ENG018 SCHOOL OF ENGINEERING, SPORTS and SCIENCES BENG (HONS) ELECTRICAL & ELECTRONICS ENGINEERING 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 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 ρ v = 3RX10-4 (C/m 3 ), 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 3X10 5 (A/m 2 ). Find the voltage drop across the length of the wire if the wire material has a conductivity of 2X10 7 (S/m). [10 marks] Total 25 marks Question 2 a) A proton moving with a speed of 2X10 6 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
Page 3 of 13 Question 2 continued (i) Only one turn and (ii) 10 turns? [3 marks] [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 10 7 t +πz/15+π/6) (V/m). Determine: (i) The direction of wave propagation (ii) The wave frequency f (iii) Its wave length λ (iv) Its phase velocity up [2 marks] [4 marks] [2 marks] [2 marks] Question 3 continues over the page Please turn the page
Page 4 of 13 Question 3 continued 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 = Ia 2 A/m 2(a 2 +z 2 ) 3/2 [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 (10 8 t+βx) ay V/m (i) Find the direction of wave propagation (ii) Calculate β and the time it takes to travel a distance of l/2 [2 marks] [7 marks] Question 4 continues over the page Please turn the page
Page 5 of 13 Question 4 continued b) In Free space (z 0), a plane wave 2 with H=10cos(10 8 t-βz) ax ma/m Is incident normally on a lossless medium (ε = 2ε o, μ = 8μ o ) 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 Please turn the page
Page 6 of 13 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? b) Calculate the current that must be fed to the antenna. c) Find the average power radiated by the antenna. [5 marks] [10 marks] [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
Page 7 of 13 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.
Page 8 of 13
Page 9 of 13 ε o = 8.85X10 12 F/m, μ o = 4πX10 7 H/m
Page 10 of 13 ω = βc S = V max V min = 1 + Γ 1 Γ
Page 11 of 13 Antenna and Radar formula Hertzian monopole Half wave dipole
Page 12 of 13 For Transmission line Distortionless line, Open-circuited line
Page 13 of 13 Short-circuited line,