(SEM IV) THEORY EXAMINATION 2018-19 ELECTROMAGNETIC FIELD THEORY

SECTION–A — Short Fundamental Questions Covering the Entire EMFT Syllabus (14 Marks)

Section–A contains seven short questions, but each touches a fundamental concept of electromagnetic field theory. The paper begins with a coordinate-transformation question, asking the student to convert the point (−2,6,3)(-2,6,3)(−2,6,3) from Cartesian to spherical coordinates, ensuring they know how EM quantities transform between coordinate systems.

The next question tests vector calculus by asking for the gradient of a scalar field f(x,y,z)=x2+y+zf(x,y,z)=x^2+y+zf(x,y,z)=x2+y+z at point P(2,0,1)P(2,0,1)P(2,0,1). This ensures the student understands how spatial rate-of-change of fields is computed.

The third question asks to prove that the line integral of a static electric field around a closed path is zero, reinforcing the conservative nature of electrostatic fields and the condition ∇×E⃗=0\nabla \times \vec{E} = 0∇×E=0 in static conditions.

Another concept in this section is reflection and transmission coefficients, which describe how EM waves behave when they hit media boundaries—how much is reflected back and how much passes through.

The paper then asks for the relaxation time constant, an important parameter that tells how fast free charges decay inside a conductor when subjected to an electric field.

The sixth question asks for the equation of an electromagnetic wave, indicating that students must recall the standard time-harmonic form of electric or magnetic fields during propagation.

Finally, Ampher’s (Ampere’s) circuital law in static magnetic fields is asked, which defines the relationship between magnetic field intensity and enclosed current.
 

SECTION–B — Long Questions on Vector Transformation, Fields, EM Waves & Transmission Lines (21 Marks)

Section–B allows students to choose any three detailed questions. These questions test derivation skills, physical interpretation, and numerical calculations.

One question asks to transform the vector field A⃗=r a^r\vec{A} = r \, \hat{a}_rA=ra^r​ into Cartesian and cylindrical coordinates, testing deep understanding of basis vectors and coordinate relationships.

Another key question asks the student to evaluate the electric field intensity due to a finite uniformly charged wire, which requires integrating Coulomb’s law over a finite line distribution.

One of the numerical questions describes a plane electromagnetic wave propagating in the zzz-direction through a dielectric with relative permittivity ϵr=5\epsilon_r = 5ϵr​=5. The electric field is along xxx-direction with RMS value 0.1 V/m. Students must determine the direction and magnitude of the magnetic field, as well as find the frequency of the wave, using intrinsic impedance and wave propagation equations.

Another question asks for the magnetic field intensity due to a current-carrying wire, a direct application of the Biot–Savart law or Ampere’s law.

The final option asks for the general expression of voltage and current on a transmission line, requiring the derivation of the wave equations using distributed parameters R,L,G,CR, L, G, CR,L,G,C.
 

SECTION–C — Circulation of a Vector Field OR Cylindrical Coordinate Geometry (7 Marks)

Section–C offers two choices.
The first asks for the closed-path line integral (circulation) of the vector field

A⃗=ρcos⁡ϕ a^ρ+sin⁡ϕ a^ϕ\vec{A} = \rho \cos\phi\, \hat{a}_\rho + \sin\phi\, \hat{a}_\phiA=ρcosϕa^ρ​+sinϕa^ϕ​

around a circular path in the xyxyxy-plane. This requires evaluating a contour integral using cylindrical coordinate limits.

The alternate option asks students to explain a point coordinate and all possible surfaces in cylindrical coordinates, meaning they must clearly describe constant-ρ\rhoρ, constant-ϕ\phiϕ, and constant-zzz surfaces and their geometric significance.
 

SECTION–D — Electrostatics: Electric Potential OR Continuity Equation (7 Marks)

This section focuses on detailed electrostatic calculations.

The first option gives two point charges placed at (2, −1, 3) and (0, 4, −2), with charges −4 nC and 5 nC respectively. Students must compute the electric potential at point (1,0,1) assuming zero potential at infinity. The question then introduces a right-angle triangle and asks to find electric forces at the corners, requiring vector summation of Coulomb forces.

The alternate question asks for a full derivation of the continuity equation for electrostatics, which relates charge density and current density, and demonstrates conservation of charge.
 

SECTION–E — Maxwell’s Equations OR Magnetic Field of Infinite Current Wire (7 Marks)

In this section, the first option requires writing all four Maxwell’s equations in time-varying form and explaining their physical significance:

Gauss’s Law (Electric)

Gauss’s Law (Magnetic)

Faraday’s Law of Induction

Ampere–Maxwell Law

Students must explain what each equation physically governs—electric flux, absence of magnetic monopoles, induced EMF, and displacement current.

The alternate question asks to explain the Biot–Savart law and derive the magnetic field intensity due to an infinitely long straight conductor carrying current, which results in the classic circular magnetic field expression around a conductor.
 

 SECTION–F — Magnetic Field of a Solenoid OR Charged Particle Motion in Fields (7 Marks)

Section–F again provides two choices.

The first option asks for the magnetic field intensity inside a long solenoid of length LLL, with NNN turns carrying a current III. Since the solenoid is much longer than its radius, uniform field approximations apply.

The second option contains two subparts:
(i) A charged particle moves with a constant velocity of 4 m/s along the x-direction in a region where an electric field E⃗=20a^y\vec{E}=20 \hat{a}_yE=20a^y​ V/m is present. Students must determine the magnetic field B0B_0B0​ needed so that the velocity remains constant, using the condition that net Lorentz force is zero.
(ii) A short note on magnetic scalar and vector potentials, and Faraday’s law of electromagnetic induction, reinforcing conceptual depth.

SECTION–G — EM Wave Propagation in Lossy Medium OR Poynting Vector & Theorem (7 Marks)

The final section evaluates understanding of EM wave propagation and energy flow.

The first option requires deriving expressions for attenuation constant, propagation constant, and intrinsic impedance for an electromagnetic wave traveling through a lossy dielectric medium. Students must combine Maxwell’s equations with material parameters σ,ϵ,μ\sigma, \epsilon, \muσ,ϵ,μ.

The alternate option asks to explain the Poynting vector, derive the Poynting theorem, and interpret each term in the expression, which describes energy transport and power density of EM waves.
 

FINAL SUMMARY — Complete Descriptive Overview of the REC-402 Exam Paper

The Electromagnetic Field Theory exam paper thoroughly examines analytical and conceptual mastery across all major EM topics. Section–A touches essential concepts such as coordinate transformations, gradient calculations, conservative electric fields, and foundational Maxwell ideas. Section–B evaluates vector transformations, electric and magnetic field derivations, EM wave calculations, and transmission-line theory. Subsequent sections move deeper into circulation integrals, electrostatic potentials, continuity equations, Maxwell equations, Biot-Savart, solenoid fields, charged particle dynamics, wave propagation in lossy media, and energy flow via Poynting vector.