FYTB13, Electromagnetism

Runs every fall (first half) and spring (second half).

Spring 2019

Intro meeting, spring 2019: Monday, March 25, at 10:15 PM, in Lecture Hall D (L315).

Links

Literature

Introduction to Electrodynamics by D. J. Griffiths

There also exists as a "Pearson new international edition" in paper-back (ISBN-10: 1-292-02142-X, ISBN-13: 978-1-292-02142-3) which however is not recommended. This is a collection of the chapters in the book, two out of three of the appendices and the pages on the inside of the cover (vector derivatives etc). It contains essentially the same material although all cross-references between chapters have been removed as each chapter is presented on its own (meaning that all chapters are presented as chapter nr 1 and that the index is a bit different than the original one). This also affects some of the problems and in fact some of them have been deleted. I will point to these cases during the course. You can find a list of corrections to this paper-back edition here. (See also the homepage of the author.)

If you get your hands on a copy of the 3rd edition that will also work.

People

• Course leader and lecturer: Johan Rathsman (johan.rathsman at thep.lu.se)
• Exercise sessions: Korinna Zapp (korinna.zapp at thep.lu.se)
• Hand-in tasks (see below): Simona Pirani
• SI sessions: Eivind Jørstad

Schedule

Entire schedule is available at Live@Lund.

Preliminary course outline, spring 2019

w. 13-14

Chpt 1: Vector Calculus: nabla (del), grad, div, curl; Gauss' and Stokes' theorems; Dirac's delta function; plane, cylindrical, and spherical coordinates.

w. 14-15

Chpt 2: Coulomb's law, Gauss' law, electric potential, work and energy, conductors and capacitors

w. 16

Chpt 3: Laplace' eqn, separation of variables, multipole expansion

w. 17

Chpt 4: Polarization, polarization field, D-field, linear dielectrics

w. 18

Chpt 5: Lorentz force, Biot-Savart, Ampère's law, vector potential

w. 19

Chpt 6: Magnetization, magnetization field, H-field, linear media

w. 20-21

Chpts 7, 8.1: Electromotive force, induction, Maxwell's eqns, Poynting's theorem,

Chpt. 9.1-9.2: Wave eqn., EM waves in vacuum.

w. 22

Chpt 9.3: EM waves in matter

Chpt 10.1: The potential formulation, gauge transformations, relativistic formulation (N.B. this is chapter 12.1 in the Pearson new international edition).

w. 23

Repetition and written exam

Lecture plan

• Lecture 1, Monday March 25: chapter 1.1.1 until 1.2.5, Handout
  Focus questions:
  • What is the meaning of gradient, curl and divergence on differential form.
• Lecture 2, Thursday March 28: chapter 1.2.6 until 1.4.1 ( will introduce spherical and cylindrical coordinates)
  Focus questions:
  • What is the meaning of the second derivatives: div grad (Laplace), curl grad, div curl? Why do some of them vanish?
  • What is the meaning of of a line, surface and volume integral?
  • What are the fundamental theorems for gradient, curl and divergence?
  • What is the physical meaning of gradient, curl and divergence.
  • How are spherical and cylindrical coordinates defined?
• Lecture 3, Tuesday April 2: chapter 1.4.1 until 1.6.2 and appendix A and B
Focus questions:
• What are the line, surface and volume elements in spherical and cylindrical coordinates?
• What are the gradient, curl, divergence and Laplace operator in spherical and cylindrical coordinates?
• How is the Dirac delta function defined?
• What is the physical meaning of the Dirac delta function? (What is the charge distribution of: a point charge, a line charge, an infinitely thin spherical or cylindrical shell?)
• To what extent is a vector field uniquely defined by its divergence and curl?
• Lecture 4, Thursday April 4: chapter 2.1 and 2.2
Focus questions:
• What is the reason for using Gauss's law instead of Coloumb's law?
• What is the superposition principle and why is it valid?
• How is Gauss's law on integral form obtained from the one on differential form?
• What is the meaning of the Coulomb-field being conservative?
• How can Gauss's law be used to calculate the electric field in spherically symmetric configurations?

Hand-in tasks

Each of the three or four hand-in tasks will be published via Canvas (L@L), and individual solutions are to be submitted as PDF via L@L, typically within six days, i.e, at the latest on the Thursday in the week after the exercise session, at 5 PM. The solutions should be written in a nice and easily readable manner, or typeset using a computer.

N.B. the bonus rules.

Exams

Exam rules: You can bring one A4-sheet of own notes. Notes on vector calculus and trigonometry will be provided. NO electronic equipment whatsoever will be allowed.

