1

GATE ECE 1992

Subjective

+8

-0

A uniform plane wave traveling in free space along the +$$z$$ direction and having its electric field along the$$ x$$-direction, is normally incident on a thick brass sheet, infinite in extent (along the $$x$$-and $$y$$-directions). The electric field intensity of the wave is given by
$$${E_x} = 1225\,\cos \,\left( {5.89 \times {{10}^{10}}t - \beta z} \right)\,\,\,\,V/m$$$.

Calculate the power per square metre that causes heating of the brass sheet, taking $${ \in _r} = 1,\,\,\,{\mu _r} = 1$$ and $$\sigma = 1.649 \times {10^7}\,\,\,\,\,$$ mhos/metre for brass.

2

GATE ECE 1991

Subjective

+8

-0

A uniform plane electromagnetic wave traveling in free-space enters into a lossless medium at normal incidence. In the medium its velocity reduces by 50% and in free space sets up a standing wave having a reflection coefficient of - 0.125. Calculate the permeability and the permittivity of the medium.

3

GATE ECE 1990

Subjective

+8

-0

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 in the copper slab, calculate the following

(a) Attenuation constant

(b) Phase constant

(c) Skin depth

(d) Phase velocity and

(e) Group velocity

for copper assume the following values

Conductivity $$\sigma = 5.8 \times {10^7}$$ $$mho/m$$

Permeability $$\mu = 4\pi \times {10^{ - 7}}$$ $$H/m$$

Permeability $$\varepsilon = {1 \over {36\pi }} \times {10^{ - 9}}$$ $$F/m$$

4

GATE ECE 1987

Subjective

+8

-0

An electric field is given by $$\overrightarrow E = \overrightarrow a {}_x\,{\rm A}\,\,\sin \,\beta ySin\,\,\omega t$$ is present in a charge free medium infinite in extent

(a) Determine the associated magnetic field.

(b) What type of wave does the above field represent?

Questions Asked from Uniform Plane Waves (Marks 8)

Number in Brackets after Paper Indicates No. of Questions

GATE ECE Subjects

Network Theory

Control Systems

Electronic Devices and VLSI

Analog Circuits

Digital Circuits

Microprocessors

Signals and Systems

Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform

Communications

Electromagnetics

General Aptitude