Lent Term, 2015
Electromagnetism
University of Cambridge Part IB Mathematical Tripos
David Tong
Department of Applied Mathematics and Theoretical Physics,
Centre for Mathematical Sciences,
Wilberforce Road,
Cambridge, CB3 OBA, UK
http://www.damtp.cam.ac.uk/user/tong/em.html
, Maxwell Equations
ρ
∇·E=
ϵ0
∇·B=0
∂B
∇×E=−
∂t
∂E
∇ × B = µ0 J + ϵ0
∂t
–1–
,Recommended Books and Resources
There is more or less a well established route to teaching electromagnetism. A number
of good books follow this.
• David J. Griffiths, “Introduction to Electrodynamics”
A superb book. The explanations are clear and simple. It doesn’t cover quite as much
as we’ll need for these lectures, but if you’re looking for a book to cover the basics then
this is the first one to look at.
• Edward M. Purcell and David J. Morin “Electricity and Magnetism”
Another excellent book to start with. It has somewhat more detail in places than
Griffiths, but the beginning of the book explains both electromagnetism and vector
calculus in an intertwined fashion. If you need some help with vector calculus basics,
this would be a good place to turn. If not, you’ll need to spend some time disentangling
the two topics.
• J. David Jackson, “Classical Electrodynamics”
The most canonical of physics textbooks. This is probably the one book you can find
on every professional physicist’s shelf, whether string theorist or biophysicist. It will
see you through this course and next year’s course. The problems are famously hard.
But it does have div, grad and curl in polar coordinates on the inside cover.
• A. Zangwill, “Modern Electrodynamics”
A great book. It is essentially a more modern and more friendly version of Jackson.
• Feynman, Leighton and Sands, “The Feynman Lectures on Physics, Volume II”
Feynman’s famous lectures on physics are something of a mixed bag. Some explanations
are wonderfully original, but others can be a little too slick to be helpful. And much of
the material comes across as old-fashioned. Volume two covers electromagnetism and,
in my opinion, is the best of the three.
A number of excellent lecture notes, including the Feynman lectures, are available
on the web. Links can be found on the course webpage:
http://www.damtp.cam.ac.uk/user/tong/em.html
–2–
, Contents
1. Introduction 1
1.1 Charge and Current 2
1.1.1 The Conservation Law 4
1.2 Forces and Fields 4
1.2.1 The Maxwell Equations 6
2. Electrostatics 8
2.1 Gauss’ Law 8
2.1.1 The Coulomb Force 9
2.1.2 A Uniform Sphere 11
2.1.3 Line Charges 12
2.1.4 Surface Charges and Discontinuities 13
2.2 The Electrostatic Potential 16
2.2.1 The Point Charge 17
2.2.2 The Dipole 19
2.2.3 General Charge Distributions 20
2.2.4 Field Lines 23
2.2.5 Electrostatic Equilibrium 24
2.3 Electrostatic Energy 25
2.3.1 The Energy of a Point Particle 27
2.3.2 The Force Between Electric Dipoles 29
2.4 Conductors 30
2.4.1 Capacitors 32
2.4.2 Boundary Value Problems 33
2.4.3 Method of Images 35
2.4.4 Many many more problems 37
2.4.5 A History of Electrostatics 39
3. Magnetostatics 41
3.1 Ampère’s Law 42
3.1.1 A Long Straight Wire 42
3.1.2 Surface Currents and Discontinuities 43
3.2 The Vector Potential 46
3.2.1 Magnetic Monopoles 47
–3–
Electromagnetism
University of Cambridge Part IB Mathematical Tripos
David Tong
Department of Applied Mathematics and Theoretical Physics,
Centre for Mathematical Sciences,
Wilberforce Road,
Cambridge, CB3 OBA, UK
http://www.damtp.cam.ac.uk/user/tong/em.html
, Maxwell Equations
ρ
∇·E=
ϵ0
∇·B=0
∂B
∇×E=−
∂t
∂E
∇ × B = µ0 J + ϵ0
∂t
–1–
,Recommended Books and Resources
There is more or less a well established route to teaching electromagnetism. A number
of good books follow this.
• David J. Griffiths, “Introduction to Electrodynamics”
A superb book. The explanations are clear and simple. It doesn’t cover quite as much
as we’ll need for these lectures, but if you’re looking for a book to cover the basics then
this is the first one to look at.
• Edward M. Purcell and David J. Morin “Electricity and Magnetism”
Another excellent book to start with. It has somewhat more detail in places than
Griffiths, but the beginning of the book explains both electromagnetism and vector
calculus in an intertwined fashion. If you need some help with vector calculus basics,
this would be a good place to turn. If not, you’ll need to spend some time disentangling
the two topics.
• J. David Jackson, “Classical Electrodynamics”
The most canonical of physics textbooks. This is probably the one book you can find
on every professional physicist’s shelf, whether string theorist or biophysicist. It will
see you through this course and next year’s course. The problems are famously hard.
But it does have div, grad and curl in polar coordinates on the inside cover.
• A. Zangwill, “Modern Electrodynamics”
A great book. It is essentially a more modern and more friendly version of Jackson.
• Feynman, Leighton and Sands, “The Feynman Lectures on Physics, Volume II”
Feynman’s famous lectures on physics are something of a mixed bag. Some explanations
are wonderfully original, but others can be a little too slick to be helpful. And much of
the material comes across as old-fashioned. Volume two covers electromagnetism and,
in my opinion, is the best of the three.
A number of excellent lecture notes, including the Feynman lectures, are available
on the web. Links can be found on the course webpage:
http://www.damtp.cam.ac.uk/user/tong/em.html
–2–
, Contents
1. Introduction 1
1.1 Charge and Current 2
1.1.1 The Conservation Law 4
1.2 Forces and Fields 4
1.2.1 The Maxwell Equations 6
2. Electrostatics 8
2.1 Gauss’ Law 8
2.1.1 The Coulomb Force 9
2.1.2 A Uniform Sphere 11
2.1.3 Line Charges 12
2.1.4 Surface Charges and Discontinuities 13
2.2 The Electrostatic Potential 16
2.2.1 The Point Charge 17
2.2.2 The Dipole 19
2.2.3 General Charge Distributions 20
2.2.4 Field Lines 23
2.2.5 Electrostatic Equilibrium 24
2.3 Electrostatic Energy 25
2.3.1 The Energy of a Point Particle 27
2.3.2 The Force Between Electric Dipoles 29
2.4 Conductors 30
2.4.1 Capacitors 32
2.4.2 Boundary Value Problems 33
2.4.3 Method of Images 35
2.4.4 Many many more problems 37
2.4.5 A History of Electrostatics 39
3. Magnetostatics 41
3.1 Ampère’s Law 42
3.1.1 A Long Straight Wire 42
3.1.2 Surface Currents and Discontinuities 43
3.2 The Vector Potential 46
3.2.1 Magnetic Monopoles 47
–3–
