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Electricity and Magnetism forMathemacians: Exercises Solutions
DocumentationRelease 0.0
Nathan Musoke, Dario Brooks, Mohammad Kidwai
September 07, 2016
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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
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Electricity and Magnetism for Mathemacians: Exercises Solutions Documentation, Release 0.0
2 Contents
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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
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4 Chapter 1. Maxwell’s Equations
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CHAPTER 2
Electromagnetic Waves
5
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6 Chapter 2. Electromagnetic Waves
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CHAPTER 3
Mechanics and Maxwell’s Equations
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8 Chapter 3. Mechanics and Maxwell’s Equations
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CHAPTER 4
Potentials
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CHAPTER 5
Lagrangians and Electromagnetic Forces
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12 Chapter 5. Lagrangians and Electromagnetic Forces
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CHAPTER 6
Differential Forms
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CHAPTER 7
The Hodge Operator
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CHAPTER 8
The Electromagnetic Two-Form
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CHAPTER 9
Some Mathematics Needed for Quantum Mechanics
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CHAPTER 10
Some Quantum Mechanical Thinking
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CHAPTER 11
Quantum Mechanics of Harmonic Oscillators
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CHAPTER 12
Quantizing Maxwell’s Equations
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CHAPTER 13
Manifolds
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CHAPTER 14
Vector Bundles
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CHAPTER 15
Connections
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CHAPTER 16
Curvature
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CHAPTER 17
Maxwell via Connections and Curvature
35