ENG018 UNIVERSITY OF BOLTON SCHOOL OF … · engineering electromagnetism module no: eee6002 date: 17 january 2018 time: 2.00 ... module no. eee6002 𝜖 =8.85𝑋10−12𝐹/𝑚

ENG018

UNIVERSITY OF BOLTON

SCHOOL OF ENGINEERING, SPORTS and SCIENCES

BENG (HONS) ELECTRICAL & ELECTRONICS ENGINEERING

EXAMINATION SEMESTER 1 - 2017/2018

ENGINEERING ELECTROMAGNETISM

MODULE NO: EEE6002

Date: 17 January 2018 Time: 2.00 – 4.00

INSTRUCTIONS TO CANDIDATES: There are six questions.

Answer ANY FOUR questions.

All questions carry equal marks.

Marks for parts of questions are shown in brackets.

Electronic calculators may be used provided that data and program storage memory is cleared prior to the examination.

CANDIDATES REQUIRE: Formula Sheet (attached).

Page 2 of 13 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING, SPORTS AND SCIENCES B.ENG (HONS) ELECTRICAL & ELECTRONICS ENGINEERING EXAMINATION SEMESTER 1 - 2017/2018 ENGINEERING ELECTROMAGNETISM MODULE NO. EEE6002

Question 1 (a) A spherical shell centred at the origin extends between R = 2 cm and R = 3 cm. If

the volume charge density is given by 𝜌𝑣 = 3RX10-4 (C/m3), find the total charge

contained in the shell.

[5 marks]

(b) Four charges of 10 𝜇C each are located in free space at points with Cartesian

coordinates (-3,0,0), (3,0,0),(0,-3,0), and (0,3,0). Find the force on a 20 𝜇C charge

located at (0,0,4). All distances are in metres.

[10 marks]

(c) The current flowing through a 100-m-long conducting wire of uniform cross section

has a density of 3X105 (A/m2). Find the voltage drop across the length of the wire if the

wire material has a conductivity of 2X107 (S/m).

[10 marks]

Total 25 marks

Question 2

a) A proton moving with a speed of 2X106 m/s through a magnetic field with magnetic flux density of 2.5 T experiences a magnetic force of magnitude 4X10-

13 N. What is the angle between the magnetic field and the proton’s velocity?

[7 marks]

b) A wire carrying a current of 4 A is formed into a circular loop. If the magnetic

field at the centre of the loop is 20 A/m, what is the radius of the loop if the loop

has

Question 2 continues over the page

Please turn the page


Question 2 continued

(i) Only one turn and

[3 marks]

(ii) 10 turns?

[2 marks]

c) A straight cylindrical-shaped conductor has a radius of 1.5 cm and carries an

alternating current of 5 A. Assuming it is a bare conductor and surrounded by

air, Calculate per metre length:

(i) Its inductance due to its current internal flux only and

[7 marks]

(ii) Its inductance due to its external flux. [6 marks]

Total 25 marks

Question 3

a) The electric field of a traveling electromagnetic wave is given by

E(z, t) = 10cos(𝜋𝑋 107 t +𝜋z/15+𝜋/6) (V/m). Determine:

(i) The direction of wave propagation [2 marks]

(ii) The wave frequency f [4 marks]

(iii) Its wave length 𝜆 [2 marks]

(iv) Its phase velocity up [2 marks]





b) If a circular wire loop is placed centred on the x-y plane with a radius a.

(i) prove that the magnetic field intensity at p(0,0,z) is 𝐻 =I𝑎2

2(𝑎2+𝑧2)3/2 A/m

[10 marks]

(ii) What would it be at the centre of the loop

[2 marks]

(iii) If p moves infinitely in the positive direction of z what would be H?

[3 marks]

Total 25 marks

Question 4

a) The electric field in free space is given by

E= 100 cos (108t+βx) ay V/m

(i) Find the direction of wave propagation

[2 marks]

(ii) Calculate β and the time it takes to travel a distance of l/2

[7 marks]





b) In Free space (z≤ 0), a plane wave 2 with

H=10cos(108t-βz) ax mA/m

Is incident normally on a lossless medium (𝜀 = 2𝜀𝑜 , 𝜇 = 8𝜇𝑜) in region z≥0.

(i) Determine the reflected wave Hr and Er

[8 marks]

(ii) Find the transmitted wave Ht and Et [8 marks]

Total 25 marks

Question 5

a) A distortionless line has Zo = 60 Ω, a = 20 mNp/m, u = 0.6c, where c is the speed of light in a vacuum. Find R, L, G, C, and X at 100 MHz.

[15 marks]

b) Determine the length of a shorted 50 Ω lossless transmission line such that its input impedance at 2.25 GHz identical to that of a capacitor with capacitance Ceq = 4 pF. The wave velocity on the line is 0.75 c.

[10 marks]

Total 25 marks



Question 6 An electric field strength of 10 μV/m is to be measured at an observation point θ = π/2, 500 km from a half-wave (resonant) dipole antenna operating in air at 50 MHz.

a) What is the length of the dipole?

[5 marks]

b) Calculate the current that must be fed to the antenna.

[10 marks]

c) Find the average power radiated by the antenna.

[5 marks]

d) If a transmission line with Zo = 75 Ω is connected to the antenna, determine the standing wave ratio.

[5 marks]

Total 25 marks

END OF QUESTIONS


Formula sheet

These equations are given to save short‐term memorisation of details of derived equations and are given without any explanation or definition of symbols; the student is expected to know the meanings and usage.



𝜖𝑜 = 8.85𝑋10−12𝐹/𝑚 , 𝜇𝑜 = 4𝜋𝑋10−7 𝐻/𝑚


ω = βc

𝑆 =|𝑉𝑚𝑎𝑥|

|𝑉𝑚𝑖𝑛|=

1 + |Γ|

1 − |Γ|


Antenna and Radar formula Hertzian monopole

Half –wave dipole


For Transmission line

Distortionless line

,

Open-circuited line


Short-circuited line

,

Documents

ENG018 UNIVERSITY OF BOLTON SCHOOL OF … · engineering electromagnetism module no: eee6002 date: 17 january 2018 time: 2.00 ... module no. eee6002 𝜖 =8.85𝑋10−12𝐹/𝑚