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22-Elec-A7 Electromagnetics: December 2019

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

  1. Question 1 Standing-wave measurement on a mismatched line
  2. Question 2 Oblique incidence at a lucite–air interface
  3. Question 3 Step transient on a doubly mismatched line
  4. Question 4 WR-90 rectangular waveguide at 10 GHz
  5. Question 5 Faraday induction in a circular loop
  6. Question 6 Parallel-plate capacitor and displacement current
  7. Question 7 Charged conducting sphere

Start with Question 1 →

Paper format. 16-Elec-A7 Electromagnetics, December 2019 — 3 hours, closed book, approved calculator only. Seven questions of equal value (20 marks each); the paper states that five completed questions constitute a complete paper. All seven are solved here, because the set is intended as a study resource.

Reference texts (22-Elec-A7 Electromagnetics). F. T. Ulaby & U. Ravaioli, Fundamentals of Applied Electromagnetics, 8th ed.; M. N. O. Sadiku, Elements of Electromagnetics, 7th ed.; W. H. Hayt & J. A. Buck, Engineering Electromagnetics, 9th ed.; D. M. Pozar, Microwave Engineering, 4th ed.; C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed.

Constants used throughout. $c = 3.00\times 10^{8}\ \text{m/s}$, $\varepsilon_0 = 8.854\times 10^{-12}\ \text{F/m}$, $\mu_0 = 4\pi\times 10^{-7}\ \text{H/m}$, $\eta_0 = 376.7\ \Omega$. Where a boundary case could turn on the choice between $c = 3\times 10^{8}$ and $c = 2.998\times 10^{8}$ m/s, both readings are stated.

Figure reading. In Figure 1(b) the maxima sit at z = 0, 1.5 and 3.0 m and the minima at z = 0.75 and 2.25 m, so the wavelength is 3.00 m. Three independent checks confirm that reading — the quarter-wave maximum-to-minimum spacing, the fact that the stated 3.75 m line is then exactly 1.25 wavelengths, and the fact that z = l then lands on a voltage minimum where the quarter-wave transformer result must give $Z_{\text{in}} = Z_0/S$.