ELECTROMAGNETIC FIELD THEORY – B.Tech (SEM-IV), REC-402
This is a 3-hour, 70-mark theoretical examination designed to assess a student’s understanding of vector calculus, electrostatics, magnetostatics, Maxwell’s equations, EM waves, transmission lines, polarization, and electromagnetic energy concepts.
The question paper is divided into three structured sections—short concepts (A), analytical/numerical problems (B), and detailed derivation-based questions (C).
SECTION A — Short Conceptual Questions (2 × 7 = 14 Marks)
This section contains 7 short questions meant to test basic electromagnetic theory fundamentals.
Topics include:
Poisson’s & Laplace equations Point form of Ohm’s law & Gauss’s law
Biot-Savart’s law Maxwell’s equations (differential + integral form)
Applications of Smith chart Converting point (5,3,6) to cylindrical coordinates
Faraday’s law
These questions test definitions, formulas, basic laws, and coordinate transformation skills.
SECTION B — Descriptive & Numerical Questions (3 × 7 = 21 Marks)
Students must attempt any 3 out of 5 questions.
Topics include:
(a) Capacitance of Back-to-Back Cones
Calculation of capacitance formed between two infinitesimally separated conical surfaces.
(b) Ampere’s Circuital Law + Numerical
Statement & derivation
Magnetic field intensity H on the axis of a circular coil
Coil: 50 m diameter, current = 28×10⁵ A
Observation point: 100 m from center
(c) Magnetostatic Energy
Proof that:
Wm=12∫VμH2 dvW_m = \frac{1}{2} \int_V \mu H^2 \, dvWm=21∫VμH2dv
(d) Magnetic Flux Density of Wire
B-field at distance d from an infinite straight current-carrying wire
Modification when wire is semi-infinite
(e) Uniform Plane Wave in Good Conductor
Given:
H=0.1e−15lcos(2π×108t−15z) i^H = 0.1 e^{-15l} \cos (2\pi \times 10^8 t - 15z) \, \hat{i}H=0.1e−15lcos(2π×108t−15z)i^
Tasks:
Calculate conductivity
Determine corresponding E-field component
Find average power loss through a conductor block
This section checks problem-solving, derivations, and EM wave parameter calculations.
SECTION C — Advanced Analytical Questions (7 × 1 each = 35 Marks)
Each question contains two alternatives (a or b).
Q3 – Maxwell’s Equations / Vector Calculus
State, explain, and give significance of Maxwell’s equations (time-varying case)
OR
Compute divergence of vector
- A=8x2ix^+5x2y2iy^+xyz3iz^A = 8x^2 \hat{i_x} + 5x^2y^2 \hat{i_y} + xyz^3 \hat{i_z}A=8x2ix^+5x2y2iy^+xyz3iz^
Find ∇ of scalar function x2yzx^2yzx2yz
Explain gradient of a scalar field
Q4 – Electrostatic Energy / Skin Effect
System of charges placed at specific coordinates — energy after each placement
OR
Explain skin effect, derive α and β for a conducting medium
Q5 – Transmission Lines / Poynting Theorem
Define propagation constant & characteristic impedance
Derive boundary conditions for E-field between two dielectrics
OR
State & derive Poynting theorem
Q6 – Line Parameters / Polarization
For a transmission line at 500 MHz:
Given Z₀ = 80 Ω, α = 0.04 Np/m, β = 1.5 rad/m
Compute parameters R, L, G, C
OR
Explain polarization and its major types (linear, circular, elliptical)
Q7 – Electric Potential / Wave Reflection
Find potential function & E-field between two concentric cylinders
Boundary: V = V₀ at r = a, V = 0 at r = b
OR
Explain normal incidence reflection of plane waves
Reflection & transmission coefficients for E (F) and H fields
This section checks core derivation skills, EM theory application, and conceptual depth.
OVERALL PURPOSE OF THE EXAM
The paper evaluates whether students can:
Use vector calculus operations (grad, div, curl)
Apply electrostatic & magnetostatic laws
Understand Maxwell’s equations fully
Analyze EM wave propagation in conductors & dielectrics
Calculate transmission-line parameters
Explain polarization, reflection, and boundary conditions
Derive power flow expressions (Poynting vector)
Solve numerical problems involving fields, potentials, and magnetic effects
It integrates theory, derivation, computation, and physical understanding, essential for RF, antenna, microwave, power, and communication engineering.
