EEE 241 — Fundamentals Of Electromagnetics
Quiz 3 Practice Exam 200 Questions With
Answers & Rationales| Arizona State University |
2026/2027 Update | 100% Correct
1. The gradient of a scalar field produces a:
A) Scalar
B) Vector
C) Matrix
D) Tensor
Answer: B
Rationale: Gradient of a scalar gives a vector pointing in direction of maximum increase.
2. The divergence of a vector field produces a:
A) Vector
B) Scalar
C) Matrix
D) Tensor
Answer: B
Rationale: Divergence measures net outward flux per unit volume and is scalar.
3. The curl of a vector field produces a:
A) Scalar
B) Vector
C) Matrix
D) Tensor
Answer: B
Rationale: Curl gives circulation per unit area and is a vector.
,4. In spherical coordinates, the unit vector \(\hat{a}_\phi\) is:
A) Radial
B) Polar
C) Azimuthal
D) Cartesian
Answer: C
Rationale: \(\phi\) is azimuthal angle; \(\hat{a}_\phi\) points in increasing azimuth.
5. The dot product of two perpendicular vectors is:
A) 1
B) 0
C) Infinity
D) Undefined
Answer: B
Rationale: Dot product \(A·B=AB\cosθ\); for θ=90°, cos90°=0.
6. The cross product of a vector with itself is:
A) 1
B) Unit vector
C) Zero vector
D) Scalar
Answer: C
Rationale: \(A×A=0\) because sin0°=0.
7. \(\nabla \times (\nabla V)\) is always:
A) V
2
,B) Zero
C) \(\nabla V\)
D) \(\nabla^2 V\)
Answer: B
Rationale: Curl of gradient is identically zero for any scalar field.
8. \(\nabla \cdot (\nabla \times A)\) is always:
A) A
B) Zero
C) \(\nabla A\)
D) \(\nabla^2 A\)
Answer: B
Rationale: Divergence of curl is identically zero for any vector field.
9. The unit of electric field intensity is:
A) Volt
B) Volt/meter
C) Ampere/meter
D) Coulomb/meter
Answer: B
Rationale: Electric field is force per unit charge, expressed as V/m or N/C.
10. The unit of electric flux density \(D\) is:
A) C/m
B) C/m²
C) V/m
D) A/m
Answer: B
3
, Rationale: Electric flux density is charge per unit area.
11. Coulomb’s law force between two charges is:
A) Directly proportional to distance
B) Inversely proportional to square of distance
C) Inversely proportional to distance
D) Independent of distance
Answer: B
Rationale: \(F \propto 1/r^2\) for point charges in free space.
12. Permittivity of free space \(\epsilon_0\) is approximately:
A) \(4\pi\times10^{-7}\)
B) \(8.854\times10^{-12}\) F/m
C) \(1.257\times10^{-6}\) H/m
D) \(3\times10^8\) m/s
Answer: B
Rationale: \(\epsilon_0 = 8.854\times10^{-12}\) F/m.
13. Gauss’s law states that electric flux through a closed surface equals:
A) Charge density
B) Enclosed charge divided by \(\epsilon_0\)
C) Electric field
D) Potential
Answer: B
Rationale: \(\oint D·dS = Q_{enc}\).
14. The electric field inside a perfect conductor in electrostatic equilibrium is:
4
Quiz 3 Practice Exam 200 Questions With
Answers & Rationales| Arizona State University |
2026/2027 Update | 100% Correct
1. The gradient of a scalar field produces a:
A) Scalar
B) Vector
C) Matrix
D) Tensor
Answer: B
Rationale: Gradient of a scalar gives a vector pointing in direction of maximum increase.
2. The divergence of a vector field produces a:
A) Vector
B) Scalar
C) Matrix
D) Tensor
Answer: B
Rationale: Divergence measures net outward flux per unit volume and is scalar.
3. The curl of a vector field produces a:
A) Scalar
B) Vector
C) Matrix
D) Tensor
Answer: B
Rationale: Curl gives circulation per unit area and is a vector.
,4. In spherical coordinates, the unit vector \(\hat{a}_\phi\) is:
A) Radial
B) Polar
C) Azimuthal
D) Cartesian
Answer: C
Rationale: \(\phi\) is azimuthal angle; \(\hat{a}_\phi\) points in increasing azimuth.
5. The dot product of two perpendicular vectors is:
A) 1
B) 0
C) Infinity
D) Undefined
Answer: B
Rationale: Dot product \(A·B=AB\cosθ\); for θ=90°, cos90°=0.
6. The cross product of a vector with itself is:
A) 1
B) Unit vector
C) Zero vector
D) Scalar
Answer: C
Rationale: \(A×A=0\) because sin0°=0.
7. \(\nabla \times (\nabla V)\) is always:
A) V
2
,B) Zero
C) \(\nabla V\)
D) \(\nabla^2 V\)
Answer: B
Rationale: Curl of gradient is identically zero for any scalar field.
8. \(\nabla \cdot (\nabla \times A)\) is always:
A) A
B) Zero
C) \(\nabla A\)
D) \(\nabla^2 A\)
Answer: B
Rationale: Divergence of curl is identically zero for any vector field.
9. The unit of electric field intensity is:
A) Volt
B) Volt/meter
C) Ampere/meter
D) Coulomb/meter
Answer: B
Rationale: Electric field is force per unit charge, expressed as V/m or N/C.
10. The unit of electric flux density \(D\) is:
A) C/m
B) C/m²
C) V/m
D) A/m
Answer: B
3
, Rationale: Electric flux density is charge per unit area.
11. Coulomb’s law force between two charges is:
A) Directly proportional to distance
B) Inversely proportional to square of distance
C) Inversely proportional to distance
D) Independent of distance
Answer: B
Rationale: \(F \propto 1/r^2\) for point charges in free space.
12. Permittivity of free space \(\epsilon_0\) is approximately:
A) \(4\pi\times10^{-7}\)
B) \(8.854\times10^{-12}\) F/m
C) \(1.257\times10^{-6}\) H/m
D) \(3\times10^8\) m/s
Answer: B
Rationale: \(\epsilon_0 = 8.854\times10^{-12}\) F/m.
13. Gauss’s law states that electric flux through a closed surface equals:
A) Charge density
B) Enclosed charge divided by \(\epsilon_0\)
C) Electric field
D) Potential
Answer: B
Rationale: \(\oint D·dS = Q_{enc}\).
14. The electric field inside a perfect conductor in electrostatic equilibrium is:
4
