(SEM IV) THEORY EXAMINATION 2017-18 ELECTROMAGNETIC FIELD THEORY

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​∫V​μH2dv

(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.