university of bolton school of engineering … · wires with identical radius of 8.5 mm and spacing...

TW28

UNIVERSITY OF BOLTON

SCHOOL OF ENGINEERING

BEng(Hons) Electrical and Electronics

Engineering

SEMESTER 1 EXAMINATION 2016/2017

ENGINEERING ELECTROMAGNETISM

MODULE NO: EEE6002

Date: Wednesday 11 January 2017 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).

of 13 School of Engineering BEng Electrical and Electronic Semester 1 Examination 2016/2017 Engineering Electromagnetism Module Number: EEE6002

Q1. (a) A laser beam traveling through fog was observed to have an intensity of 1 (µW/m2) at a distance of 2 m from the laser gun and an intensity of 0.2 (µW/m2) at a distance of 3 m. Given that the intensity of an electromagnetic wave is proportional to the square of its electric-field amplitude, find (i) The electric field traveling wave

[3 marks] (ii) The laser intensity traveling wave

[3 marks] (iii) The attenuation constant α of fog.

[4 marks]

(b) The vector field 𝐻 = 𝑥𝑦2𝑧𝒂𝑥 + 𝑥2𝑦𝑧𝒂𝒚 + 𝑥𝑦𝑧2𝒂𝒛

(i) Express the above vector field in cylindrical and spherical coordinates

[8 marks] (ii) In both cylindrical and spherical coordinates, determine H at (3, -4, 5).

[7 marks]

[Total 25 marks]

Please turn the page


Q2. (a) A voltage source given by Vs(t) = 25 cos(2π × 103 t −30o) (V) is connected to a series RC load . If R = 1 MΩ and C = 200 pF, (i) Obtain an expression for Vc(t)

[5 marks] (ii) Find the voltage across the capacitor.

[4 marks] (b) The acceleration of a particle is given by a = 2.4 az m/s2. The initial position of the particle is r = (0, 0, 0), while its initial velocity is v = -2ax + 5az m/s. (i) Find the position of the particle at time t = 1.

[9 marks] (ii) Determine the velocity of the particle as a function of t.

[7 marks]



Q3. (a) The potential difference between two points in volts is numerically equal to the work in joules per coulomb necessary to move a coulomb of charge between the two points. A two-wire airline (single-phase system) has conductors of straight cylindrical bare wires with identical radius of 8.5 mm and spacing of 1.85 m. (i) What is the charge on each conductor?

[2 marks]

(ii) What is the voltage drop between the two conductor ? [4 marks]

(iii) Find the capacitance of a two-wire airline (single-phase system). Then calculate the capacitance of each wire to ground.

[4 marks] (b) The finite sheet 0≤ x≤ 1, 0 ≤ y < 1 on the z = 0 plane has a charge density 𝜌𝑠= xy(x2 + y2 + 25)3/2 nC/m2. Find: (i) The total charge on the sheet.

[6 marks]

(ii) The electric field at (0, 0, 5). [6 marks]

(iii) The force experienced by a -1 mC charge located at (0, 0, 5)

[3 marks]



Q4.

(a) A manufacturer produces a ferrite material with µ= 750 µo, ε=5εo, and

σ = 10-6 S/m at 10 MHz. (i) Would you classify the material as lossless, lossy or conducting ?

[3 marks] (ii) Calculate β and l

[5 marks] (iii) Determine the phase difference between two points separated by 2 m.

[3 marks] (iv) Find the intrinsic impedance.

[2 marks] (b) A signal in air (z ≥0) with the electric field component E= 10 sin (ωt + 3z) ax V/m Hit normally the ocean surface at z=0 as in Figure Q4. Assuming that the ocean surface is smooth and that ε= 80 εo, µ=µo, σ =4 mhos/m in ocean, determine (i) ω

[2 marks] (ii) The wavelength of the signal in air

[2 marks] (iii) The loss tangent and intrinsic impedance of the ocean

[4 marks] (iv) The Reflected E field

[4 marks]


Figure Q4.

Please turn the page Q5.

(a) A lossless transmission line operating at 4.5 GHz has L = 2.4 µH/m and Zo =

85 Ω. Calculate the phase constant β and the phase velocity u.

[5 marks]

(b) A 50-Ω coaxial cable feeds a 75 + j20 Ω dipole antenna. Find Γ and s.

[5 marks]

(c) A 60 Ω lossless line is connected to a source with Vg = 10<0o Vrms and Zg = 50 - j40 Ω and terminated with a load j40 Ω. If the line is 100 m long and β = 0.25 rad/m, calculate Zin and V at

(i) The sending end

[5 marks] (ii) The receiving end

[5 marks] (iii) 4 m from the load

[5 marks]

[Total 25 marks]



Q6.

(a) In a bistatic radar system of Figure Q6, the ground-based antennas are

separated by 4 km and the 2.4 m2 target is at a height of 3 km. The system

operates at 5 GHz. For Gdt of 36 dB and Gdr of 20 dB, determine the minimum

necessary radiated power to obtain a return power of 8 X 10-12 W.

[10 marks]

Figure Q6. A bistatic radar system

(b) A half-wave dipole with Zin =73 + j 42.5 Ω fed by a 50 Ω transmission line, calculate the reflection coefficient and the standing wave ratio.

[5 marks] (c) A 1-m-long car radio antenna operates in the AM frequency of 1.5 MHz. How much current is required to transmit 4 W of power?

[10 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


Antenna and Radar formula Hertzian monopole

For Tranmission line

,

university of bolton school of engineering … · wires with identical radius of 8.5 mm and spacing...

Documents