Solution Manual For Introduction to
Electrodynamics, 5th Edition by David J.
Griffiths. All Chapters 1-12 2026/2027 –
Verified Q&As with Detailed Rationales
(Test Bank Bundle - 69 Questions)
---
*QUESTION 1:*
The divergence of a curl of any vector field is always:
A) Zero
B) The vector field itself
C) The Laplacian of the field
D) The gradient of the divergence
> 🎯 *CORRECT ANSWER:* A) Zero
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Vector identity ∇⋅(∇×A) = 0.
> * *Why Distractors Fail:* Vector/Laplacian/gradient are different identities.
> * *Core Takeaway:* Div(curl) = 0.
---
*QUESTION 2:*
,The curl of the gradient of a scalar function is always:
A) The scalar function
B) Zero
C) The Laplacian of the function
D) The gradient of the function
> 🎯 *CORRECT ANSWER:* B) Zero
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* ∇×(∇V) = 0.
> * *Why Distractors Fail:* Scalar/Laplacian/gradient are not the result.
> * *Core Takeaway:* Curl(gradient) = 0.
---
*QUESTION 3:*
Coulomb's law in vector form relates the electric field to:
A) The magnetic field
B) The charge distribution
C) The vector potential
D) The current density
> 🎯 *CORRECT ANSWER:* B) The charge distribution
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* E is due to static charges.
> * *Why Distractors Fail:* Magnetic field/current/vector potential are magnetostatics.
> * *Core Takeaway:* Coulomb = charge.
---
,*QUESTION 4:*
Gauss's law in differential form is:
A) ∇⋅E = ρ/ε₀
B) ∇×E = -∂B/∂t
C) ∇⋅B = 0
D) ∇×B = μ₀J
> 🎯 *CORRECT ANSWER:* A) ∇⋅E = ρ/ε₀
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Differential form of Gauss's law.
> * *Why Distractors Fail:* B is Faraday; C is no monopoles; D is Ampere.
> * *Core Takeaway:* Gauss = ∇⋅E.
---
*QUESTION 5:*
The electric potential V is related to the electric field E by:
A) E = -∇V
B) E = ∇V
C) E = -∂V/∂t
D) E = ∇×V
> 🎯 *CORRECT ANSWER:* A) E = -∇V
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Gradient of scalar potential.
> * *Why Distractors Fail:* Sign/space/time/curl are incorrect.
> * *Core Takeaway:* E = -grad V.
, ---
*QUESTION 6:*
A point charge q at the origin produces an electric potential V. The potential at a distance r is:
A) q/(4πε₀r)
B) q/(4πε₀r²)
C) qr/(4πε₀)
D) q/(4πε₀) ln(r)
> 🎯 *CORRECT ANSWER:* A) q/(4πε₀r)
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Scalar potential of point charge.
> * *Why Distractors Fail:* 1/r² is field; others dimensionally wrong.
> * *Core Takeaway:* V ∼ 1/r.
---
*QUESTION 7:*
The magnetic field B for a long straight wire carrying current I is proportional to:
A) r
B) 1/r
C) 1/r²
D) ln(r)
> 🎯 *CORRECT ANSWER:* B) 1/r
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Biot-Savart law.
> * *Why Distractors Fail:* 1/r² is monopole; r/ln are wrong.
> * *Core Takeaway:* B ∼ 1/r.
Electrodynamics, 5th Edition by David J.
Griffiths. All Chapters 1-12 2026/2027 –
Verified Q&As with Detailed Rationales
(Test Bank Bundle - 69 Questions)
---
*QUESTION 1:*
The divergence of a curl of any vector field is always:
A) Zero
B) The vector field itself
C) The Laplacian of the field
D) The gradient of the divergence
> 🎯 *CORRECT ANSWER:* A) Zero
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Vector identity ∇⋅(∇×A) = 0.
> * *Why Distractors Fail:* Vector/Laplacian/gradient are different identities.
> * *Core Takeaway:* Div(curl) = 0.
---
*QUESTION 2:*
,The curl of the gradient of a scalar function is always:
A) The scalar function
B) Zero
C) The Laplacian of the function
D) The gradient of the function
> 🎯 *CORRECT ANSWER:* B) Zero
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* ∇×(∇V) = 0.
> * *Why Distractors Fail:* Scalar/Laplacian/gradient are not the result.
> * *Core Takeaway:* Curl(gradient) = 0.
---
*QUESTION 3:*
Coulomb's law in vector form relates the electric field to:
A) The magnetic field
B) The charge distribution
C) The vector potential
D) The current density
> 🎯 *CORRECT ANSWER:* B) The charge distribution
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* E is due to static charges.
> * *Why Distractors Fail:* Magnetic field/current/vector potential are magnetostatics.
> * *Core Takeaway:* Coulomb = charge.
---
,*QUESTION 4:*
Gauss's law in differential form is:
A) ∇⋅E = ρ/ε₀
B) ∇×E = -∂B/∂t
C) ∇⋅B = 0
D) ∇×B = μ₀J
> 🎯 *CORRECT ANSWER:* A) ∇⋅E = ρ/ε₀
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Differential form of Gauss's law.
> * *Why Distractors Fail:* B is Faraday; C is no monopoles; D is Ampere.
> * *Core Takeaway:* Gauss = ∇⋅E.
---
*QUESTION 5:*
The electric potential V is related to the electric field E by:
A) E = -∇V
B) E = ∇V
C) E = -∂V/∂t
D) E = ∇×V
> 🎯 *CORRECT ANSWER:* A) E = -∇V
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Gradient of scalar potential.
> * *Why Distractors Fail:* Sign/space/time/curl are incorrect.
> * *Core Takeaway:* E = -grad V.
, ---
*QUESTION 6:*
A point charge q at the origin produces an electric potential V. The potential at a distance r is:
A) q/(4πε₀r)
B) q/(4πε₀r²)
C) qr/(4πε₀)
D) q/(4πε₀) ln(r)
> 🎯 *CORRECT ANSWER:* A) q/(4πε₀r)
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Scalar potential of point charge.
> * *Why Distractors Fail:* 1/r² is field; others dimensionally wrong.
> * *Core Takeaway:* V ∼ 1/r.
---
*QUESTION 7:*
The magnetic field B for a long straight wire carrying current I is proportional to:
A) r
B) 1/r
C) 1/r²
D) ln(r)
> 🎯 *CORRECT ANSWER:* B) 1/r
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Biot-Savart law.
> * *Why Distractors Fail:* 1/r² is monopole; r/ln are wrong.
> * *Core Takeaway:* B ∼ 1/r.
