Instructor's Solutions Manual For Introduction to Electrodynamics, 5th Edition by Griffiths | All 1-12 Chapters Covered With Questions And Verified Solutions With Rationales And Case Study.

Instructor's Solutions Manual For Introduction to Electrodynamics, 5th
Edition by Griffiths (Cambridge University Press, 2023) By Isbn:
9781009397728 | All 1-12 Chapters Covered With Questions And
Verified Solutions With Rationales And Case Study.

, TABLE OF CONTENT


1 Vector Analysis

2 Electrostatics

3 Potentials

4 Electric Fields in Matter

5 Magnetostatics

6 Magnetic Fields in Matter

7 Electrodynamics

8 Conservation Laws

9 Electromagnetic Waves

10 Potentials and Fields

11 Radiation

12 Electrodynamics and Relativity

,Chapter 1: Vector Analysis

Multiple Choice Questions

Question 1

The gradient of a scalar field ϕ(x,y,z)\phi(x,y,z)ϕ(x,y,z) gives:

A. A scalar
B. A vector pointing in the direction of maximum increase of ϕ\phiϕ
C. A vector pointing in the direction of minimum increase of ϕ\phiϕ
D. A tensor

Answer: B

Rationale:
The gradient ∇ϕ\nabla \phi∇ϕ points in the direction of maximum rate of change of the scalar field.



Question 2

The divergence of a vector field F\mathbf{F}F measures:

A. Rotation of the field
B. Net flux per unit volume
C. Magnitude of vector
D. Gradient of a scalar

Answer: B

Rationale:
Divergence indicates how much a vector field spreads out from a point.



Question 3

The curl of a vector field F\mathbf{F}F is:

A. ∇⋅F\nabla \cdot \mathbf{F}∇⋅F
B. ∇×F\nabla \times \mathbf{F}∇×F
C. ∇ϕ\nabla \phi∇ϕ
D. F2\mathbf{F}^2F2

Answer: B

Rationale:
Curl measures the rotation of a vector field at a point.



Question 4

Which of the following is a vector operator identity?

, A. ∇⋅(∇×F)=0\nabla \cdot (\nabla \times \mathbf{F}) = 0∇⋅(∇×F)=0
B. ∇×(∇ϕ)=ϕ\nabla \times (\nabla \phi) = \phi∇×(∇ϕ)=ϕ
C. ∇⋅(∇ϕ)=∇ϕ\nabla \cdot (\nabla \phi) = \nabla \phi∇⋅(∇ϕ)=∇ϕ
D. ∇×(F⋅G)=F×G\nabla \times (\mathbf{F} \cdot \mathbf{G}) = \mathbf{F} \times
\mathbf{G}∇×(F⋅G)=F×G

Answer: A

Rationale:
The divergence of a curl is always zero.



Question 5

A conservative vector field satisfies:

A. ∇⋅F=0\nabla \cdot \mathbf{F} = 0∇⋅F=0
B. ∇×F=0\nabla \times \mathbf{F} = 0∇×F=0
C. ∇⋅F≠0\nabla \cdot \mathbf{F} \neq 0∇⋅F =0
D. ∇×F≠0\nabla \times \mathbf{F} \neq 0∇×F =0

Answer: B

Rationale:
A conservative field is the gradient of a scalar, so its curl is zero.



Question 6

The Laplacian of a scalar field ϕ\phiϕ is defined as:

A. ∇⋅(∇ϕ)\nabla \cdot (\nabla \phi)∇⋅(∇ϕ)
B. ∇×(∇ϕ)\nabla \times (\nabla \phi)∇×(∇ϕ)
C. ∇ϕ\nabla \phi∇ϕ
D. F⋅∇ϕ\mathbf{F} \cdot \nabla \phiF⋅∇ϕ

Answer: A

Rationale:
The Laplacian is the divergence of the gradient.



Question 7

Which coordinate system is most useful for problems with spherical symmetry?

A. Cartesian
B. Cylindrical
C. Spherical
D. Polar

Answer: C