PHY321 Electrodynamics - Spring Semester 2018

Main topics

  • Electrostatics
  • Magnetostatics
  • Electrodynamics
  • Relativistic formulation
  • Electromagnetic waves
  • Wave optics

Recommended Literature

Main textbook:

  • W. Nolting: "Grundkurs Theoretische Physik 3: Elektrodynamik"

For selected topics:

  • J.D. Jackson: "Classical Electrodynamics"
  • R. Kroeger and R. Unbehauen: "Elektrodynamic"

It is highly recommended to read the "mathematical preparations" in Chapter 1 of Nolting's book.

Language

Lecture and exercise in English.

Organisation

Lecture

Exercises

  • Thursday 08:00 - 09:45

Module Requirements (Testatbedingungen)

In order to pass the module each of the following requirements must be met:

  • 50% of the points of exercise sheets 1 to 12
  • 33% of the points of exercise sheets 1 to 6 and 33% of the points of exercise sheet 7 to 12
  • Pass the exam (date to be fixed between July 9-13)

 

Final exam

Date:  July 12, 2018, 09:00 – 12:00, Y15-G-20

Allowed collection of formulas:  3 handwritten double-sided A4 pages or 2 double-sided A4 pages in Latex. Only your personal Latex formulas are allowed, i.e. it is not allowed to include external PDF files of figures in a Latex document.

Allowed tools: standard pocket calculator without data storage and internet connection. No other electronic devices are allowed.

 

Repetition exam

Date:  September 11, 2018, 09:00 – 12:00, Y16-G-15

Format of the exam:  

  • 60 min written part: same format (short questions and problems) and same rules as for the exam of July 12 (see above).
  • 30 min oral part (individual). The oral part is going to be focussed on the knowledge of the main theoretical aspects of the lecture, the corresponding formulas, the essential aspects of their derivation, as well as their physical interpretation and simple applications.

The exact (personalised) schedule will be communicated in due time.

 

Organisation of exercises

  • First exercise class on Thu Feb 22
    • Takes place in Y16-G-05 for everybody
    • Group assignments
    • Repetition of basic vector calculus (unmarked but important)
  • Exercise sheets 1-12:
    • Available online on Wednesday of week n (starting on Feb 21)
    • Hints on Thursday of week n (starting Feb 22) in the exercise classes
    • Solution to be handed in on Tuesday of week n+1 (starting Feb 27) into the box marked "Uebungen" in front of Y36-K-42
    • Discussion of solutions on Thursday of week n+1 (starting on Thu Mar 01)
    • Solutions can be handed in in groups of two students.

The exercises play a crucial role for the understanding of the lecture!

Series To be handed in by Discussed on Solution
Exercise sheet 0 (PDF, 127 KB) --- 22.02.2018 Solution 0 (PDF, 708 KB)
Exercise sheet 1 (PDF, 98 KB) 27.02.2018 01.03.2018 Solution 1 (PDF, 213 KB)
Exercise sheet 2 (PDF, 149 KB) 06.03.2018 08.03.2018 Solution 2 (PDF, 158 KB)
Exercise sheet 3 (PDF, 141 KB) 13.03.2018 15.03.2018 Solution 3 (PDF, 168 KB)
Exercise sheet 4 (PDF, 154 KB) 20.03.2018 22.03.2018 Solution 4 (PDF, 164 KB)
Exercise sheet 5 (PDF, 129 KB) 27.03.2018 29.03.2018 Solution 5 (PDF, 103 KB)
Exercise sheet 6 (PDF, 134 KB) 10.04.2018 12.042018 Solution 6 (PDF, 151 KB)
Exercise sheet 7 (PDF, 123 KB) 17.04.2018 19.04.2018 Solution 7 (PDF, 127 KB)
Exercise sheet 8 (PDF, 107 KB) 24.04.2018 26.04.2018 Solution 8 (PDF, 159 KB)
Exercise sheet 9 (PDF, 135 KB) 02.05.2018 (12 noon) 03.05.2018 Solution 9 (PDF, 127 KB)
Exercise sheet 10 (PDF, 171 KB) 08.05.2018 10.05.2018 Solution 10 (PDF, 198 KB)
Exercise sheet 11 (PDF, 170 KB) 17.05.2018 17.05.2018 Solution 11 (PDF, 144 KB)
Exercise sheet 12 (PDF, 124 KB) 29.05.2018 31.05.2018 Solution 12 (PDF, 139 KB)
Exam (PDF, 194 KB) 12.07.2018 12.07.2018 Solution Exam (PDF, 163 KB)

 

Lectures

Date Topic
21.02.18
  1. Introduction: Generalities; units 
  2. Electrostatics: Coulomb law; E-field (Nolting 2.1.1-2)
23.02.18

