Code:
AE14 Subject:
ELECTROMAGNETICS AND
RADIATION
Time: 3 Hours Max. Marks: 100
NOTE: There are 9 Questions in all.
· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.
· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.
· Any required data not explicitly given, may be suitably assumed and stated.
Q.1 Choose the correct or best alternative in the following: (2x10)
a. When the separation between two charges increases, the electric potential energy of charges
(A) increases. (B) decreases.
(C) remains the same. (D) may increase or decreases.
b. Which one of the following conditions will not guarantee a distortionless Transmission Line?
(A) R=0, G=0 (B) LG=RC
(C) R >>
L, G >>C (D)
R <<L, G <<C
c. A uniform plane wave in air is incident normally on an infinitely thick slab. If the refractive index of the glass slab is 1.5, then the percentage of the incident power that is reflected from the air-glass interface is
(A) 0% (B) 4%
(C) 20% (D) 10%
d. Some unknown
material has a conductivity of 
, and a permeability of 
. The skin depth
for the material at 1 GHz is
(A)
15.9 
(B)
20.9
(C) 25.9 (D)
30.9
e. An
electromagnetic wave is incident obliquely at the surface of a dielectric
medium 
from
dielectric medium 
. The angle of incidence and the
critical angle are 
and 
respectively. The phenomenon of
total reflection occurs when
(A)
and 
(B)
and
(C) and (D) and
f. Find the
magnetic field at the point P due to a current carrying conductor as shown in
the figure. The curve portion is a semicircle of radius 
and the straight wires are
long.
(A)
(B)
(C) 
(D)
g. Poisson’s equation is
(A)
(B)
(C) 
(D)
h. The radio wave is
incident on layer of ionosphere at an angle of 
with the vertical. If the critical
frequency is 1.2 MHz, the maximum usable frequency (MUF) is
(A) 1.2 MHz (B) 2.4 MHz
(C) 0.6 MHz (D) 1.386 MHz
i. A transmission
line with a characteristic impedance 
is connected to a transmission line
with characteristic impedance 
. If the system is being driven by a
generator connected to the first line, then the overall transmission
coefficient will be
(A)
(B)
(C) 
(D)
j. A rectangular
waveguide has dimension 
, its cutoff frequency for the
dominant mode is
(A) 5 GHz (B) 10 GHz
(C) 15 GHz (D) 20 GHz
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Determine the electric potential energy of a uniformly charged sphere of radius R. (8)
b. Find the electric field at a point P on the perpendicular bisector of a uniformly charged rod. The length of the rod is L, the charge on it is Q and the distance of P from the centre of the rod is a. (8)
Q.3 a. Prove
that a uniform plane wave is transverse in nature and 
(12)
b. Derive expression for
attenuation constant 
and phase constant 
for lossless
transmission lines. (4)
Q.4 a. Explain critical frequency and maximum usable frequency. Determine the value of frequency at which an Electromagnetic wave must be propagated for D-region having refractive index of 0.5. (given N=400 electrons/cc for D-region). (8)
b. Derive the wave equations from Maxwell’s equation for free space, lossless charge free region. (8)
Q.5 a. Find the magnetic field at a distance r from a long straight wire carrying a steady current I. (5)
b. Find
the magnetic field due to an infinite uniform surface current 
covering the x –
y plane. (5)
c. Evaluate 
for a cubical box
bounded by x = 0 & x = 1, y = 0 & y = 1, z = 0 & z = 1 and the
magnetic field is given by 
. (6)
Q.6 a. An electromagnetic wave travel in free space with the
electric component 
. Determine
(i) and 
(ii) the magnetic field component.
(iii) time average power in wave. (3+3+4)
b. In a loss less medium
for which 
,
and H =
0.1 Cos 
+0.5 Sin 
. Calculate
electric field intensity. (6)
Q.7 a. What is stub matching? Outline the solution for the single stub matching problem. (8)
b. A 30m long loss less
transmission line with 
operating at 2 MHz is terminated
with a load 
.
If 
on
the line, find
(i) the reflection coefficient, (K).
(ii) the voltage standing wave ratio, (S). (4+4)
Q.8 a. Discuss the propagation characteristics of a rectangular wave guide propagating under TM mode and hence explain propagation constant, guide wavelength and cut off frequency. (10)
b. A
rectangular wave guide has the following characteristics: b = 1.5 cm, a =
3 cm, 
, 
(i)
Calculate
the cutoff frequency for 
and 
modes.
(ii)
Calculate
the guide wavelength and characteristic impedance, 
at 4.0 GHz for 
modes. (6)
Q.9 a. Establish the expression for normalised E-field and H-field pattern for a half wave dipole. (4+4)
b. A magnetic field strength
of 
is
required at a point on 
,
2 Km from an antenna in air. Neglecting ohmic loss how much power must antenna transmit if it is
(i)
a hertzian
dipole of length 
.
(ii) A half wave dipole. (4+4)