CLASSICAL ELECTRODYNAMICS
PRACTICE EXAM (GRADUATE LEVEL /
QUALIFYING EXAM) QUESTION AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. Gauss’s law in differential form is
A. ∇·E = 0
B. ∇×E = 0
C. ∇·E = ρ/ε₀
D. ∇×B = μ₀J
Answer: C
Rationale: Gauss’s law relates the divergence of the electric field to charge
density via ε₀.
2. The electric field inside a hollow conducting sphere with no internal charge
is
A. Nonzero and radial
B. Nonzero and tangential
C. Depends on radius
D. Zero everywhere
,Answer: D
Rationale: In electrostatic equilibrium, the electric field inside a conductor is
zero.
3. The potential energy of a charge q in an electric potential V is
A. q/V
B. V/q
C. qV
D. −qV
Answer: C
Rationale: Electric potential energy is defined as U = qV.
4. The boundary condition for the normal component of E across a surface
charge σ is
A. Continuous
B. Zero
C. (E₂ − E₁)·n = σ/ε₀
D. (E₂ − E₁)×n = 0
Answer: C
Rationale: Surface charge causes a discontinuity in the normal component of E.
5. The electric field due to an infinite line charge varies with distance r as
A. 1/r²
B. 1/r
C. r
D. Constant
Answer: B
Rationale: Cylindrical symmetry leads to E ∝ 1/r from Gauss’s law.
, 6. The Laplace equation is valid in regions where
A. Current exists
B. Charge density is uniform
C. Charge density is zero
D. Electric field is zero
Answer: C
Rationale: Laplace’s equation applies in charge-free regions.
7. The method of images is primarily used to solve problems involving
A. Magnetic materials
B. Time-dependent fields
C. Conducting boundaries
D. Dielectrics only
Answer: C
Rationale: Image charges replace conductors to satisfy boundary conditions.
8. The polarization vector P represents
A. Free charge density
B. Magnetic dipole moment
C. Dipole moment per unit volume
D. Electric flux density
Answer: C
Rationale: Polarization is defined as dipole moment density.
9. The displacement field D satisfies
A. ∇·E = ρ_f
B. ∇·D = ρ_free
PRACTICE EXAM (GRADUATE LEVEL /
QUALIFYING EXAM) QUESTION AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. Gauss’s law in differential form is
A. ∇·E = 0
B. ∇×E = 0
C. ∇·E = ρ/ε₀
D. ∇×B = μ₀J
Answer: C
Rationale: Gauss’s law relates the divergence of the electric field to charge
density via ε₀.
2. The electric field inside a hollow conducting sphere with no internal charge
is
A. Nonzero and radial
B. Nonzero and tangential
C. Depends on radius
D. Zero everywhere
,Answer: D
Rationale: In electrostatic equilibrium, the electric field inside a conductor is
zero.
3. The potential energy of a charge q in an electric potential V is
A. q/V
B. V/q
C. qV
D. −qV
Answer: C
Rationale: Electric potential energy is defined as U = qV.
4. The boundary condition for the normal component of E across a surface
charge σ is
A. Continuous
B. Zero
C. (E₂ − E₁)·n = σ/ε₀
D. (E₂ − E₁)×n = 0
Answer: C
Rationale: Surface charge causes a discontinuity in the normal component of E.
5. The electric field due to an infinite line charge varies with distance r as
A. 1/r²
B. 1/r
C. r
D. Constant
Answer: B
Rationale: Cylindrical symmetry leads to E ∝ 1/r from Gauss’s law.
, 6. The Laplace equation is valid in regions where
A. Current exists
B. Charge density is uniform
C. Charge density is zero
D. Electric field is zero
Answer: C
Rationale: Laplace’s equation applies in charge-free regions.
7. The method of images is primarily used to solve problems involving
A. Magnetic materials
B. Time-dependent fields
C. Conducting boundaries
D. Dielectrics only
Answer: C
Rationale: Image charges replace conductors to satisfy boundary conditions.
8. The polarization vector P represents
A. Free charge density
B. Magnetic dipole moment
C. Dipole moment per unit volume
D. Electric flux density
Answer: C
Rationale: Polarization is defined as dipole moment density.
9. The displacement field D satisfies
A. ∇·E = ρ_f
B. ∇·D = ρ_free