Written exam: See schedule
Registration is compulsory, via the Student Portal

Lecture notes

• 1. Vector Calculus (grad, div, curl, Gauss' and Stokes' theorems, spherical and cylindrical coordinates, delta functions)
  (Notes with various related formulas, updated April 1, 2019)
• 2. Electrostatics (Coulomb's law, Gauss' law, electric potential, work and energy, conductors and capacitors)

Problem solving sessions

Exercises

There are lots of useful problems in the book by Griffiths. Note that there are two classes of problems:

• within the text - designed to be done as you go along (but can still be quite lengthy)
• end of chapter - longer and of a more general nature

• Chpt 1: 1.4, 1.11b, 1.15, 1.18, 1.19, 1.22, 1.26d, 1.27, 1.28, 1.32c, 1.33, 1.34; 1.39, 1.41, 1.44d, 1.45c, 1.46, 1.47, 1.48, 1.49, 1.50a, 1.53
• Chpt 2: 2.2, 2.6, 2.9, 2.12, 2.13, 2.15, 2.16, 2.17, 2.18, 2.19, 2.20, 2.21, 2.24, 2.25, 2.28, 2.31, 2.34, 2.36, 2.39, 2.41, 2.43
  (3rd ed: 2.2, 2.6, 2.9, 2.12, 2.13, 2.15, 2.16, 2.17, 2.18, 2.19, 2.20, 2.21, 2.24, 2.25, 2.28, 2.31, 2.32, 2.34, 2.36, 2.37, 2.39)
• Chpt 3: 3.1, 3.2, 3.3, 3.13, 3.14, 3.18, 3.20, 3.21, 3.27, 3.29, 3.30, 3.32, 3.33, 3.34, 3.36
  (3rd ed: 3.1, 3.2, 3.3, 3.12, 3.13, 3.17, 3.19, 3.20, 3.26, 3.27, 3.28, 3.30, 3.31, 3.32, 3.33)
• Chpt 4: 4.5, 4.7, 4.8, 4.10, 4.11, 4.14, 4.15, 4.16, 4.17, 4.18, 4.19, 4.20, 4.21, 4.22, 4.23, 4.26
  (3rd ed: 4.5, 4.7, 4.8, 4.10, 4.11, 4.14, 4.15, 4.16, 4.17, 4.18, 4.19, 4.20, 4.21, 4.22, 4.23, 4.26)
• Chpt 5: 5.3, 5.5, 5.6, 5.8, 5.10a, 5.13, 5.14, 5.16, 5.17, 5.21, 5.24, 5.26a, 5.30, 5.32, 5.34, 5.37a, 5.37b, 5.38
  (3rd ed: 5.3, 5.5, 5.6, 5.8, 5.10a, 5.12, 5.13, 5.15, 5.16, 5.20, 5.23, 5.25a, 5.29, 5.31, 5.33, 5.35, 5.36, 5.60)
• Chpt 6: 6.7, 6.8, 6.9, 6.12, 6.13, 6.14, 6.16, 6.17, 6.21
  (3rd ed: 6.7, 6.8, 6.9, 6.12, 6.13, 6.14, 6.16, 6.17, 6.21 )
• Chpt 7: 7.7, 7.8, 7.12, 7.14, 7.22, 7.24, 7.28, 7.34, 7.35
  (3rd ed: 7.7, 7.8, 7.12, 7.14, 7.20, 7.22, 7.26, 7.31, 7.32)
• Chpt 8: 8.2
  (3rd ed: 8.2)
• Chpt 9: 9.2, 9.3, 9.8, 9.9, 9.12, 9.15, 9.16, 9.17, 9.18
  (3rd ed: 9.2, 9.3, 9.8, 9.9, 9.11, 9.14, 9.15, 9.16, 9.17)
• Chpt 10: 10.1, 10.3, 10.4, 10.5, 10.6
  (3rd ed: 10.1, 10.3+10.5, 10.4, 10.6, 10.7)

• Chpt 1: 1.54, 1.57 (cyl coord), 1.59, 1.61, 1.62 (3rd ed: 1.53, 1.56 (cyl coord), 1.58, 1.60, 1.61)
• Chpt 2: 2.46, 2.47, 2.48, 2.49, 2.50
  (3rd ed: 2.42, 2.43, 2.44, 2.45, 2.46)
• Chpt 3: 3.43, 3.44, 3.46, 3.47, 3.48, 3.52
  (3rd ed: 3.37, 3.38, 3.40, 3.41, 3.42, 3.45)
• Chpt 4: 4.30, 4.33, 4.35, 4.36, 4.39, 4.41
  (3rd ed: 4.30, 4.31, 4.32, 4.33, 4.36, 4.38)
• Chpt 5: 5.41, 5.48, 5.57, 5.58, 5.61
  (3rd ed: 5.39, 5.47a, 5.55, 5.56, 5.59)
• Chpt 6: 6.25, 6.26
  (3rd ed: 6.23, 6.24 )
• Chpt 7: 7.44, 7.47, 7.60
  (3rd ed: 7.42, 7.45, 7.55)
• Chpt 8: 8.13, 8.23a
  (3rd ed: 8.9, 8.15a)
• Chpt 9: 9.35, 9.39
  (3rd ed: 9.33, 9.37)
• Chpt 10: —

Old exams

Nov 2018 (and solutions)

May 2018 (and solutions)

Oct 2017 (and solutions)

May 2017 (and solutions)

Collection of some mathematical formulas that are useful for electromagnetism (updated April 1, 2019). Will be handed out at exam.

Formulas you can use without deriving them (unless asked to).

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