(SEM III) THEORY EXAMINATION 2023-24 ELECTROMAGNETIC FIELD THEORY

This question paper is designed for the Electromagnetic Field Theory (EMFT) course and evaluates the conceptual understanding, analytical skills, and problem-solving abilities of students. The paper is divided into three structured sections – A, B, and C, covering the entire syllabus including vector calculus, Maxwell’s equations, wave propagation, magnetic fields, electrostatics, magnetostatics, and transmission lines.

Section A contains short, concept-based questions aimed at testing fundamental definitions and physical significance of core EMFT topics.

Section B consists of medium-length analytical questions requiring derivations, proofs, and applications of Maxwell’s equations, boundary conditions, and classical electromagnetic laws.

Section C includes long-answer, application-oriented questions where students demonstrate deep understanding of vector transformations, energy expressions, wave analysis, and transmission line equations.

The paper ensures comprehensive evaluation through a balance of theory, mathematics, and electromagnetic field applications, giving students an opportunity to apply learned concepts to both ideal and real-world scenarios.

SECTION A

(Attempt all questions. Each question carries 2 marks.)
2 × 7 = 14 Marks

a. Give the physical significance of divergence.
b. Compute ∇ × V if V = xyz.
c. Write Maxwell’s equations for static fields in point form.
d. Give the physical significance of ∇·B = 0.
e. Explain the concept of magnetic flux density.
f. Differentiate between self-inductance and mutual inductance.
g. State Faraday’s law.

Additional Questions (Add any 2):
h. What is the physical meaning of the curl of a vector field?
i. Define electric displacement vector and explain its significance in dielectrics.
j. Explain the term “retarded potentials” in electromagnetic fields.

SECTION B

(Attempt any three questions. Each question carries 7 marks.)
7 × 3 = 21 Marks

a. Find the Laplacian if V = ρ² z cos(2φ).
b. Establish the boundary conditions for both D and E fields.
c. Explain Ampere’s Circuital Law and derive its major applications.
d. What is magnetic energy? Derive the mathematical expression for magnetostatic energy density.
e. Derive uniform plane wave equations for a lossy dielectric medium.

Additional Question:
f. Derive Poisson’s and Laplace’s equations and explain where each is applied in electromagnetics.

SECTION C

(Attempt any one from each part. Each question carries 7 marks.)
7 × 1 = 7 Marks per part

Q3.

a. Given the vector function
A⃗ = (3x + c₁z) aₓ + (c₂x – 5z) aᵧ + (4x – c₃y + c₄z) a_z.
Examine the values of c₁, c₂, c₃, c₄ if A is irrotational and solenoidal.

b. Convert vector A⃗ = r sinθ a_r from spherical to Cartesian coordinate system.

Q4.

a. For the given vector D = x²y aₓ + z a_z, examine the volume charge density at (1,1,1) and calculate electrostatic energy for the region –1 < x < 1, –1 < y < 1, –1 < z < 1.

b. Compute div(grad V) in all coordinate systems.

Q5.

a. Explain the Biot–Savart law. Determine H for infinite, finite, and semi-infinite length conductors.

b. Derive Maxwell’s equations associated with curling fields for static fields in integral form.

Q6.

a. Establish boundary conditions for B and H fields. Also discuss the modified Ampere’s Circuital Law.

b. Explain magnetic scalar and vector potentials. Prove that B = ∇ × A.

Q7.

a. Establish relations for propagation constant, attenuation constant, phase constant, and phase velocity for lossless and distortionless transmission lines.

b. Derive the telegraph equations for transmission lines.