Lec 21 - 2. Mar
March0109 9:54 PM
Recap: a solution to
for the same boundary conditions is given by
Looks easy enough, but: Integrand has poles at 7.2.3 Evaluation of Green function integral Evaluate via Residue Theorem =>Embedding into complex pa
Electromagnetic Theory, PHYS 441B Norbert L tkenhaus u Due: Wednesday, 21. Jan 2009, 10:30 80 Points
Assignment 1
Remark: All known results from situations in Electrostatics and Magnetostatics can be used in without derivation in assignments and exa
Electromagnetic Theory, PHYS 441B Norbert L tkenhaus u Due: Wednesday, 28. Jan 2009, 10:30 110 Points
Assignment 2
Remark: All known results from situations in Electrostatics and Magnetostatics can be used in without derivation in assignments and ex
Electromagnetic Theory, PHYS 441B Norbert L tkenhaus u Due: Wednesday, 4. February 2009, 10:30 90 Points + 20 Bonus points
Assignment 3
Remark: All known results from situations in Electrostatics and Magnetostatics can be used in without derivation
Electromagnetic Theory, PHYS 441B Norbert L tkenhaus u Due: Wednesday, 11. February 2009, 10:30 100 Points
Assignment 4
Remark: All known results from situations in Electrostatics and Magnetostatics can be used in without derivation in assignments a
Electromagnetic Theory, PHYS 441B Due: Wednesday, 4.March 2009, 10:30 100 Points
Assignment 5
Remark: All known results from situations in Electrostatics and Magnetostatics can be used in without derivation in assignments and exams. Problem 1: Consi
Electromagnetic Theory, PHYS 441B Due: Wednesday, 11.March 2009, 10:30 100 Points
Assignment 6
Problem 1: Wave packet propagation
Use your favorite math program (Maple, Mathematica, Matlab) to make a wave packet simulation in one dimension. Choose a
Electromagnetic Theory, PHYS 441B Due: Wednesday, 18.March 2009, 10:30 90 Points
Assignment 7
Remark: All known results from situations in Electrostatics and Magnetostatics can be used in without derivation in assignments and exams. Problem 1: Griff
Electromagnetic Theory, PHYS 441B Due: Wednesday, 25.March 2009, 10:30 100 Points
Assignment 8
Remark: All known results from situations in Electrostatics and Magnetostatics can be used in without derivation in assignments and exams. Problem 1: Grif
L31 - 31. Mar
March3008 9:37 PM
9. Macroscopic Maxwell Equations
9.1 Microscopic Maxwell Equations e and b are exact fields! charge distribution current distribution due to electrons/protons in matter
9.2 Maxwell Equations in averaged form (Jackson
Lec 30 - 23. Mar
March1709
8.7.5 Recovering Maxwell's Equations 8.7.5.1 Inhomogeneous Equations Evaluate:
Result:
gauge condition
8.7.5.2 Homogeneous Equations Define dual Field tensor
if any indices are identical even permutation of odd permutat
Lec 22 - 4. Mar
March0409 9:54 PM
7.3 Application to Electrodynamics
7.3.1 Formal solution Lorentz Gauge
Solutions:
Note: If gauge condition is fulfilled initially, it is also fulfilled at later times. 7.3.2 Causality Structure of Electrodynamics
Lec 23 - 6. Mar
January2908 9:54 PM
7.4.2 Multipole Expansion 7.4.2.1 Reminder: Multipole Expansion in Magnetostatics
multipole expansion for fields sufficiently far from the source area
magn. monopole
magn. dipole
magn. quadrupole
7.4.2.2 Mult
Lec 24 - 9. Mar
March0809 10:54 PM
Recap: Electric Dipole Radiation Magnetic field
Electric field Outside source area:
Scaling: Two independent length scales
1) Source dimension d Multipole expansion requires 2) Second length scale from field dist
Lec 25 - 11. Mar
March1608 8:32 PM
7.6 Solutions for moving point charge 7.6.1 Problem description Setting: point charge charge trajectory
(parameterized by time t)
Non-trivial calculation! Here: calculate follows along similar lines 7.6.2 Lienard
Lec 26 - 13. Mar
March1209 9:32 PM
Recap:
acceleration
7.6.4 Power radiated by moving point charge (Griffith 11.2) assume: point charge initially at origin initially at rest => calculate power radiated through sphere of radius r at time => radiati
Lec -15. Mar
March1509 1:38 PM
8. Relativistic Formulation of Electrodynamics
8.1 Four-vector notation for Lorentz transformation space-time coordinate vector Lorentz Boost in direction
with matrix
index notation
Inverse: exchange General Lorentz
Lec 28 - 18. Mar
March1709 9:28 PM
8.4 General transformation rules
Matrix translation rules: - use free reordering of index notation - use transposition, e.g. remember: first index is row index second index column vector (upper or lower position i
Lec 29 - 20. Mar
8.7 Electrodynamics in relativistic formulation 4-vector current 4-vector potential Gauge condition: and
March1709
Continuity equation With the previous subsections, we finished the relativistic formulation of Electrodynamics. Th
Electromagnetic Theory, PHYS 441B Due: Wednesday, 1.April 2009, 10:30 80 Points
Assignment 9
Remark: All known results from situations in Electrostatics and Magnetostatics can be used in without derivation in assignments and exams. Problem 1: Griffi
Formula Sheet
J = E (Ohm's law)
d E = - dt (flux rule)
= M I (self-inductance M) 0 d 1 dl M12 = 4 S1 S2 |rl1 -r2 (mutual inductance) 2
= - J (conservation t (umech + uem ) = - S t (p + pem ) = T t mech
laws)
1 S = 0 E B (Poynting vecto
Lec 13 - 04. Feb
February0309 9:54 PM
5.5 Complex notation for real fields 5.5.1 Definitions are real fields over => can still start from complex solutions of differential equations => use free parameters to enforce real valued solutions or => use c
Lec 14 - 08. Feb
January2908 9:54 PM
5.5 Polarization The vector component of these solutions gives rise to the polarization as
polarization
spectral decomposition
One spectral component:
with 5.5.1 Linear Polarization
linear polarization: dire
Lec 15 - 11. Feb
February0909 9:54 PM
Recap: boundary conditions
surface charges
surface current Special case Region 1: ideal conductor (freely flowing charges equalize all charges)
typically: superconductor: always
(surface charge)
Lecture Not
Lec 17 - 13. Feb
February1309 9:54 PM
with dispersion relation Note: solution with n=0 OR m=0 excluded! Why? As also => would lead to TEM modes and TEM modes do not exist here
6.3.3 Interpretation of solutions via plane waves: Note: extended soluti
Lec 18 - 23. Feb
6.5 Dispersion relation, Phase & Group velocities of waves 6.5.1 Dispersion relation consider in z=direction suppress x,y dependence plane waves in free space wave guides
monochromatic wave in z-direction wave solution in z-direc
Lec 19 - 25. Feb
February2509 9:54 PM
Recap: Dispersion relation: free space: rectangular wave guide: Phase velocity:
Group velocity for wave packet centered at 3-dim formulation 6.6 Energy transport in wave guides time dependence of TM mode for
Lec 20 - 5. Mar
January2908 9:54 PM
7. Solution to Maxwell's Eqns for arbitrary sources
arbitrary current charges find
=> Greens function Note, Griffith does not follow this approach, but uses the result! Derivation via Green functions is a good mo