic wave propagating in the$$Y$$-direction in a lossless medium will satisfy the equat... The skin - depth of copper at a frequency of$$3 GHz$$is$$1$$micron ($${{{10}^{ - 6}}}$$metre). At$$12 GHz$$, for a non - magnetic conductor wh... In a good conductor the phase relation between the tangential components of electric field Et and the magnetic field Ht is as follows... For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when ## Marks 5 A medium has breakdown strength of$$16$$KV/m r.m.s. Its relative permeability is$$1.0$$and relative permittivity is$$4.0$$. A plane electromagnet... A plane wave in free space with$$\overrightarrow E = \left( {\sqrt \pi } \right)\left( {10.0\,\widehat x + 11.8\,\widehat y} \right)\exp \left[ {j...
A plane wave with $$\overrightarrow E = 10\,{e^{j\left( {\omega t - \beta z} \right)\,}}\,\,{\overrightarrow a _{_y}}$$ is incident normally on a thi...
The electric field vector of a wave is given as $$\vec E = {E_0}{\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {{8{{\vec a}_x} ... A uniform plane wave is normally incident from air on an infinitely thick magnetic material with relative permeability 100 and relative permittivity 4... A uniform plane wave having parallel polarization is obliquely incident on an air - dielectric interface as shown in Fig. If the wave has an electric ... A wave traveling in the$$+Z$$-direction, is the resultant of two linearly polarized components,$${E_x}\,\,\, = \,\,\,\,\,\,3\,\,\,\,\cos \omega...
Match the following descriptions with each of the diagrams given in Fig. Fields are near the interface, but on opposite sides of the boundary. Vectors...

## Marks 8

A uniform plane wave traveling in free space along the +$$z$$ direction and having its electric field along the$$x$$-direction, is normally incident ...
A uniform plane electromagnetic wave traveling in free-space enters into a lossless medium at normal incidence. In the medium its velocity reduces by ...
A 300 MHz plane E.M. wave is propagating in free space. The wave is incident normally on an infinite copper slab. For the transmitted wave i...
An electric field is given by $$\overrightarrow E = \overrightarrow a {}_x\,{\rm A}\,\,\sin \,\beta ySin\,\,\omega t$$ is present in a charge free me...
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