22-Elec-A7 Electromagnetics, May 2013: worked solutions

Paper format. National Examinations, May 2013 — 07-Elec-A7, Electromagnetics. Three hours, closed book; one of two approved calculators (Casio or Sharp) permitted. Eight questions, all of equal value; any five constitute a complete paper and only the first five presented are marked. All eight are solved here, since the set is a study resource. Aids printed on the cover page: ε₀ = 8.85 × 10⁻¹² F/m and μ₀ = 4π × 10⁻⁷ H/m; Question 2 additionally supplies the quarter-wave relation.

Reference texts (22-Elec-A7 Electromagnetics).

D. M. Pozar, Microwave Engineering, 4th ed. — transmission lines, matching, waveguides.
M. N. O. Sadiku, Elements of Electromagnetics, 7th ed. — plane waves, guided waves, radiation.
W. H. Hayt and J. A. Buck, Engineering Electromagnetics, 9th ed. — field theory and transients on lines.
C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. — short elements, image theory.
F. T. Ulaby and U. Ravaioli, Fundamentals of Applied Electromagnetics, 8th ed. — oblique incidence, surface currents.
S. J. Chapman, Electric Machinery Fundamentals, 5th ed. — rotating-loop induction and torque (Question 3).

Conventions used throughout. The paper itself quotes propagation velocities as $3\times10^{8}\ \text{m/s}$, so free space is taken as $c=3.00\times10^{8}\ \text{m/s}$ and the intrinsic impedance as $\eta_0=\mu_0 c=120\pi=376.99\ \Omega$. Lines are treated as lossless, and "rms" is stated explicitly wherever the exam asks for it.

22-Elec-A7 Electromagnetics: May 2013