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04-BS-9: December 2018

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

  1. Question 1 Capacitance of a Parallel-Plate Capacitor with Graded Permittivity
  2. Question 2 Inductance of a Solenoid with a Half-Inserted Magnetic Core
  3. Question 3 Magnetic Flux Density from a Finite-Thickness Sub-Surface Current Layer
  4. Question 4 Minimum Midpoint Charge to Cancel Mutual Repulsion of Two Point Charges
  5. Question 5 Motional EMF Induced in a Moving Rod Crossing a Vertical Field
  6. Question 6 Reflection and Refraction of a Plane Wave at an Air–Water Interface
  7. Question 7 Magnetic Flux Density at the Center of a Three-Quarter-Circle Current Loop
  8. Question 8 Velocity Selector — Magnetic Field Cancelling an Electric Deflecting Force

Start with Question 1 →

National Exams — December 2018 — 04-BS-9 Basic Electromagnetics. Three-hour, closed-book exam (approved Casio/Sharp calculator only). Aids given: $\varepsilon_0=8.85\times10^{-12}$ F/m, $\mu_0=4\pi\times10^{-7}$ H/m, $e=1.6\times10^{-19}$ C. Format: eight questions offered; any five constitute a complete paper and only the first five appearing in the answer book are marked. All eight are solved below for completeness.

Reference texts: Sadiku, Elements of Electromagnetics / Hayt & Buck, Engineering Electromagnetics — Gauss's law and boundary conditions for graded (spatially-varying) dielectrics, magnetic-circuit (reluctance) analysis of a partially-filled long solenoid, superposition of infinite current sheets and Ampère's law, Coulomb's-law equilibrium of collinear point charges, Faraday's law and motional EMF, the Biot–Savart law for arc segments, and the Lorentz force in a velocity selector; Young & Freedman, University Physics with Modern Physics — Snell's law and plane-wave reflection/refraction at a dielectric interface.