THEORY EXAMINATION (SEM–IV) 2016-17 ELECTROMAGNETIC FIELD THEORY

Subject: Electromagnetic Field Theory (EC402MTU)

Exam Type: Theory
Semester: IV (4th Semester)
Session: 2016–17
Time: 3 Hours
Maximum Marks: 100

Section A – Short Answer Questions (10 × 2 = 20 Marks)

This section tests fundamental electromagnetic principles, coordinate transformations, and vector calculus.

Topics Covered:

Physical Significance of Divergence and Curl — interpretation in electric and magnetic field analysis.

Inductance per Unit Length of Coaxial Conductors — derivation based on magnetic flux linkage.

Vector Conversion — expressing B=10rr^+rcos⁡θθ^\mathbf{B} = \frac{10}{r} \hat{r} + r \cos \theta \hat{\theta}B=r10​r^+rcosθθ^ in cylindrical coordinates.

Transmission and Reflection Coefficients — basic definitions used in wave propagation.

Relation E=−∇V\mathbf{E} = -\nabla VE=−∇V — proving the link between electric field and scalar potential.

Coordinate Transformation — converting the point (1, 1, 6) from Cartesian to spherical coordinates.

Laplace’s Equation Verification — checking whether S=ρ2zcos⁡2ϕS = \rho^2 z \cos^2 \phiS=ρ2zcos2ϕ satisfies Laplace’s equation.

Displacement Current in Copper Wire — calculation using given current, conductivity, and frequency.

Stokes’ and Divergence Theorems — statements connecting surface and volume integrals.

Gauss’s Law and Maxwell’s Equation — derivation of Maxwell’s divergence form of electric flux density.

Section B – Descriptive / Numerical Questions (5 × 10 = 50 Marks)

This section focuses on field derivations, Maxwell’s equations, polarization, and boundary conditions.

Key Questions Include:

Poynting Theorem: Derivation and physical interpretation of power flow in electromagnetic fields.

Electric Flux Density Calculation: For D=5r24r^D = \frac{5r^2}{4} \hat{r}D=45r2​r^ in spherical coordinates, find the volume enclosed between r = 1 and r = 2.

Polarization:  Explanation of the phenomenon and types (linear, circular, and elliptical).

Magnetic Field Due to Infinite Conductor: Proof that H=I2πrH = \frac{I}{2\pi r}H=2πrI​ A/m using Ampere’s Law.

Boundary Conditions for Static Electric Fields: Tangential and normal conditions between two dielectrics.

Electric Field at a Point: Find EEE at P(1,1,1) due to four identical 3 nC charges located at corners of a square.

Maxwell’s Equations: State and explain for time-varying fields in differential and integral forms, with physical meaning.

Uniform Plane Wave in a Conductor:

Given H=0.1e−15zcos⁡(2π×108t−15z)i^H = 0.1 e^{-15z} \cos(2\pi × 10^8 t - 15z) \hat{i}H=0.1e−15zcos(2π×108t−15z)i^ A/m, find

Conductivity (σ)

Electric field (E)

Average power loss in a block of unit area and thickness t

Section C – Long Analytical Questions (2 × 15 = 30 Marks)

This section emphasizes wave equations, propagation constants, and reflection theory.

Questions Include:

Plane Wave Propagation:

Given E=2e−αzsin⁡(108t−βz)j^E = 2 e^{-\alpha z} \sin(10^8 t - \beta z) \hat{j}E=2e−αzsin(108t−βz)j^​ V/m,

For a medium with εr=1,μr=20,σ=3 S/m\varepsilon_r = 1, \mu_r = 20, \sigma = 3 \, S/mεr​=1,μr​=20,σ=3S/m,

Find α\alphaα, β\betaβ, and HHH.

Plane Wave in Lossy Dielectric (Conducting Medium):

Derive complete expressions for propagation constant (γ), attenuation constant (α), and phase constant (β).

Reflection of Plane Wave (Normal Incidence):

Derive expressions for reflection and transmission coefficients for electric (E) and magnetic (H) fields.

Discuss behavior for perfect dielectric and perfect conductor cases

Major Topics Covered

Vector calculus in electromagnetic theory (Divergence, Curl, Gradient)

Maxwell’s equations (static and time-varying)

Poynting theorem and energy flow

Polarization and boundary conditions

Wave propagation in free space and conductors

Reflection and transmission of EM waves

Plane wave parameters (α, β, γ) in lossy dielectrics

Purpose of the Paper

This exam evaluates understanding of electromagnetic field theory fundamentals, linking mathematics with physical field behavior.
It focuses on both analytical derivations (like Maxwell’s and Poynting’s theorems) and practical computations (like wave propagation and boundary behavior).