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(Solved) Sheet 1 of 7 EXAMINATION PAPER Code: ENGD2009 Session - 2015/2016 Faculty of Technology Module Code - ENGD2009 Module Title - Electromagnetics Date...

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Sheet 1 of 7
Code: ENGD2009
Session - 2015/2016
Faculty of Technology
Module Code - ENGD2009
Module Title - Electromagnetics
Date Time Allowed - 2 hours
Instructions to, and information for, candidates:
• Section A contributes 30 marks. Attempt all questions.
• Section B contributes 30 marks. Attempt three questions.
• Section C contributes 20 marks. Attempt one question.
Note: 0 = 10−9
36 F−1 and 0 = 4 10−7 −1
Total marks achievable = 80 Programmable calculators are permitted during this examination
provided they are ‘reset’ using the reset button found on the
underneath of some calculators, ‘cancelled’ (by battery removal) or
otherwise checked and proved not to carry textual information, or
formulae required by the examination, other than normal
scientific/statistical functions. Please turnover… Code: ENGD2009 Sheet 2 of 7 Section A.
Attempt all (5) questions.
(Questions are each worth six marks in this section).
a) Define the term unit vector and show how a unit vector can
be obtained from the vector describing the distance between
two points in three dimensional space.
(3 marks) b) � + 11
� − 2.5�
If a displacement vector is given as = −3
calculate the magnitude and the direction of this vector
(3 marks) a) Define the operator Del, ∇, in rectangular Cartesian
coordinates A2. b) (2 marks)
State how ∇ operates on a vector quantity to give the Curl of
that vector, show how this would expand for the two
� − 5� and explain the
dimensional vector quantity = −3
significance of the direction of the Curl.
(4 marks) A3.
a) State an equation for Stoke’s theorem, defining all terms
(3 marks) b) State an equation for Gauss’s Divergence theorem, defining
all terms used.
(3 marks) Please turnover… Code: ENGD2009 Sheet 3 of 7 A4.
a) Using an annotated diagram, show how divergence can be
obtained by considering a continuous surface surrounding a
point at which the divergence is to be obtained.
(2 marks) b) Considering the magnetic field strength around a wire
inductor and a parallel plate capacitor explain why ∇. = 0
but ∇. can be non-zero.
(4 marks) a) Using an appropriate annotated sketch or equations,
describe the difference between a conduction current and a
displacement current
(4 marks) b) Suggest why the magnitude of the displacement current
might be assumed to be frequency dependent but the
assumption of frequency dependence cannot be as
obviously made for conduction current.
(2 marks) A5. End of Section A Please turnover… Code: ENGD2009 Sheet 4 of 7 Section B
Attempt three (3) questions
(Questions are worth 10 marks in this section.)
Define the following giving an illustrative example for each using
your own vector or scalar quantities.
c) Gradient
(10 marks) B2
a) Given two dielectric materials with an electric field incident on
the interface. Illustrate a piecewise implementation of
∮ . = and use this to derive the fact that the tangential
electric field must be continuous across the interface.
(8 marks) b) Describe the impact this analysis has on the tangential
electric fields at the interface if the second material is a
perfect electrical conductor.
(2 marks) a) Starting with Coulomb’s law show how the electric field at a
point in space due to a charge at the origin can be obtained.
(5 marks) b) Given a charge of 1nC at the origin calculate the electric field
strength at the point (1, 2, 4) and the units are mm.
(5 marks) B3. Please turnover… Code: ENGD2009 Sheet 5 of 7 B4.
a) State Faraday’s law of electromagnetic induction and use
this to show the relationship between the terminal voltages
and the the number of turns of wire for the primary and
secondary windings around a continuous iron core of the
(5 marks) b) Further develop the relationship developed in part (a) to
show how a transformer can be used as an impedance
converter, giving the number of turns required on the
secondary of such a transformer to convert a 50Ω
characteristic impedance system to a 100Ω characteristic
impedance, if there are 30 turns on the primary side.
(5 marks) B5.
Starting from Gauss’ law, derive Poisson’s and Laplace’s
(10 marks) End of Section B Please turnover… Code: ENGD2009 Sheet 6 of 7 SECTION C
Attempt ONE question ONLY in this Section
(Questions are worth 20 marks each in this Section)
C1. A single wire 4m above ground transports a current of 100A to a
remote load. It is horizontally separated from the current carrying
the return current by 0.5 m
a) Sketch the system
(2 marks) b) Starting with Ampere’s circuital law, derive an expression for
the field at any point P from one wire. State your
(14 marks) c) Using the formula derived in Question C1b calculate the field
2m below the transmission line and at ground level,
equidistant from both wires (ignoring any effects of the
(4 marks) C2. A vertical cylinder is part of an environmental “scrubber” to remove
particles from exhaust gasses. The particles are charged as they
enter the cylinder. The cylinder is 10m high with metallic grids that
can be charged to a given potential difference (there is a distributed
mechanism for removing the particles which is not part of the
question), and a steady flow through the cylinder ensures that it
behaves quasi-statically. Ideally, there will be 0 (zero) particles per
cubic metre at the top of the cylinder for an input quantity of one
billion particles per cubic metre at the bottom of the cylinder. Each
particle carries an average charge equivalent to 50 electron charges
(the electron charge is ~ 1.6x10-19 C). A linear variation between the
top and the bottom can be assumed. It is found that a 25kV
potential difference between the two ends of the cylinder is sufficient
to ensure the particulate density is sufficient to allow the scrubbing
technique to work, ensuring zero particles at the top of the tower.
Assume ε = ε0 = 8.854 x 10-12 F/m Please turnover… Code: ENGD2009 Sheet 7 of 7 a) Illustrate the system and state whether Poisson’s or
Laplace’s equations are the most suitable for solution of this
problem, giving reasons.
(3 marks) b) Obtain an expression for the potential, V, at any point
(height) in the cylinder, in terms of charge density,
dimensions, potential difference between the two ends and
material properties of the fluid.
(14 marks) c) Calculate the potential at the geometrical centre of the
(3 marks) C3.
a) Starting with Maxwell’s equations in differential form, develop
an expression for the general solution for the electric field
component of an electromagnetic wave propagating in the x
direction (noting that ∇ × ∇ × = ∇(∇. ) − ∇2 ).
(14 marks) b) Assume the medium is lossless, derive an expression for the
propagation constant gamma, γ and use that to show that the
speed of electromagnetic propagation, in a vacuum, is
constant and, hence, determine its value.
(6 marks) End of Section C


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