EMT EC

ACEEngineering AcademyHyderabad New Delhi Vijayawada

204, II Floor, Rahman Plaza, Opp. Methodist School, Abids, Hyderabad-500001,

Ph:: 040-24750242 , 040-24750263, 040-24752469 , 040-24750437

IES – 2012 Grand Test –Conventional Paper

SUB: Electro Magnetics

EC: Electronics & Telecommunication Engineering

Max.Marks: 100 Time: 1 ½ Hour

INSTRUCTIONS

Candidates should attempt FIVE questions in all.

Question No.1 is compulsory. The remaining FOUR questions are to be

attempted by selecting two questions each from Sections A & B.

The number of marks carried by each questions is indicated at the end of

the question.

Answers must be written in English

Assume suitable data, if necessary and indicate the same clearly.

Whenever a question is attempted, all its subdivisions must be attempted.

Unless otherwise indicated, symbols and notations have their usual

meanings.

ACE :: 2 :: ACE

EMT EC

Z01

Z02

o

o

01.(a) A closed surface is defined in spherical coordinates by

;6.12.1;3.01.0;53 r Find the volume enclosed.

(b) Given two vectors ,sinˆ5cos)ˆ4ˆ3( 21 taFandtaaF yzx determine the

polarization of the vector F = F1 + F2.

(c) Using Faraday’s law in differential form find B, given./ˆ)2106(cos10 8 mVaztE x

(d) For uniform plane wave propagation in fresh water ),80,/10( 03

omS ,

find attenuation constant and phase shift constant at 100 MHZ frequency.

(e) Consider the junction of two lines having characteristic impedances

,7550 0201 ZandZ as shown below. Compute voltage reflection coefficient

at the junction. Also, compute the current reflection coefficient and reflected power

when incident power on the junction is Pi = 1 Watt.

(f) For an air dielectric short-circuited line of characteristic impedance 50 Ω, find the

minimum value of length for which its input impedance is equivalent to that of an

inductor of 0.25×10-6 Henry at 100 MHz.

(g) What is the Brewster angle ? what is the polarization of the reflected wave for an

elliptically polarized wave incident on a dielectric interface at the Brewster angle.

(h) An antenna has a field pattern given by .900cos)( 02 forE Find the half-

power beam width.

(i) A rectangular waveguide is 3.7 cm × 1.8 cm, on its cross section. Calculate the cut off

frequency of the mode next to dominant mode.

(j) A lossless transmission line has a distributed inductance of 8 μH per meter and a

distributed shunt capacitance of 300 pF per meter. Calculate the input impedance of a

1 – meter section of this line terminated in an open circuit at 70 MHz.

ACE :: 3 :: ACE

EMT EC

y

x

r = 3

SECTION – A

02. (i) The electrostatic field intensity ‘E’ is derivable as the negative gradient of a scalar

electric potential ‘V’; Determine ‘E’ at the point (1,1,0) if

.4

sin

yeVV x

o

(5 Marks)

(ii) Given ,ˆ2ˆ yx axaxyF verify Stoke’s theorem over a quarter circular disk with a

radius 3 in the first quadrant as shown in figure below. (7 Makrs)

(iii) Let ./ˆ6ˆ3ˆ6 22222 mCayzxazxaxyzD zyx Find the total charge lying within

the region bounded by x = 1 and 3, y = 0 and 1, and z = -1 and 1 by separately

evaluating each side of the divergence theorem. (8 Marks).

03.

(i) Write the integral form of Maxwell’s equations. Using divergence and Stoke’s theorems

obtain the differential form of Maxwell’s equations. (8 Marks)

(ii) Derive the boundary conditions for electric and magnetic fields at the interface of two

perfect dielectrics. (8 Marks)

(iii) Are conduction and displacement currents in phase for time-harmonic fields?

Explain. (4 Marks)

04. (i) The electric field of a uniform plane wave propagating in a dielectric medium is given

by

mVztaztaztE yx

310sinˆ

310cos2ˆ),( 88

(a) Determine the frequency and wavelength of the wave

(b) What is the dielectric constant of the medium

ACE :: 4 :: ACE

EMT EC

(c) Describe the polarization of the wave

(d) Find the corresponding H – field.

(ii) The magnetic field intensity of a linearly polarized UPW propagating in the +y direction

in sea water

80,4,1 rr m

s is

0310sin1.0ˆ 10 yatmAtaH x

Determine the attenuation constant, the intrinsic impedance and the skin depth. Also,

find the location at which the amplitude of H is 0.01 A/m. (8 Marks)

SECTION – B

05. (i) An electromagnetic wave in dielectric medium ),(1 01 impinges obliquely on a

boundary plane with dielectric medium ),(2 02 . Let 21 and denote the incident

and transmitted angles, respectively. Prove the following for perpendicular polarization.

(10 Marks)

)(sin

sinsin2;

)(sin

)(sin

12

12

12

12

T

(ii) For an incident wave with parallel polarization, find the relation between the critical

angle and the Brewster angle, when wave is obliquely incident at an interface of two

non- magnetic dielectric media. (10 Marks)

06. (i) A loss-less transmission line of length 434.0 and characteristic impedance 100 Ω is

terminated in an impedance (260 + j180) Ω. Find the voltage reflection coefficient, the

standing wave ratio, the input impedance and the location of a voltage maximum on

the line. (12 Marks)

(ii) What is meant by a “distortion less line”? what relation must the distributed

parameters of a line satisfy in order for the line to be distortion less (4 Marks)

(iii) Why are the stubs used in impedance matching usually of the short-circuited type

instead of the open-circuited type? (4 Marks)

ACE :: 5 :: ACE

EMT EC

07. (i) A standard air-filled S-band rectangular waveguide has dimensions a = 7.21 cm and

b = 3.40 cm. What mode types can be used to transmit em waves having the

following wave length ? (6 Marks)

(a) = 10 cm (b) = 5 cm

(ii) What is an evanescent mode?

What is meant by an eigen mode?

What is meant by the dominant mode? (4 Marks)

(iii) Find the directive gain and the directivity of a Hertzian dipole. Also, find the

radiation efficiency of Hertzian dipole made of a metal wire of radius ‘a’, length ‘d’

and conductivity . (8 Marks)

(iv) Differentiate Fresnel-zone field with Fraunhofer-zone field. (2 Marks)