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Electricity and Magnetism forMathemacians: Exercises Solutions
DocumentationRelease 0.0
Nathan Musoke, Dario Brooks, Mohammad Kidwai
September 07, 2016
Contents
1 Maxwell’s Equations 3
2 Electromagnetic Waves 5
3 Mechanics and Maxwell’s Equations 7
4 Potentials 9
5 Lagrangians and Electromagnetic Forces 11
6 Differential Forms 13
7 The Hodge Operator 15
8 The Electromagnetic Two-Form 17
9 Some Mathematics Needed for Quantum Mechanics 19
10 Some Quantum Mechanical Thinking 21
11 Quantum Mechanics of Harmonic Oscillators 23
12 Quantizing Maxwell’s Equations 25
13 Manifolds 27
14 Vector Bundles 29
15 Connections 31
16 Curvature 33
17 Maxwell via Connections and Curvature 35
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Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
This document contains working solutions to exercises in the book.
Contents 1
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
2 Contents
CHAPTER 1
Maxwell’s Equations
Exercise 2.3.1. For the function 𝑓(𝑥, 𝑦, 𝑧) = 𝑥2 + 𝑦3 + 𝑥𝑦2 + 4𝑧, compute 𝑔𝑟𝑎𝑑(𝑓), which is the same as computing∇(𝑓).Solution.
∇(𝑓) =
(︂𝜕𝑓
𝜕𝑥,𝜕𝑓
𝜕𝑦,𝜕𝑓
𝜕𝑧
)︂=
(︀2𝑥, 3𝑦2 + 2𝑥𝑦, 4
)︀
3
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
4 Chapter 1. Maxwell’s Equations
CHAPTER 2
Electromagnetic Waves
5
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
6 Chapter 2. Electromagnetic Waves
CHAPTER 3
Mechanics and Maxwell’s Equations
7
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
8 Chapter 3. Mechanics and Maxwell’s Equations
CHAPTER 4
Potentials
9
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
10 Chapter 4. Potentials
CHAPTER 5
Lagrangians and Electromagnetic Forces
11
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
12 Chapter 5. Lagrangians and Electromagnetic Forces
CHAPTER 6
Differential Forms
13
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
14 Chapter 6. Differential Forms
CHAPTER 7
The Hodge Operator
15
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
16 Chapter 7. The Hodge Operator
CHAPTER 8
The Electromagnetic Two-Form
17
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
18 Chapter 8. The Electromagnetic Two-Form
CHAPTER 9
Some Mathematics Needed for Quantum Mechanics
19
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
20 Chapter 9. Some Mathematics Needed for Quantum Mechanics
CHAPTER 10
Some Quantum Mechanical Thinking
21
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
22 Chapter 10. Some Quantum Mechanical Thinking
CHAPTER 11
Quantum Mechanics of Harmonic Oscillators
23
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
24 Chapter 11. Quantum Mechanics of Harmonic Oscillators
CHAPTER 12
Quantizing Maxwell’s Equations
25
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
26 Chapter 12. Quantizing Maxwell’s Equations
CHAPTER 13
Manifolds
27
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
28 Chapter 13. Manifolds
CHAPTER 14
Vector Bundles
29
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
30 Chapter 14. Vector Bundles
CHAPTER 15
Connections
31
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
32 Chapter 15. Connections
CHAPTER 16
Curvature
33
Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
34 Chapter 16. Curvature
CHAPTER 17
Maxwell via Connections and Curvature
35