Examius
🇮🇳 UPSC ESE E&T · flashcards
UPSC ESE E&T Electromagnetics Flashcards
55 question-and-answer cards covering Electromagnetics as it is examined in UPSC ESE E&T. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Electromagnetics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
How do reluctances combine in series and parallel?
Series: S_eq = ΣSᵢ (same flux through each). Parallel: 1/S_eq = Σ(1/Sᵢ) (flux divides).
What is leakage flux and fringing in a magnetic circuit?
Leakage flux is flux that does not follow the intended core path (returns through surrounding medium). Fringing is the bulging/spreading of flux lines across an air gap, increasing effective gap area.
Define self-inductance L and give its defining relations.
L = NΦ/I = λ/I (flux linkage per unit current). The induced EMF is e = −L·di/dt. Unit: henry (H) = Wb/A = V·s/A.
Give the inductance of a long solenoid.
L = μN²A/l = μn²·(volume), where N is total turns, A cross-section area, l length, n = N/l.
Define mutual inductance M and the coupling coefficient k.
M = N₂Φ₂₁/I₁; induced EMF in coil 2 is e₂ = −M·di₁/dt. Coupling: M = k√(L₁L₂), with 0 ≤ k ≤ 1.
What is the energy stored in an inductor and the magnetic energy density?
W = ½LI². Energy density wₘ = ½μH² = B²/(2μ).
How do inductors (no mutual coupling) combine in series and parallel?
Series: L_eq = ΣLᵢ. Parallel: 1/L_eq = Σ(1/Lᵢ).
State all four of Maxwell's equations in differential form.
∇·D = ρv (Gauss-electric); ∇·B = 0 (Gauss-magnetic, no monopoles); ∇×E = −∂B/∂t (Faraday); ∇×H = J + ∂D/∂t (Ampere–Maxwell).
State Maxwell's equations in integral form.
∮D·dS = Q_enc; ∮B·dS = 0; ∮E·dl = −d/dt∫B·dS; ∮H·dl = I + d/dt∫D·dS.
List the three constitutive relations linking the field vectors in a medium.
D = εE, B = μH, and J = σE (Ohm's law in point form).
What is the physical meaning of ∇·B = 0?
Magnetic flux lines are continuous and form closed loops; isolated magnetic monopoles do not exist, so net magnetic flux through any closed surface is zero.
Give the wave (Helmholtz) equation for E derived from Maxwell's equations in free space.
∇²E = με ∂²E/∂t² (and similarly for H). Wave speed v = 1/√(με); in vacuum c = 1/√(μ₀ε₀) ≈ 3×10⁸ m/s.
Define the intrinsic impedance of a medium and give its free-space value.
η = √(μ/ε) = E/H (ratio of field magnitudes for a plane wave). In free space η₀ = √(μ₀/ε₀) ≈ 377 Ω (120π Ω).
Define skin depth δ and give its formula for a good conductor.
δ = 1/α = √(2/(ωμσ)) — the depth at which the wave amplitude falls to 1/e (~37%). Fields concentrate near the conductor surface as frequency rises.
What is the Poynting vector and what does it represent?
P = E × H (W/m²); it gives the instantaneous direction and magnitude of electromagnetic power flow per unit area. Time-average: P_avg = ½Re(E × H*).
Define the characteristic impedance Z₀ of a lossless transmission line.
Z₀ = √(L/C), where L and C are per-unit-length inductance and capacitance. It is real for a lossless line.
Define the reflection coefficient Γ at a transmission-line load.
Γ = (Z_L − Z₀)/(Z_L + Z₀). Γ = 0 for a matched load (Z_L = Z₀), −1 for a short, +1 for an open circuit.
Define VSWR and relate it to the reflection coefficient.
VSWR = V_max/V_min = (1 + |Γ|)/(1 − |Γ|). It ranges from 1 (matched, no reflection) to ∞ (total reflection).
Give the input impedance of a lossless line of length l terminated in Z_L.
Z_in = Z₀ · (Z_L + jZ₀tanβl)/(Z₀ + jZ_L tanβl), where β = 2π/λ is the phase constant.
What is a quarter-wave transformer and its impedance-matching condition?
A λ/4 line section used to match a load to a line; it requires Z₀(section) = √(Z_in·Z_L). A λ/4 line inverts impedance: Z_in = Z₀²/Z_L.
Why can't a hollow rectangular waveguide support the TEM mode, and what modes does it support?
TEM needs two conductors; a single hollow conductor cannot support it. Waveguides support TE (Ez=0) and TM (Hz=0) modes only, each with a cutoff frequency.
Give the cutoff frequency of a rectangular waveguide for mode TE_mn / TM_mn (dimensions a×b).
f_c = (c/2)·√((m/a)² + (n/b)²). The dominant mode is TE₁₀ with f_c = c/(2a).
Define phase velocity and group velocity in a waveguide and their relation.
v_p = c/√(1−(f_c/f)²) > c; v_g = c·√(1−(f_c/f)²) < c. Their product v_p·v_g = c². Energy travels at v_g.
What happens to a signal below the cutoff frequency in a waveguide?
It is evanescent (attenuated/non-propagating) — the propagation constant becomes purely real (attenuating), so the mode decays exponentially and no power is transmitted.
What this deck covers
The Electromagnetics deck follows the UPSC ESE E&T Electromagnetics syllabus — 3 chapters and 12 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 18.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 109 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Electromagnetics flashcards FAQ
How many Electromagnetics flashcards are in this UPSC ESE E&T deck?
55 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these UPSC ESE E&T flashcards free?
Yes. The preview here is free to read with no signup, and the full 55-card deck is free inside the Examius app.
What do the Electromagnetics cards cover?
They follow the UPSC ESE E&T Electromagnetics syllabus — 3 chapters and 12 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.