EEE 241 QUIZ 3– FUNDAMENTALS OF
ELECTROMAGNETICS ARIZONA STATE UNIVERSITY
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SOLUTIONS) 2026-2027 UPDATED BEST VERSION
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1. In an orthogonal coordinate system, which of the following is always true?
A) The dot product of two different unit vectors is zero.
B) The dot product of two different unit vectors is zero.
C) The cross product of any two unit vectors is always the same, regardless of
coordinates.
D) The unit vectors are fixed in direction everywhere in space.
Rationale: In an orthogonal coordinate system, the unit vectors are mutually
perpendicular, so their dot product is zero.
2. Which of the following correctly expresses the transformation between Cartesian (x, y, z)
and spherical (R, θ, φ) coordinates?
A) x = R sin θ cos φ, y = R sin θ sin φ, z = R cos θ
B) x = R sin θ cos φ, y = R sin θ sin φ, z = R cos θ
C) x = R cos θ cos φ, y = R cos θ sin φ, z = R sin θ
D) x = R sin θ sin φ, y = R sin θ cos φ, z = R cos θ
Rationale: The standard transformation from spherical to Cartesian coordinates is x =
R sin θ cos φ, y = R sin θ sin φ, and z = R cos θ.
3. Given vectors A = 2i + 4j + 2k, B = -2i + 4j + 2k, and C = i + j + k, compute A × (B + C).
A) -2i + 10j - 11k
B) -2i + 10j - 11k
C) 7i - 10j + 11k
, D) 10i + 7j - 8k
Rationale: First compute B + C = (-1)i + 5j + 3k, then take the cross product A × (B + C) =
-2i + 10j - 11k.
4. The divergence of a vector field is a measure of:
A) The rotational tendency of the field.
B) The net outward flux per unit volume.
C) The line integral around a closed path.
D) The gradient of a scalar field.
Rationale: Divergence measures the net outward flux of a vector field per unit volume
at a given point.
5. Which of the following is NOT a fundamental postulate of electrostatics?
A) Electric field lines begin on positive charges and end on negative charges.
B) The electric field is always conservative.
C) The work done in moving a charge around a closed loop is zero.
D) The electric flux density is solenoidal.
Rationale: While the electric field is conservative in electrostatics, this is a derived
property, not a fundamental postulate. The postulates include Coulomb's law and
Gauss's law.
6. Gauss's law in differential form is:
A) ∇ × E = 0
B) ∇ · D = ρv
C) ∇ · E = ρv/ε0
D) ∇ × D = ρv
Rationale: Gauss's law in differential form states that the divergence of the electric
flux density D equals the volume charge density ρv.
7. The electric field intensity at a distance r from a point charge Q in free space is:
A) Q / (4πε0 r)
B) Q / (4πε0 r²)
C) Q / (2πε0 r)
D) Q / (2πε0 r²)
Rationale: By Coulomb's law, E = Q / (4πε0 r²) for a point charge in free space.
8. The work done in moving a charge q from point A to point B in an electric field E is:
A) q ∫ E · dl
B) -q ∫ E · dl
C) q ∫ E × dl
, D) -q ∫ E × dl
Rationale: The work done by an external agent is W = -q ∫ E · dl, where the integral is
from A to B.
9. The electric potential V at a distance r from a point charge Q is:
A) Q / (4πε0 r²)
B) Q / (4πε0 r)
C) Q / (2πε0 r)
D) Q r / (4πε0)
Rationale: The electric potential due to a point charge is V = Q / (4πε0 r).
10. The relationship between electric field E and potential V is:
A) E = ∇V
B) E = -∇V
C) E = ∇ × V
D) E = -∇ × V
Rationale: The electric field is the negative gradient of the electric potential, E = -∇V.
11. The capacitance of a parallel-plate capacitor with plate area A, separation d, and
dielectric constant ε is:
A) ε d / A
B) ε A / d
C) A / (ε d)
D) d / (ε A)
Rationale: Capacitance is given by C = εA/d.
12. The energy stored in a capacitor is:
A) CV
B) ½ CV²
C) C²V
D) ½ C²V
Rationale: The energy stored in a capacitor is W = ½ CV².
13. Poisson's equation is:
A) ∇²V = 0
B) ∇²V = -ρv/ε
C) ∇²V = ρv/ε
D) ∇²V = -ρv/ε0
Rationale: Poisson's equation relates the Laplacian of potential to the charge density:
∇²V = -ρv/ε.
