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GENERAL SIR JOHN KOTELAWALA DEFENCE UNIVERSITY
Faculty of Engineering
Department of Electrical, Electronic and Telecommunication Engineering
BSc Engineering Degree
Semester 4 Examination – December 2013
(Intake 29 - EE/ET)
ET 4042 – FIELDS AND ELECTROMAGNETICS
Time allowed: 3 hours
17 December, 2013
ADDITIONAL MATERIAL PROVIDED
Laplace Transform Table
4 cycle semi-log paper
INSTRUCTIONS TO CANDIDATES
This paper contains 6 questions on 7 pages
Answer any FIVE questions only
This is a closed book examination
Use separate answer book for SECTION A and SECTION B
This examination accounts for 70% of the module assessment. A total maximum mark
obtainable is 100. The marks assigned for each question and parts thereof are indicated in
square brackets
If you have any doubt as to the interpretation of the wordings of a question, make your own
decision, but clearly state it on the script
Assume reasonable values for any data not given in or provided with the question paper,
clearly make such assumptions made in the script
All examinations are conducted under the rules and regulations of the KDU
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This Page is Intentionally Left Blank
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εo = 8.84 x 10-12 F/m
μo = 4π x 10-7 H/m
SECTION A
Question 1
(a)
State Gauss Law in electrostatics.
[03]
(b)
A co-axial cable has a core radius r1 and sheath radius r2. The space between the core
and the sheath is filled with a dielectric material having a relative permittivity εr.
Applying Gauss Law, show that expression (1.1) gives the capacitance per length l of
the cable.
[05]
(c)
The co-axial cable shown in Figure Q1.1 has two concentric layers of dielectric
between the core of radius r1 = 1 mm and the sheath of radius r3 = 3 mm. The
dielectric layers separate at radius r2 = 2 mm. The relative permittivity of inner
dielectric εr1 = 4 and that of the outer dielectric εr2 = 3. Length of the cable is 100 m.
The voltage applied between the core and the sheath is 1.5 kV and the sheath is
grounded.
Determine,
(i) The maximum electric field intensity in each layer of dielectric
[06]
(ii) Capacitance of the cable
[04]
(iii) Total energy stored in the dielectric medium of the cable.
[02]
εr2
εr1
r3
r2
r1
Figure Q1.1
Page 3 of 8
Question 2
(a)
Figure Q2.1 shows a permanent magnet excited circuit to set up a flux density of 0.6 T
in the air gap. The circuit has a uniform cross sectional area throughout, an air gap
length of 2 mm and a mean iron length of 180 mm. The relative permeability of iron is
2000. Demagnetizing data for the permanent magnet is given in Table Q2.1.
Determine the length of the permanent magnet required
[10]
Table Q2.1
. Bm (T)
Hm (kA/m)
0.8
0
0.7
-10
0.6
-15
0.5
-20
0.4
-24
0.3
-27
0.2
-30
0.0
-35
Air gap
Mean flux path
Mild Steel core
Permanent Magnet
Figure Q2.1
(b)
Figure Q2.2 shows an electromagnetic actuator of circular cross section with inner and
outer diameters d1 and d2. The exciting coil has N turns and the mild steel used in the
circuit can be assumed to have infinite permeability. At the position shown the air gap
length is x. Derive an expression for the force F exerted on the work piece when a
current I is sent through the coil.
[10]
x
Mild steel core
Coil of turns N
Movable mild
steel plunger
d2
d1
Work piece
Force F
Figure Q2.2
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Question 3
(a)
Figure Q3.1 shows two lossy dielectric media of permittivities εr1 & εr2 and
resistivities ρ1 & ρ2, separated by a plane boundary. Electric field intensity E1 in
medium-1 reaches the boundary at an angle α1 to the normal. Derive expressions for,
(i) Outgoing electric field intensity E2 in medium-2
[04]
(ii) Direction angle α2 of the field intensity in medium-2
[04]
(iii) Surface density ρs of free charges appearing on the boundary
[04]
E1
α1
ρs
α2
εr1
ρ1
εr2
ρ2
E2
Figure Q3.1
(b)
A point charge Q is in a medium of relative permittivity εr, at a distance d away from
an infinite plane conducting boundary. Derive an expression for the force acting on
the charge due to the induced charges on the boundary.
[04]
(c)
What is image method of field calculation in electrostatics?
[02]
Suggest three practical systems that can use image methods for the calculation of
capacitance, conveniently.
[02]
Page 5 of 8
Question 4
(a)
(b)
Derive an expression for the self inductance per unit length of a twin overhead line of
conductor radius a, and conductor separation D.
[07]
Figure Q4.1 shows two concentric coils of radii r1 and r2 having no. of turns N1 and N2
in a medium of relative permeability μr with an axial separation d. Derive an
expression for the mutual inductance between the two coils. You may assume that
coil-2 radius r2 is very small.
[07]
N1 turns
Radius r1
μr
N2 turns
Radius r2
X
X
d
Figure Q4.1
(c)
Derive an expression for the magnetic field intensity at the centre of a rectangular coil
of side lengths 2a and 2b, having N turns and carrying current I.
Page 6 of 8
[06]
SECTION B
Question 5
(a)
State Maxwell’s equations in electromagnetic field theory.
[08]
(b)
Using Maxwell’s fourth equation, derive an expression for the Amperes Law in
stationary conditions of electric field. Hence, show that the total current component is
transverse or solenoidal.
[04]
(c)
Equations (5.1), (5.2), (5.3) and (5.4) are given:
Poisson equation in free space:
Continuity Equation:
Lorentz condition for electromagnetic field theory in free space:
Vector potential in free space in cylindrical coordinates:
Symbols , , and denote the scalar potential, charge distribution, current density
and vector potential respectively. The initial state of the scalar potential is zero.
Q6 (a)
(b)
(i) Obtain an expression for the scalar potential as a function of space and time
[03]
(ii) Obtain an expression for the charge distribution of the system.
[03]
(iii) Show that it is impossible to obtain a total non solenoidal current with non zero
value of
with the conditions in (c) (ii) above.
[02]
Use the Maxwell’s equations in electromagnetic field theory to explain the basic laws
of electricity and magnetism.
[08]
The vector representation of the electric field in cylindrical coordinates of a coaxial
transmission line in free space is given by equation (6.1), where , , and are real
constants.
(i) Obtain an expression for the magnetic field of the transmission line as a function
of space and time. Show that the electric and magnetic fields are perpendicular to
each other.
[04]
(ii) Obtain an expression for the current density of the system. Check whether the
current component is solenoidal or irrotational.
[06]
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(iii) Obtain an expression for the charge distribution of the system.
End of question paper
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[02]