Electric potential; Gauss and Stokes theorems;

Maxwell equations of electrostatics in differential and integral form

(Nolting 1.5.1-2 & 2.1.2-3)

28.02.18 Poisson equation; E-field at interfaces; cartesian multipole expansion (Nolting 2.1.3-4; 2.2.4; 2.2.6-7) 
2.3.18 Spherical multipole expansion (Nolting 2.3.8); Formulation of general Boundary value problems (Nolting 2.3.1-2)
7.3.18 Existence and uniqueness of solution (Nolting 2.3.1-2); Green theorems (Nolting 1.5.3); Green function; formal solution of Dirichlet/Neumann problems (Nolting 2.3.3)
9.3.18 Method of image charges (Nolting 2.3.4)
14.3.18 Seperation of variables (Nolting 2.3.6); Electrostatic field energy (Nolting 2.1.5)
16.3.18 Capacitors (Kroeger/Unbehauen 5.6); Microscopic and macroscopic fields in Dielectrics (Nolting 2.4.1)
21.3.18 Maxwell equations, field-behaviour at interfaces and field energy in dielectrics (Nolting  2.4.1, 2.4.3)
23.3.18 3. Magnetostatics:  Electric currents, continuity, Ohm's law, thread of current, electric power (Nolting 3.1); Ampere law, Magnetic field, Biot-Savart law (Nolting 3.2.1)
28.3.18 Biot-Savart law for current distributions; Lotentz force, torque; vector potential; gauge invariance; Maxwell equations of magnetostatics  (Nolting 3.2.1-3.2.3)
11.4.18 Solenoid; Magnetic multipole expansion; dipole moment; magnetic force and torque on a confined current distribution (Nolting 3.3)   
13.4.18 Magnetostatics in matter: magnetisation, microscopic currents, magnetic field H, Maxwell equations, classification  of magnetic materials, behaviour at interfaces  (Nolting 3.4.1-3.4.3)
18.4.18

Boundary-value magnetostatic problems (Nolting 3.4.4); 

4. Electrodynamics: Faraday law ; Maxwell displacement current; Maxwell's equations in the vacuum (Nolting 4.1.1-2)  

20.4.18 Maxwell equations. in matter; Electrodynamic potentials; gauge invariance; Coulomb gauge; Lortenz gauge (Nolting 4.1.2-3); Green function of wave equation  (Jackson 6.6; see also Nolting 4.3.5. 4.3.7)
25.4.18 Spherical wave solutions (Jackson 6.6; see also Nolting 4.3.5. 4.3.7); Electromagnetic field energy; Pointing vector;  field momentum (Nolting 4.1.4-5)
27.4.18 Maxwell stress tensor (Nolting 4.1.5); Quasi-stationary fields: induction and self-induction, magnetic field energy, alternating currents (Nolting 4.2.1-3)
2.5.18 5. Relativistic formulation of electrodynamics. Coordinate transformations: contravariant and covariant vectors,
tensors, metric tensor. Special relativity: Galilei and Lorentz transformations (Jackson 11.1, 11.3-6, 11.9-10) 
4.5.18 Light cone, proper time, time dilatation, space contraction,
relativistic 4-velocity, 4-momentum and force. Relativistic electrodynamics: current 4-vector, 4-potential, wave
equation, field-strength tensor, Lorentz transformation of E- and B-fields (Jackson 11.1, 11.3-6, 11.9-10)
9.5.18

Dual strength tensor, field invariants, Maxwell equations, Lorentz force (Jackson 11.1, 11.3-6, 11.9-10).

6. Electromagnetic waves. Wave solutions of Maxwell equations Plane waves (Nolting 4.3.1)

11.5 Plane transverse waves, linear polarisation  (Nolting 4.3.2-3)
16.5 circular polarisation; Wave packets  (Nolting 4.3.3-4); Straight wave guides (Jackson 8.2); 
18.5 Straight wave guides (Jackson 8.2-4); Retarded potentials (Jackson 12.11)
23.5 Radiation of a moving point charge: Lienard-Wiechert potentials; E- and B-fields,  Poynting vector, radiation power  (Jackson 14.1-3; see also Nolting 4.5.5)
25.5

Bremsstrahlung; synchrotron radiation  (Jackson 14.1-3; see also Nolting 4.5.5); Hertz dipole (Jackson 9.1-2, 9.4; see also Nolting 4.5.2-3)

30.5 7. Electromagnetic waves in matter. Wave equations in metal (Nolting 4.3.9) and insulators (Nolting 4.3.10). Reflection and refraction. Energy transport in different media.
1.6

Dispersion. Lorentz oscillator model;

(Connection between D- and E-field; Kramers-Kronig relations) (PDF, 332 KB)