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 12 January 2016 Time: 10.00-12.00 INSTRUCTIONS TO CANDIDATES: There are 5 questions on this paper. Answer any 4 questions All questions carry equal marks. Formula sheets provided
Page 2 of 6 Q1 a) Express the vector field H = xy 2 z ax + x 2 yz ay + xyz 2 az in cylindrical coordinate and determine H at (3, -4, 5) b) Let A = 2xy ax + xz ay y az. Evaluate A dv over a cylindrical region ρ 3, 0 z 5 c) Evaluate the divergence and curl for the given vector F = ρz 2 cosφ aρ + zsin 2 Φ az 5 marks) d) If F = x 2 ax + y 2 ay +(z 2 1) az, find s F.dS, where S is defined by ρ = 2, 0 z 2, 0 Φ 2π e) Calculate the total outward flux of vector F = ρ 2 sin Φ aρ + z cos Φ aφ + ρz az Q2 a) The finite sheet 0 x 1, 0 y 1 on he z = 0 plane has a charge density ρs = xy(x 2 + y 2 + 25) 3/2 nc/m 2. Find (i) The total charge on the sheet (ii) The total electric field at (0, 0, 5) (iii) The force experienced by a -1mC charge located at (0,0,5) (7 marks) Q2 continued over the page
Page 3 of 6 Q2 continued b) Evaluate the electric flux density D and the volume charge density ρv for E E = xy ax + x 2 ay c) A parallel-plate capacitor with plate separation of 2 mm has a 1KV voltage applied to its plates. If the space between its plates is filled with polystyrene (εr = 2.55) find E, P and ρps d) Conducting spherical shells with radii a = 10 cm and b = 30 cm are maintained at a potential difference of 100 V such that V(r = b) = 0 and V(r = a) = 100 V. Determine V and E in the region between the shells. If εr = 2.5 in the region, determine the total charge induced on the shells and the capacitance of the capacitor. (8 marks) Q3 a) A thin ring of radius 5 cm is placed on plane z = 1 cm so that its center is at (0,0,1 cm). If the ring carries 50 ma along aφ, evaluate H at (0, 0, - l cm) and at (0, 0, 10 cm) b) A toroid of circular cross section whose center 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 100mA current, find ІHІ at (3 cm, -4 cm, 0) and at (6 cm, 9 cm, 0). Q3 continued over the page
Page 4 of 6 Q3 continued c) For a current distribution in free space, A = (2x 2 y + yz)ax + (xy 2 - xz 3 )ay - (6xyz 2x 2 y 2 )az Wb/m (i) Calculate B. (ii) Find the magnetic flux through a loop described by x = 1, 0 < y, z < 2 (iii) Show that V A = 0 and V B = 0. (7 marks) d) A rectangular coil of area 10 cm 2 carrying current of 50A lies on plane 2x + 6y - 3z = 7 such that the magnetic moment of the coil is directed away from the origin. Calculate its magnetic moment. If the coil is surrounded by a uniform field of 0.6ax + 0.4ay +0.5az Wb/m 2 (i) Find the torque on the coil. (ii) Show that the torque on the coil is maximum if placed on plane 2x 8y + 4z = 84. Calculate the value of the maximum torque. (8 marks) Please turn the page
Page 5 of 6 Q4 a) Consider the loop of Figure 1. If B = 0.5az Wb/m 2, R = 20Ω, l = 10 cm, and the rod is moving with a constant velocity of 8ax m/s, find (i) The induced emf in the rod (ii) The current through the resistor (iii) The motional force on the rod (iv) The power dissipated by the resistor. Figure 1 b) A medium is characterized by σ = 0, μ = 2μ0 and ε = 5ε0. If H = 2cos (ωt - 3y) az A/m, calculate ω and E. c) 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
Page 6 of 6 Q5 a) A telephone line has R = 30Ω/km, L = 100 mh/km, G = 0, and C = 20 μf/km. At f = 1kHz, obtain: (i) The characteristic impedance of the line (ii) The propagation constant (iii) The phase velocity b) A 70Ω lossless line has s = 1.6 and θγ = 300. If the line is 0.6λ long, calculate (i) The reflection coefficient Γ (ii) Load impedance ZL (iii) The input impedance Zin (iv) The distance of the first minimum voltage from the load c) Antenna with impedance 40 + j30 Ω is to be matched to a 100Ω lossless line with a shorted stub. Determine (i) The required stub admittance (ii) The distance between the stub and the antenna (iii) The stub length (iv) The standing wave ratio on each ratio of the system END OF QUESTIONS