##

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

Â I need to solve this this past paper .............

in given time

Sheet 1 of 7

EXAMINATION PAPER

Code: ENGD2009

Session - 2015/2016

Faculty of Technology

Module Code - ENGD2009

Module Title - Electromagnetics

Date Time Allowed - 2 hours

Start

Finish

_________________________________________________________

Instructions to, and information for, candidates:

â€¢ Section A contributes 30 marks. Attempt all questions.

â€¢ Section B contributes 30 marks. Attempt three questions.

â€¢ Section C contributes 20 marks. Attempt one question.

Note: 0 = 10âˆ’9

36 Fâˆ’1 and 0 = 4 10âˆ’7 âˆ’1

Total marks achievable = 80 Programmable calculators are permitted during this examination

provided they are â€˜resetâ€™ using the reset button found on the

underneath of some calculators, â€˜cancelledâ€™ (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 turnoverâ€¦ Code: ENGD2009 Sheet 2 of 7 Section A.

Attempt all (5) questions.

(Questions are each worth six marks in this section).

A1.

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) ï¿½ + 11

ï¿½ âˆ’ 2.5ï¿½

If a displacement vector is given as = âˆ’3

calculate the magnitude and the direction of this vector

(3 marks) a) Define the operator Del, âˆ‡, in rectangular Cartesian

coordinates A2. b) (2 marks)

State how âˆ‡ operates on a vector quantity to give the Curl of

that vector, show how this would expand for the two

ï¿½ âˆ’ 5ï¿½ and explain the

dimensional vector quantity = âˆ’3

significance of the direction of the Curl.

(4 marks) A3.

a) State an equation for Stokeâ€™s theorem, defining all terms

used.

(3 marks) b) State an equation for Gaussâ€™s Divergence theorem, defining

all terms used.

(3 marks) Please turnoverâ€¦ 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 âˆ‡. = 0

but âˆ‡. 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 turnoverâ€¦ Code: ENGD2009 Sheet 4 of 7 Section B

Attempt three (3) questions

(Questions are worth 10 marks in this section.)

B1.

Define the following giving an illustrative example for each using

your own vector or scalar quantities.

a)

b)

c) Gradient

Divergence

Curl

(10 marks) B2

a) Given two dielectric materials with an electric field incident on

the interface. Illustrate a piecewise implementation of

âˆ® . = 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 Coulombâ€™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 turnoverâ€¦ Code: ENGD2009 Sheet 5 of 7 B4.

a) State Faradayâ€™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

transformerâ€™.

(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 50â„¦

characteristic impedance system to a 100â„¦ characteristic

impedance, if there are 30 turns on the primary side.

(5 marks) B5.

Starting from Gaussâ€™ law, derive Poissonâ€™s and Laplaceâ€™s

equations.

(10 marks) End of Section B Please turnoverâ€¦ 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 Ampereâ€™s circuital law, derive an expression for

the field at any point P from one wire. State your

assumptions.

(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

ground).

(4 marks) C2. A vertical cylinder is part of an environmental â€œscrubberâ€ 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 Îµ = Îµ0 = 8.854 x 10-12 F/m Please turnoverâ€¦ Code: ENGD2009 Sheet 7 of 7 a) Illustrate the system and state whether Poissonâ€™s or

Laplaceâ€™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

system.

(3 marks) C3.

a) Starting with Maxwellâ€™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 âˆ‡ Ã— âˆ‡ Ã— = âˆ‡(âˆ‡. ) âˆ’ âˆ‡2 ).

(14 marks) b) Assume the medium is lossless, derive an expression for the

propagation constant gamma, Î³ 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

**Solution details:**
This attachment is locked

We have a ready expert answer for this paper which you can use for in-depth understanding, research editing or paraphrasing. You can buy it or order for a fresh, original and plagiarism-free copy from our tutoring website www.aceyourhomework.com (Deadline assured. Flexible pricing. TurnItIn Report provided)

×
Please Enter The Email Where You Want To Receive Solution.