PHY321 Electrodynamics - Spring Semester 2019

Language

Lecture and exercises in English.

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: "Elektrodynamik")

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

Lecture notes:

  • Hand-written (informal) lecture notes will be made available week by week (each Tuesday morning) on this webpage.

 

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
  • Participation to 2 "Präsenzübungen" (2 to 4 exercise sessions take place in the form of "Präsenzübungen") 
  • Pass the exam

 

Final exam

Date and place: Thursday July 11, 2019, 09:00 – 12:00 Y24-G-45

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:  

Format of the exam:  

Organisation

Lecture

Exercises

  • Friday 08:00 - 09:45

Organisation of exercises

  • First exercise class on Fri Feb 22
    • Takes place in Y23-G-04 for everybody
    • Group assignments
    • Repetition of basic vector calculus (unmarked but important)
  • Exercise sheets 1-12:
    • Available online on Thursday of week n at 12:00 (starting on Feb 21)
    • Hints on Friday of week n (starting Feb 22) in the exercise classes
    • Solution to be handed in on Wednesday of week n+1 (starting Feb 27) into the box marked "Uebungen" in front of Y36-K-42
    • Discussion of solutions on Friday of week n+1 (starting on Mar 01)
    • Solutions can be handed in in groups of two students

Investing a significant amount of time for solving the exercises during the semester is crucial for the understanding of the lecture and plays a very important role as a preparation for the written exam!

Series To be handed in by Discussed on Solution
Exercise sheet 0 (PDF, 131 KB) --- 22.02.2019 Solution 0 (PDF, 708 KB)
Exercise sheet 1 (PDF, 94 KB) 27.02.2019 01.03.2019 Solution 1 (PDF, 220 KB)
Exercise sheet 2 (PDF, 149 KB) 06.03.2019 08.03.2019 Solution 2 (PDF, 177 KB)
Exercise sheet 3 (PDF, 149 KB) 13.03.2019 15.03.2019 Solution 3 (PDF, 150 KB)
Exercise sheet 4 (PDF, 117 KB) 27.03.2019 29.03.2019  
Exercise sheet 5 (PDF, 302 KB) Praesenzuebung 22.03.2019 29.03.2019  
Exercise sheet 6 03.04.2019 05.04.2019  
Exercise sheet 7 10.04.2019 12.042019  
Exercise sheet 8 08.05.2019 10.05.2019  
Exercise sheet 9 Praesenzuebung 03.05.2019 10.05.2019  
Exercise sheet 10 15.05.2019 17.05.2019  
Exercise sheet 11 22.05.2019 24.05.2019  

Exercise sheet 12

29.05.2019 31.05.2019  

 

Lectures

Date Topic Script
Wed 20.02.19
  1. Introduction: Generalities; units 
  2. Electrostatics: Coulomb law; E-field and potential (Nolting 2.1.1-2) (script 1-9)
script 1-17 (PDF, 1611 KB)
Fri 22.02.19

Gauss and Stokes theorems; Maxwell equations of electrostatics in differential and integral form; Poisson equation; E-field at interfaces;  (Nolting 1.5.1-2 & 2.1.2-4) (script 10-16)

 
Wed 27.02.19 cartesian multipole expansion (Nolting 2.2.4; 2.2.6-7); Spherical coordinates; (script 17-21) script 18-36 (PDF, 1853 KB)
Fri 1.3.19

Spherical multipole expansion (Nolting 2.3.8);

Formulation of general Boundary value problems (Nolting 2.3.1-2); 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); (script 22-31)

 
Wed 6.3.19 Method of image charges (Nolting 2.3.4); (script 32-36) script 37-48 (PDF, 1089 KB)
Fri 8.3.19 Seperation of variables (Nolting 2.3.6); Electrostatic field energy (Nolting 2.1.5);  (script 37-44)  
Wed 13.3.19 Electrostatic field energy (Nolting 2.1.5); Capacitors (Kroeger/Unbehauen 5.6);  (script 44-49) script 49-60 (PDF, 1488 KB)
Fri 15.3.19 Microscopic and macroscopic fields in Dielectrics (Nolting 2.4.1); Maxwell equations, field-behaviour at interfaces in dielectrics (Nolting  2.4.1, 2.4.3) (script 50-55)  
Wed 20.3.19

Field energy in dielectrics (2.4.3);

3. Magnetostatics:  Electric currents, continuity, thread of current (Nolting 3.1); (script 55-59)

script 61-70 (PDF, 1229 KB)
Fri 22.3.19 Ohm's law, electric power (Nolting 3.1); Ampere law; Magnetic field, Biot-Savart law; Lorentz force, torque; parallel wires (Nolting 3.2.1); (script 59-64)  
Wed 27.3.19 vector potential; gauge invariance; Maxwell equations of magnetostatics  (Nolting 3.2.3)...  
Fri 29.3..19 Solenoid; Magnetic multipole expansion; dipole moment; magnetic force and torque on a confined current distribution (Nolting 3.3)     
Wed 3.4.19 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)  
Fri 5.4.19

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)  

 
Wed 10.4.19 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)  
Fri 12.4.19 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)  
Wed 17.4.19 Maxwell stress tensor (Nolting 4.1.5); Quasi-stationary fields: induction and self-induction, magnetic field energy, alternating currents (Nolting 4.2.1-3)  
Fri 3.5.19 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) 
 
Wed 8.5.19 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)
 
Fri 10.5.19

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)

 
Wed 15.5.19 Plane transverse waves, linear polarisation  (Nolting 4.3.2-3)  
Fri 17.5.19 circular polarisation; Wave packets  (Nolting 4.3.3-4); Straight wave guides (Jackson 8.2);   
Wed 22.5.19 Straight wave guides (Jackson 8.2-4); Retarded potentials (Jackson 12.11)  
Fri 24.5.19 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)  
Wed 29.5.19

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)

 
Fri 31.5.19 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.  
 

Dispersion. Lorentz oscillator model;

(Connection between D- and E-field; Kramers-Kronig relations)