EEE 241 — FUNDAMENTALS OF ELECTROMAGNETICS QUIZ 3
EXAM |2026 QUESTIONS AND CORRECT ANSWERS WITH
DETAILED RATIONALES EACH | CURRENTLY TESTING AND
FREQUENTLY TESTED QUESTIONS
Section 1: Vector Analysis and Coordinate Systems (Questions 1-30)
1. Which of the following is a scalar quantity?
A) Electric Field
B) Magnetic Flux Density
C) Electric Potential
D) Force
Correct Answer: C) Electric Potential
Rationale: Electric potential is a scalar quantity, defined as energy per unit charge.
Electric field, magnetic flux density, and force are all vector quantities with both
magnitude and direction.
2. The dot product of two vectors A and B is zero. What is the angle between
them?
A) 0 degrees
B) 45 degrees
C) 90 degrees
D) 180 degrees
Correct Answer: C) 90 degrees
,Rationale: The dot product is defined as A·B = |A||B|cos(θ). If A·B = 0 and neither
vector is zero, then cos(θ) = 0, which means θ = 90 degrees. This indicates the
vectors are orthogonal.
3. What is the result of the cross product of a vector with itself (A × A)?
A) A scalar equal to |A|²
B) A unit vectors
C) The zero vector
D) A vector perpendicular to A
Correct Answer: C) The zero vector
Rationale: The cross-product A × B = |A||B|sin(θ)n̂. If A = B, the angle θ is 0, and
sin (0) = 0. Therefore, the magnitude is zero, resulting in the zero vector.
4. Which coordinate system is most suitable for analyzing the electric field of an
infinitely long, straight charged wire?
A) Cartesian
B) Cylindrical
C) Spherical
D) Rectangular
Correct Answer: B) Cylindrical
Rationale: An infinitely long wire has cylindrical symmetry. The electric field
depends only on the radial distance from the wire, making cylindrical coordinates
(ρ, φ, z) the most natural and simple choice for analysis.
5. In spherical coordinates, the unit vector a_φ points in the direction of:
A) Increasing radial distance
,B) Increasing polar angle θ
C) Increasing azimuthal angle φ
D) The z-axis
Correct Answer: C) Increasing azimuthal angle φ
Rationale: In spherical coordinates (r, θ, φ), the unit vector a_φ is tangential to a
circle of constant r and θ, pointing in the direction of increasing azimuthal angle
φ.
6. The gradient of a scalar field V is a:
A) Scalar
B) Vector
C) Tensor
D) Complex number
Correct Answer: B) Vector
Rationale: The gradient operator (∇) applied to a scalar field V, denoted as ∇V,
produces a vector that points in the direction of the greatest rate of increase of V,
with a magnitude equal to that rate.
7. What does the divergence of a vector field measure?
A) The rotational tendency of the field
B) The rate of expansion or contraction of the field at a point
C) The magnitude of the field
D) The direction of the field
Correct Answer: B) The rate of expansion or contraction of the field at a point
, Rationale: Divergence (∇·A) measures the net outward flux of a vector field per
unit volume at a given point. A positive divergence indicates a source, and a
negative divergence indicates a sink.
8. The curl of a conservative vector field is always:
A) A constant vector
B) A scalar
C) The zero vector
D) A unit vector
Correct Answer: C) The zero vector
Rationale: A conservative field can be expressed as the gradient of a scalar
potential (F = -∇V). A key property of such fields is that their curl is zero (∇ × ∇V =
0).
9. Which theorem relates a volume integral of the divergence of a vector field to a
surface integral over the closed bounding surface?
A) Stokes' Theorem
B) Divergence Theorem
C) Green's Theorem
D) Helmholtz's Theorem
Correct Answer: B) Divergence Theorem
Rationale: The Divergence Theorem, also known as Gauss's Theorem, states that
∫ᵥ (∇·A) dv = ∮ₛ A·ds, converting a volume integral into a surface integral.