ELECTROMAGNETICS ARIZONA STATE UNIVERSITY
LATEST UPDATED REAL FINAL PRACTICE EXAM WITH
ALL POSSIBLE COMPLETE DETAILED QUESTIONS
AND 100% CORRECT VERIFIED ANSWERS FULLY
SOLVED WITH CERTIFIED RATIONALES PLUS
RELIABLE ANSWER KEY (100% COMPLETE
SOLUTIONS) 2026-2027 UPDATED BEST VERSION
RATED A+ GRADE INSTANT DOWNLOAD PDF
1. In an orthogonal coordinate system, which of the following is always true?
A) The dot product of two different unit vectors is zero.
B) The dot product of two different unit vectors is zero.
C) The cross product of any two unit vectors is always the same, regardless of
coordinates.
D) The unit vectors are fixed in direction everywhere in space.
Rationale: In an orthogonal coordinate system, the unit vectors are mutually
perpendicular, so their dot product is zero.
2. Which of the following correctly expresses the transformation between Cartesian (x, y, z)
and spherical (R, θ, φ) coordinates?
A) x = R sin θ cos φ, y = R sin θ sin φ, z = R cos θ
B) x = R sin θ cos φ, y = R sin θ sin φ, z = R cos θ
C) x = R cos θ cos φ, y = R cos θ sin φ, z = R sin θ
D) x = R sin θ sin φ, y = R sin θ cos φ, z = R cos θ
Rationale: The standard transformation from spherical to Cartesian coordinates is x =
R sin θ cos φ, y = R sin θ sin φ, and z = R cos θ.
3. Given vectors A = 2i + 4j + 2k, B = -2i + 4j + 2k, and C = i + j + k, compute A × (B + C).
A) -2i + 10j - 11k
B) -2i + 10j - 11k
C) 7i - 10j + 11k
, D) 10i + 7j - 8k
Rationale: First compute B + C = (-1)i + 5j + 3k, then take the cross product A × (B + C) =
-2i + 10j - 11k.
4. The divergence of a vector field is a measure of:
A) The rotational tendency of the field.
B) The net outward flux per unit volume.
C) The line integral around a closed path.
D) The gradient of a scalar field.
Rationale: Divergence measures the net outward flux of a vector field per unit volume
at a given point.
5. Which of the following is NOT a fundamental postulate of electrostatics?
A) Electric field lines begin on positive charges and end on negative charges.
B) The electric field is always conservative.
C) The work done in moving a charge around a closed loop is zero.
D) The electric flux density is solenoidal.
Rationale: While the electric field is conservative in electrostatics, this is a derived
property, not a fundamental postulate. The postulates include Coulomb's law and
Gauss's law.
6. Gauss's law in differential form is:
A) ∇ × E = 0
B) ∇ · D = ρv
C) ∇ · E = ρv/ε0
D) ∇ × D = ρv
Rationale: Gauss's law in differential form states that the divergence of the electric
flux density D equals the volume charge density ρv.
7. The electric field intensity at a distance r from a point charge Q in free space is:
A) Q / (4πε0 r)
B) Q / (4πε0 r²)
C) Q / (2πε0 r)
D) Q / (2πε0 r²)
Rationale: By Coulomb's law, E = Q / (4πε0 r²) for a point charge in free space.
8. The work done in moving a charge q from point A to point B in an electric field E is:
A) q ∫ E · dl
B) -q ∫ E · dl
C) q ∫ E × dl
, D) -q ∫ E × dl
Rationale: The work done by an external agent is W = -q ∫ E · dl, where the integral is
from A to B.
9. The electric potential V at a distance r from a point charge Q is:
A) Q / (4πε0 r²)
B) Q / (4πε0 r)
C) Q / (2πε0 r)
D) Q r / (4πε0)
Rationale: The electric potential due to a point charge is V = Q / (4πε0 r).
10. The relationship between electric field E and potential V is:
A) E = ∇V
B) E = -∇V
C) E = ∇ × V
D) E = -∇ × V
Rationale: The electric field is the negative gradient of the electric potential, E = -∇V.
11. The capacitance of a parallel-plate capacitor with plate area A, separation d, and
dielectric constant ε is:
A) ε d / A
B) ε A / d
C) A / (ε d)
D) d / (ε A)
Rationale: Capacitance is given by C = εA/d.
12. The energy stored in a capacitor is:
A) CV
B) ½ CV²
C) C²V
D) ½ C²V
Rationale: The energy stored in a capacitor is W = ½ CV².
13. Poisson's equation is:
A) ∇²V = 0
B) ∇²V = -ρv/ε
C) ∇²V = ρv/ε
D) ∇²V = -ρv/ε0
Rationale: Poisson's equation relates the Laplacian of potential to the charge density:
∇²V = -ρv/ε.
