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22-Elec-A7 Electromagnetics: Undated paper

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

  1. Question 1 Oblique incidence at a free-space / silica interface
  2. Question 2 Standing-wave pattern on a mismatched 50 Ω line
  3. Question 3 Step transient on a doubly mismatched 75 Ω line
  4. Question 4 A road tunnel as a rectangular waveguide
  5. Question 5 Field and potential of a radially graded charge cloud
  6. Question 6 Resistance, current density and dissipation in a cylindrical resistor
  7. Question 7 Line charge and point charge by Gauss' law and superposition
  8. Question 8 Ampère's law for a wire with graded current density
  9. Question 9 On-axis field and self-flux of a circular current loop
  10. Question 10 Radiation resistance, efficiency and far field of a short vertical antenna

Start with Question 1 →

Paper format. National Exams, 16-Elec-A7 Electromagnetics (the archive copy carries no date on its cover; every page header reads “16-ELEC-A7 Electromagnetics / May 2019”). Three hours, closed book, one double-sided 8.5” × 11” aid sheet and an approved Casio or Sharp calculator permitted. Ten questions, each of equal value, of which five constitute a complete exam paper — the first five completed answers are the ones marked. A full marking scheme is printed on page 8. All ten questions are worked below, because the set is a study resource rather than a timed attempt.

Reference texts. The following are the standard works for this subject and are cited by chapter throughout: F. T. Ulaby and U. Ravaioli, Fundamentals of Applied Electromagnetics; M. N. O. Sadiku, Elements of Electromagnetics; W. H. Hayt and J. A. Buck, Engineering Electromagnetics; D. M. Pozar, Microwave Engineering; C. A. Balanis, Antenna Theory: Analysis and Design.

Where the paper itself omits data or contradicts its own marking scheme, the gap is flagged in a check callout rather than filled silently.

All arithmetic below;s own numbers imply: $c = 3\times10^{8}$ m/s (Q3 gives 3 m in 20 ns, exactly $c/2$, and Q2 gives $2\times10^{8}$ m/s), $\eta_0 = 120\pi = 376.99\ Ω$, $\mu_0 = 4\pi\times10^{-7}$ H/m and $\epsilon_0 = 8.854\times10^{-12}$ F/m.