Examius
🇮🇳 UPSC ESE E&T · subject
UPSC ESE E&T Electromagnetics Syllabus
The Electromagnetics syllabus for UPSC ESE E&T in full: 3 chapters and 12 topics, every one listed below, plus 55 Electromagnetics flashcards with answers.
Electromagnetics syllabus: all 3 chapters
Expand any chapter to see its topics and sub-topics.
-
Electrostatics
4 topics- Coulomb's Law
- Gauss's Law
- Electric Potential
- Capacitance
-
Magnetostatics
4 topics- Biot-Savart Law
- Ampere's Law
- Magnetic Circuits
- Inductance
-
Electromagnetic Waves
4 topics- Maxwell's Equations
- Wave Propagation
- Transmission Lines
- Waveguides
UPSC ESE E&T Electromagnetics flashcards — 55 questions with answers
State Coulomb's Law in vector form for the force on charge q1 due to q2.
F = (1/4πε₀) · (q1·q2 / r²) · r̂, where r̂ is the unit vector from q2 to q1. Like charges repel, unlike attract, along the line joining them.
What is the value of the Coulomb constant 1/(4πε₀) and the permittivity of free space ε₀?
1/(4πε₀) ≈ 9 × 10⁹ N·m²/C²; ε₀ ≈ 8.854 × 10⁻¹² F/m (C²/N·m²).
How does Coulomb force change in a dielectric medium of relative permittivity εr?
The force is reduced by a factor εr: F_medium = F_vacuum / εr, because ε = ε₀εr replaces ε₀ in the denominator.
Define electric field intensity E and give its relation to Coulomb force.
E is force per unit positive test charge: E = F/q (units V/m or N/C). For a point charge Q: E = Q/(4πε₀r²) directed radially.
State Gauss's Law in integral form and what it physically means.
∮ D·dS = Q_enclosed (or ∮ E·dS = Q_enc/ε₀). The total electric flux through a closed surface equals the net charge enclosed, independent of charge distribution outside.
Give Gauss's Law in differential (point) form.
∇·D = ρv (divergence of D equals volume charge density), equivalently ∇·E = ρv/ε₀.
Using Gauss's law, what is E for an infinite line charge of linear density ρL?
E = ρL / (2πε₀ρ), directed radially, where ρ is the perpendicular distance from the line.
Using Gauss's law, what is E for an infinite sheet of surface charge density ρs?
E = ρs / (2ε₀), directed normal to the sheet, magnitude independent of distance from the sheet.
What is the electric field inside and outside a uniformly charged conducting sphere (charge Q, radius a)?
Inside (r<a): E = 0. Outside (r>a): E = Q/(4πε₀r²), behaving as if all charge were at the center.
Define electric potential V at a point and state its unit.
V is the work done per unit positive charge to bring it from infinity (reference) to that point: V = W/q. Unit: volt (V) = J/C.
What is the electric potential due to a point charge Q at distance r?
V = Q / (4πε₀r), a scalar that is positive for positive Q and taken as zero at infinity.
State the relation between electric field E and potential V.
E = −∇V (the field is the negative gradient of potential). Conversely V = −∫E·dl. E points from high to low potential.
What is the potential energy of a system of two point charges q1 and q2 separated by r?
W = q1·q2 / (4πε₀r). It is the work needed to assemble the configuration from infinity.
Define an equipotential surface and state its relation to field lines.
A surface on which V is constant; no work is done moving a charge along it. Electric field lines are always perpendicular to equipotential surfaces.
Define capacitance and give its unit and defining formula.
Capacitance C is the charge stored per unit potential difference: C = Q/V. Unit: farad (F) = C/V.
Give the capacitance of a parallel-plate capacitor.
C = εA/d = ε₀εr·A/d, where A is plate area, d is separation, and εr the dielectric constant.
What is the energy stored in a capacitor?
W = ½CV² = ½QV = Q²/(2C). Energy density in the field is wₑ = ½εE².
How do capacitors combine in series and in parallel?
Series: 1/C_eq = Σ(1/Cᵢ) (less than smallest). Parallel: C_eq = ΣCᵢ (sum).
Give the capacitance of a coaxial cable (inner radius a, outer radius b, length L).
C = 2πεL / ln(b/a).
State the Biot–Savart Law for the magnetic field of a current element.
dH = (I dl × r̂) / (4πr²), or dB = (μ₀ I dl × r̂)/(4πr²). It gives the field contribution of a differential current element.
Show the other 35 Electromagnetics flashcards
Using Biot–Savart, what is B at the center of a circular loop of radius a carrying current I?
B = μ₀I / (2a), directed along the axis (perpendicular to the loop plane).
What is the magnetic field at a perpendicular distance ρ from a long straight wire carrying current I?
H = I/(2πρ), so B = μ₀I/(2πρ), with field lines forming concentric circles (right-hand rule).
What is the magnetic field on the axis of a circular loop (radius a) at distance z from center?
B = μ₀ I a² / [2(a² + z²)^{3/2}], directed along the axis.
State Ampere's Circuital Law in integral form.
∮ H·dl = I_enclosed. The line integral of H around a closed path equals the net current passing through the path.
Give Ampere's Law in differential (point) form (magnetostatics).
∇ × H = J (curl of H equals conduction current density). For statics there is no displacement-current term.
Using Ampere's law, what is the field inside a long solenoid with n turns per metre carrying current I?
B = μ₀nI inside (uniform, axial); B ≈ 0 outside. n = N/L.
Using Ampere's law, what is B inside a toroid with N turns carrying current I at mean radius r?
B = μ₀NI / (2πr); the field is confined within the toroid core.
Why did Maxwell add the displacement current term to Ampere's law?
To make it consistent with charge conservation for time-varying fields; without it, ∇·J ≠ 0 during capacitor charging. Term: J_d = ∂D/∂t.
Define magnetomotive force (MMF) in a magnetic circuit and its unit.
MMF = N·I (number of turns times current), the magnetic analogue of EMF that drives flux. Unit: ampere-turns (At).
Define reluctance and give its formula.
Reluctance S = l/(μA), the opposition to magnetic flux (analogous to resistance). Unit: At/Wb. Flux Φ = MMF/S (Hopkinson's law).
State the magnetic-circuit analogy with electric circuits (Ohm's law form).
Φ = MMF/S, analogous to I = V/R. MMF↔EMF, Φ↔current, reluctance↔resistance, permeance↔conductance.
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.
UPSC ESE E&T Electromagnetics FAQ
What is in the UPSC ESE E&T Electromagnetics syllabus?
UPSC ESE E&T Electromagnetics is split into 3 chapters: Electrostatics, Magnetostatics and Electromagnetic Waves. Together they contain 12 topics.
How many chapters are in UPSC ESE E&T Electromagnetics?
3 chapters, containing 12 topics. The largest chapter is Electrostatics, with 4 topics.
Are there flashcards for UPSC ESE E&T Electromagnetics?
Yes — a 55-card Electromagnetics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.