PHY321 Electrodynamics - Spring Semester 2019

Language

Lecture and exercises in English.

Main topics

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

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, 118 KB) 27.03.2019 29.03.2019 Solution 4 (PDF, 167 KB)
Exercise sheet 5 (PDF, 294 KB) Praesenzuebung 22.03.2019 29.03.2019 Solution 5 (PDF, 125 KB)
Exercise sheet 6 (PDF, 98 KB) 03.04.2019 05.04.2019 Solution 6 (PDF, 119 KB)
Exercise sheet 7 (PDF, 156 KB) 10.04.2019 12.042019 Solution 7 (PDF, 308 KB)
Exercise sheet 8 (PDF, 94 KB) 08.05.2019 10.05.2019 Solution 8 (PDF, 151 KB)
Exercise sheet 9 (PDF, 155 KB) Praesenzuebung 03.05.2019 10.05.2019 Solution 9 (PDF, 135 KB)
Exercise sheet 10 (PDF, 137 KB) 15.05.2019 17.05.2019 Solution 10 (PDF, 129 KB)
Exercise sheet 11 (PDF, 148 KB) 22.05.2019 24.05.2019 Solution 11 (PDF, 129 KB)

Exercise sheet 12 (PDF, 124 KB)

29.05.2019 31.05.2019 Solution 12 (PDF, 145 KB)

Exam FS18 (PDF, 198 KB)

     

 

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, 1474 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, 1243 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; Solenoid; Magnetic multipole expansion; dipole moment  (Nolting 3.2.3, 3.3.1) (script 64-69)

script 71-80 (PDF, 1240 KB)
Fri 29.3..19

Dipole moment; magnetic force and torque on a confined current distribution (Nolting 3.3); Magnetostatics in matter: magnetisation, microscopic currents (Nolting 3.4.1) (script 69-74)   

 
Wed 3.4.19 Magnetostatics in matter: magnetic field H, Maxwell equations, classification  of magnetic materials, behaviour at interfaces  (Nolting 3.4.1-3.4.3); (script 75-78) script 81-90 (PDF, 1248 KB)
Fri 5.4.19

Boundary-value magnetostatic problems (Nolting 3.4.4); 

4. Electrodynamics: Faraday law ; Maxwell displacement current; (Nolting 4.1.1-2) (script 78-84) 

 
Wed 10.4.19

Maxwell's equations in the vacuum and in matter; Electrodynamic potentials; gauge invariance; Coulomb  and Lortenz gauge (Nolting 4.1.1-3); Green function of wave equation, spherical wave solutions  (Jackson 6.6; see also Nolting 4.3.5. 4.3.7) (script 85-93)

script 91-103 (PDF, 1331 KB)
Fri 12.4.19 Electromagnetic field energy; Pointing vector;  field momentum; Maxwell stress tensor (Nolting 4.1.4-5); 

(script 94--98)

 
Wed 17.4.19

Quasi-stationary fields: induction and self-induction, magnetic field energy, alternating currents (Nolting 4.2.1-3)

5. Relativistic formulation of electrodynamics. Coordinate transformations: contravariant and covariant vectors,
tensors, metric tensor. (see Jackson 11.7) (script 99-106)

script 104-112 (PDF, 866 KB)
Fri 3.5.19

Special relativity: Galilei and Lorentz transformations; light cone, proper time, time dilatation, space contraction.
(Jackson 11.1, 11.3-4) (script 106-112)

script 113-120 (PDF, 806 KB)
Wed 8.5.19

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, dual strength tensor, field invariants, Maxwell equations, (Jackson 11.1, 11.3-6, 11.9-10) (script 113- 120)

script 121-133 (PDF, 1268 KB)
Fri 10.5.19

Lorentz force (Jackson 11.9).

6. Electromagnetic waves. Wave solutions of Maxwell equations Plane waves, linear polarisation (Nolting 4.3.1-3)

(script 120-129)
 
Wed 15.5.19

Circular polarisation; Wave packets  (Nolting 4.3.3-4); Straight wave guides (Jackson 8.2); (script 129 -136) 

script 134-145 (PDF, 1267 KB)
Fri 17.5.19 Straight wave guides (Jackson 8.2-4); Retarded potentials (Jackson 12.11) (script 137 -143)  
Wed 22.5.19 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) (script 143-150 ) script 146-156 (PDF, 1210 KB)
Fri 24.5.19 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) (script 150-156)  
Wed 29.5.19

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. (script 157-163 )

script 157-171 (PDF, 1675 KB)
Fri 31.5.19

Dispersion. Lorentz oscillator model; Connection between D- and E-field; Kramers-Kronig relations (script 164-171)