UPSC ESE E&T Electromagnetics Syllabus

Electromagnetics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electromagnetics in UPSC ESE E&T, not a summary of it.

1. 1

   Electrostatics

   4 topics

   • Coulomb's Law
   • Gauss's Law
   • Electric Potential
   • Capacitance
2. 2

   Magnetostatics

   4 topics

   • Biot-Savart Law
   • Ampere's Law
   • Magnetic Circuits
   • Inductance
3. 3

   Electromagnetic Waves

   4 topics

   • Maxwell's Equations
   • Wave Propagation
   • Transmission Lines
   • Waveguides

Electromagnetics flashcards for UPSC ESE E&T

20 of 55 cards from the Electromagnetics deck — real questions with worked answers.

1. 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.

2. 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).

3. 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.

4. 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.

5. 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.

6. Give Gauss's Law in differential (point) form.

   ∇·D = ρv (divergence of D equals volume charge density), equivalently ∇·E = ρv/ε₀.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. What is the energy stored in a capacitor?

    W = ½CV² = ½QV = Q²/(2C). Energy density in the field is wₑ = ½εE².

18. How do capacitors combine in series and in parallel?

    Series: 1/C_eq = Σ(1/Cᵢ) (less than smallest). Parallel: C_eq = ΣCᵢ (sum).

19. Give the capacitance of a coaxial cable (inner radius a, outer radius b, length L).

    C = 2πεL / ln(b/a).

20. 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.

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