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22-Elec-A7 Electromagnetics: December 2016

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Pulse Train on a Mismatched Transmission Line
  2. Question 2 Parallel Open- and Short-Circuited Line Sections
  3. Question 3 Characteristic Impedance of a Two-Layer Coaxial Line
  4. Question 4 Polarisation of Two Crossed Plane Waves
  5. Question 5 Rotating Direction-Finding Loop in the Earth’s Field
  6. Question 6 Two Lowest Resonances of a Rectangular Cavity
  7. Question 7 Torque on a Current Loop in a Uniform Field
  8. Question 8 Power Density Radiated by a Short Horizontal Element

Start with Question 1 →



Paper format. 07-Elec-A7 Electromagnetics, National Examinations, December 2016 — 3 hours, closed book (one of two approved Casio or Sharp calculators). Eight questions, all of equal value, and the paper states that any five questions constitute a complete paper. All eight are solved here, because this set is a study resource rather than a timed sitting. Page-1 aids as printed: ε0 = 8.85 × 10−12 F/m and μ0 = 4π × 10−7 H/m.

Reference texts for 22-Elec-A7 Electromagnetics. D. M. Pozar, Microwave Engineering, 4th ed. (transmission lines, stubs, waveguides and cavities); M. N. O. Sadiku, Elements of Electromagnetics, 7th ed. (Maxwell’s equations, plane waves, magnetostatic forces); W. H. Hayt & J. A. Buck, Engineering Electromagnetics, 9th ed. (transmission-line transients and polarisation); F. T. Ulaby & U. Ravaioli, Fundamentals of Applied Electromagnetics, 7th ed.; C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. (short elements and radiated power density).

Constants used throughout. The paper pins its own numbers: Questions 1 and 2 both state a propagation velocity of 3 × 108 m/s and Question 1 uses a 377 Ω line, so this solution works with c = 3.00 × 108 m/s and η0 = 377 Ω and reserves the printed page-1 aids for the per-unit-length quantities of Question 3. Using 2.998 × 108 m/s instead shifts every answer by less than 0.1 % and changes no conclusion.

Question numbering. The eighth question (the short horizontal current element) carries no printed number on page 3 of the original — it follows Question 7 as an unnumbered block. It is numbered Question 8 here, which is consistent with the paper’s own statement that the exam holds more than five questions of equal value.