ADVANCED ELECTROMAGNETISM
QUALIFYING EXAM QUESTION AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. Maxwell’s equations in differential form imply charge conservation through
A. Faraday’s law
B. Gauss’s law
C. Ampère’s law without displacement current
D. Ampère–Maxwell law
Answer: D
Rationale: The displacement current term ensures ∇·J + ∂ρ/∂t = 0,
expressing charge conservation.
2. The scalar potential in the Lorenz gauge satisfies
A. Poisson’s equation
B. Laplace’s equation
C. Wave equation
D. Helmholtz equation
Answer: C
Rationale: In Lorenz gauge, both scalar and vector potentials obey wave
equations.
3. In electrostatics, the uniqueness theorem requires
A. Only volume charge density
B. Boundary conditions and charge distribution
C. Only boundary conditions
D. Only potential specified everywhere
, Answer: B
Rationale: Given charge distribution and boundary conditions, the
solution is unique.
4. The Green’s function for Poisson’s equation in free space is proportional to
A. r
B. r²
C. 1/r
D. e⁻ʳ
Answer: C
Rationale: The Coulomb potential arises from the 1/r Green’s function.
5. The displacement current density is defined as
A. ε₀E
B. ∂E/∂t
C. ε₀∂E/∂t
D. μ₀∂B/∂t
Answer: C
Rationale: Maxwell introduced ε₀∂E/∂t to modify Ampère’s law.
6. A perfect conductor in electrostatic equilibrium has
A. Nonzero internal electric field
B. Uniform volume charge
C. Zero internal electric field
D. Time-varying surface charge
Answer: C
Rationale: Charges rearrange to cancel internal electric fields.
7. The boundary condition for the normal component of D across a surface
charge σ is
A. Continuous
B. Zero
C. Discontinuous by σ
D. Discontinuous by σ/ε₀
, Answer: C
Rationale: (D₂ − D₁)·n = σ_free.
8. The magnetic vector potential A is defined such that
A. E = −∇×A
B. B = ∇×A
C. B = −∇A
D. E = ∂A/∂t
Answer: B
Rationale: By definition, magnetic fields are curls of vector potentials.
9. Gauge transformations change
A. Physical fields
B. Potentials but not fields
C. Fields but not potentials
D. Charge density
Answer: B
Rationale: E and B remain invariant under gauge transformations.
10.In magnetostatics, ∇·B equals
A. ρ/ε₀
B. μ₀ρ
C. 0
D. ∂E/∂t
Answer: C
Rationale: Absence of magnetic monopoles implies zero divergence.
11.The energy density of an electric field in vacuum is
A. ε₀E²
B. ε₀E²/2
C. E²/μ₀
D. μ₀E²/2
Answer: B
Rationale: Field energy density is (1/2)ε₀E².
QUALIFYING EXAM QUESTION AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. Maxwell’s equations in differential form imply charge conservation through
A. Faraday’s law
B. Gauss’s law
C. Ampère’s law without displacement current
D. Ampère–Maxwell law
Answer: D
Rationale: The displacement current term ensures ∇·J + ∂ρ/∂t = 0,
expressing charge conservation.
2. The scalar potential in the Lorenz gauge satisfies
A. Poisson’s equation
B. Laplace’s equation
C. Wave equation
D. Helmholtz equation
Answer: C
Rationale: In Lorenz gauge, both scalar and vector potentials obey wave
equations.
3. In electrostatics, the uniqueness theorem requires
A. Only volume charge density
B. Boundary conditions and charge distribution
C. Only boundary conditions
D. Only potential specified everywhere
, Answer: B
Rationale: Given charge distribution and boundary conditions, the
solution is unique.
4. The Green’s function for Poisson’s equation in free space is proportional to
A. r
B. r²
C. 1/r
D. e⁻ʳ
Answer: C
Rationale: The Coulomb potential arises from the 1/r Green’s function.
5. The displacement current density is defined as
A. ε₀E
B. ∂E/∂t
C. ε₀∂E/∂t
D. μ₀∂B/∂t
Answer: C
Rationale: Maxwell introduced ε₀∂E/∂t to modify Ampère’s law.
6. A perfect conductor in electrostatic equilibrium has
A. Nonzero internal electric field
B. Uniform volume charge
C. Zero internal electric field
D. Time-varying surface charge
Answer: C
Rationale: Charges rearrange to cancel internal electric fields.
7. The boundary condition for the normal component of D across a surface
charge σ is
A. Continuous
B. Zero
C. Discontinuous by σ
D. Discontinuous by σ/ε₀
, Answer: C
Rationale: (D₂ − D₁)·n = σ_free.
8. The magnetic vector potential A is defined such that
A. E = −∇×A
B. B = ∇×A
C. B = −∇A
D. E = ∂A/∂t
Answer: B
Rationale: By definition, magnetic fields are curls of vector potentials.
9. Gauge transformations change
A. Physical fields
B. Potentials but not fields
C. Fields but not potentials
D. Charge density
Answer: B
Rationale: E and B remain invariant under gauge transformations.
10.In magnetostatics, ∇·B equals
A. ρ/ε₀
B. μ₀ρ
C. 0
D. ∂E/∂t
Answer: C
Rationale: Absence of magnetic monopoles implies zero divergence.
11.The energy density of an electric field in vacuum is
A. ε₀E²
B. ε₀E²/2
C. E²/μ₀
D. μ₀E²/2
Answer: B
Rationale: Field energy density is (1/2)ε₀E².
