UNIVERSITY OF BOLTON WESTERN INTERNATIONAL COLLEGE FZE B.ENG (HONS) ELECTRICAL & ELECTRONIC ENGINEERING SEMESTER ONE EXAMINATION 2016/2017

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1 UNIVERSITY OF BOLTON WESTERN INTERNATIONAL COLLEGE FZE B.ENG (HONS) ELECTRICAL & ELECTRONIC ENGINEERING SEMESTER ONE EXAMINATION 2016/2017 ENGINEERING ELECTROMAGNETISM MODULE NO: EEE6002 Date: Tuesday 10 January 2017 Time: INSTRUCTIONS TO CANDIDATES: There are 5 questions on this paper. Answer any 4 questions All questions carry equal marks. Formula sheets provided

2 Page 2 of 6 Q1. a) Transform the vector A = (3x +2y) ax + (x + z) ay + (3y 2 +5z) az to cylindrical and spherical coordinates for the point s ( 4, 8, -3). Also evaluate the given vector A at the point s in the cylindrical systems. b) For the cylindrical system in figure 1, calculate (15 marks) i) the distance AD ii) the surface area ABCD iii) volume ABDCFO Figure 1 Please turn the page

3 Page 3 of 6 Q2. a) For the Electric Flux Density D = (xy 2 +x 2 y) ax + xy ay + xyz az C/m 2, obtain i) The volume charge density at (2, 1, 4) ii) The flux through the cube defined by 0 x 2, 0, y 2, 0 z 2 b) Given that E = (3x 2 + y) ax + x ay kv/m, find the work done in moving a 3µC charge from (0, 5, 0) to (2, - 1, 0) by taking the path i) (0, 5, 0), (2, 5, 0), (2, -1, 0) ii) y = 6 + 4x c) Current-carrying components in high-voltage power equipment must be cooled to carry away the heat caused by ohmic losses. A means of pumping is based on the force transmitted to the cooling fluid by charges in an electric field. The region between the electrodes contains a uniform charge p0, which is generated at the left electrode and collected at the right electrode. Calculate the pressure of the pump if ρo = 17 mc/m 3 and Vo = 19 kv. (12 marks) Please turn the page

4 Page 4 of 6 Q3. a) In a certain conducting region H = yz (x 2 + y 2 ) ax - y 2 xz ay + 4x 2 y 2 az A/m, evaluate J at (5, 2, -3) and find the current passing through x = -1, 0 < y, z < 2 (8 marks) b) A current distribution gives rise to the vector magnetic potential A = x 2 y ax + y 2 x ay - 4xyz az Wb/m. Evaluate B at (- 1, 2, 5) and the flux through the surface defined by z = 1, 0 x 1, - 1 y 4 (9 marks) c) A toroid of circular cross section whose centre is at the origin and axis the same as the z-axis has 1000 turns with ρo = 10 cm, a = 1 cm. If the toroid carries a 100-mA current, find ΙHΙ at (3 c m, - 4 cm, 0) and at (6 cm, 9 cm, 0) (8 marks) Q4. a) In a nonmagnetic medium E = 4sin (2π x 10 7 t 0.8x) az V/m, obtain the time-average power carried by the wave, the total power crossing 100 cm 2 of plane 2x + y = 5, its εr and η (10 marks) Q4 continued over the page

5 Page 5 of 6 Q4 continued b) A plane wave propagating through a medium with εr = 8, μr = 2 has E = 0.5 e -z/3 sin (10 8 t - βz) ax V/m. Determine i) β ii) The loss tangent iii) Wave impedance iv) Wave velocity v) H field Please turn the page

6 Page 6 of 6 Q5. a) A certain transmission line operating at ω= 10 6 rad/s has α = 8 db/m, β = 1 rad/m, and Zo = 60 + j40ω, and is 2m long. If the line is connected to a source of 10 0ᵒ V, Zg = 40Ω and terminated by a load of 20 + j50 Ω, determine i) The input impedance ii) The sending-end current iii) The current at the middle of the line (6 marks) b) A 30-m-long lossless transmission line with Zo = 50Ω operating at 2 MHz is terminated with a load ZL = 60 + j40ω. If u = 0.6c on the line, find i) The reflection coefficient Γ ii) The standing wave ratio s iii) The input impedance END OF QUESTIONS

UNIVERSITY OF BOLTON WESTERN INTERNATIONAL COLLEGE FZE B.ENG(HONS) ELECTRICAL & ELECTRONIC ENGINEERING SEMESTER ONE EXAMINATION 2015/2016

OCD60 UNIVERSITY OF BOLTON WESTERN INTERNATIONAL COLLEGE FZE B.ENG(HONS) ELECTRICAL & ELECTRONIC ENGINEERING SEMESTER ONE EXAMINATION 2015/2016 ENGINEERING ELECTROMAGNETISM MODULE NO: EEE6002 Date: Tuesday