10. Stokes' Theorem relates a line integral around a closed path to a:
A) Volume integral
EXAM |2026 QUESTIONS AND CORRECT ANSWERS WITH
DETAILED RATIONALES EACH | CURRENTLY TESTING AND
FREQUENTLY TESTED QUESTIONS
Section 1: Vector Analysis and Coordinate Systems (Questions 1-30)
1. Which of the following is a scalar quantity?
A) Electric Field
B) Magnetic Flux Density
C) Electric Potential
D) Force
Correct Answer: C) Electric Potential
Rationale: Electric potential is a scalar quantity, defined as energy per unit charge.
Electric field, magnetic flux density, and force are all vector quantities with both
magnitude and direction.
2. The dot product of two vectors A and B is zero. What is the angle between
them?
A) 0 degrees
B) 45 degrees
C) 90 degrees
D) 180 degrees
Correct Answer: C) 90 degrees
,Rationale: The dot product is defined as A·B = |A||B|cos(θ). If A·B = 0 and neither
vector is zero, then cos(θ) = 0, which means θ = 90 degrees. This indicates the
vectors are orthogonal.
3. What is the result of the cross product of a vector with itself (A × A)?
A) A scalar equal to |A|²
B) A unit vectors
C) The zero vector
D) A vector perpendicular to A
Correct Answer: C) The zero vector
Rationale: The cross-product A × B = |A||B|sin(θ)n̂. If A = B, the angle θ is 0, and
sin (0) = 0. Therefore, the magnitude is zero, resulting in the zero vector.
4. Which coordinate system is most suitable for analyzing the electric field of an
infinitely long, straight charged wire?
A) Cartesian
B) Cylindrical
C) Spherical
D) Rectangular
Correct Answer: B) Cylindrical
Rationale: An infinitely long wire has cylindrical symmetry. The electric field
depends only on the radial distance from the wire, making cylindrical coordinates
(ρ, φ, z) the most natural and simple choice for analysis.
5. In spherical coordinates, the unit vector a_φ points in the direction of:
A) Increasing radial distance
,B) Increasing polar angle θ
C) Increasing azimuthal angle φ
D) The z-axis
Correct Answer: C) Increasing azimuthal angle φ
Rationale: In spherical coordinates (r, θ, φ), the unit vector a_φ is tangential to a
circle of constant r and θ, pointing in the direction of increasing azimuthal angle
φ.
6. The gradient of a scalar field V is a:
A) Scalar
B) Vector
C) Tensor
D) Complex number
Correct Answer: B) Vector
Rationale: The gradient operator (∇) applied to a scalar field V, denoted as ∇V,
produces a vector that points in the direction of the greatest rate of increase of V,
with a magnitude equal to that rate.
7. What does the divergence of a vector field measure?
A) The rotational tendency of the field
B) The rate of expansion or contraction of the field at a point
C) The magnitude of the field
D) The direction of the field
Correct Answer: B) The rate of expansion or contraction of the field at a point
, Rationale: Divergence (∇·A) measures the net outward flux of a vector field per
unit volume at a given point. A positive divergence indicates a source, and a
negative divergence indicates a sink.
8. The curl of a conservative vector field is always:
A) A constant vector
B) A scalar
C) The zero vector
D) A unit vector
Correct Answer: C) The zero vector
Rationale: A conservative field can be expressed as the gradient of a scalar
potential (F = -∇V). A key property of such fields is that their curl is zero (∇ × ∇V =
0).
9. Which theorem relates a volume integral of the divergence of a vector field to a
surface integral over the closed bounding surface?
A) Stokes' Theorem
B) Divergence Theorem
C) Green's Theorem
D) Helmholtz's Theorem
Correct Answer: B) Divergence Theorem
Rationale: The Divergence Theorem, also known as Gauss's Theorem, states that
∫ᵥ (∇·A) dv = ∮ₛ A·ds, converting a volume integral into a surface integral.
10. Stokes' Theorem relates a line integral around a closed path to a:
A) Volume integral
