The course will consist of 35 lectures at the rate of 2 lectures per
week. If no lecture days are "lost", the course will end around mid-Dec.
If days were "lost" there will be extra lectures on some weeks, so as
to still finish the course by mid-Dec.
The syllabus for the course
and a reading list of books are available. The lectures will NOT redo
material which you should have mastered in M.Sc but will emphasize:
(i) more advanced topics (ii) astrophysical applications
(iii) conceptual issues
and (iv) topics which are not usually discussed in detail in M.Sc.
A "self-test" is available to give you
an idea of the background knowledge expected from you. You should be able to answer most of
the questions in that set. If you run into problems, let me know.
Note that this set is not an assignment; you dont have to do
the problems and submit it ! It is only to give you an idea of
the required background.
There will be 4 assignment sets, one mid-term review and one final
examination as a part of the course. The assignments will be given
to you at the end of
3rd, 6th, 12th and 15th weeks and are to be returned in 2 weeks time.
The midterm review will be at the end of 9th week and final exam in
the 3rd week of December. The form of the midterm review and final exam
will be decided in the class based on the inputs received from you. The
default procedure is an open book-take home exam of 8 hour duration for
midterm and closed book-in situ 3 hour exam for the finals. Unless I get
some sensible, serious, alternative suggestions I will follow this procedure.
The evaluation procedure is the following: (a) If you score less than
50% in the final exam, you will fail the course irrespective of how well
you have done in other components. (b) Your final average grade is computed giving 20% weightage to final exam, 20% to the mid-term review and 60% to the assignments. You also need to score a minimum of 50% in the average grade
to pass the course. (c) Your final grade for the course will be the average
grade computed in (b) above.
These are denoted by the abbreviations L2,F1,F2,B2,B3,TP; the parts of the course for which
each of the texts may be relevant is indicated next to the topic in the
syllabus.
Note:
The number [n] near a topic indicates that it will be covered in the
n-th lecture. Abbreviations like L2, B2 etc. refer to textbooks in the
Reading List which could be relevant for the particular topic.
Basics and introduction [1]
classical fields: gravity and electromagnetism.
field of a charged particle; superposition.
concept of a field vs action-at-a-distance.
electromagnetism and relativity.
Special relativity - overview [1,2][L2]
Lorentz transformation and four-vectors.
invariant interval, proper time, four-velcity etc.
four-dimensional integration etc.
action for a free particle, hamiltonian, relativistic dynamics.
Electromagnetic coupling [3,4,5][L2,B2,F1,F2]
coupling of charge and field; generalised momenta.
equation of motion: definition of F_{ab}, E , B, two Maxwell's equations.
Lorentz tranformation of fields; examples; invariants.
gaugue invariance, current four-vector, conservation of charge.
reality of potential/field; Aharanov-Bohm effect.
Motion of charged particles in EM fields [5,6,7][L2]
constant, uniform fields
variable fields:
adiabatic invariants.
guiding center.
Larmor's theorem
astrophysical examples
Dynamics of the EM field [8,9,10][F2,L2]
examples of field energy, momentum, angular momentum.
action for the EM field; second pair of Maxwell's equations.
general properties of Maxwell's equations:
absence of magnetic charge
need for ``displacement current''
two views of Faraday's law
dynamics, initial conditions
fourier representation
Energy-momentum tensor of EM field [11][F2,L2]
derivation and properties;
examples of energy flow
momentum and angular momentum of relativistic systems
Electrostatics and magnetostatics [12,13][F2,L2]
multipole expansion, field of a uniformly moving charge
Debye shielding in a plasma [analogy with KG equation]
currents and current loops
Wave solutions [14,15][F2,L2,B3]
plane waves, spherical waves, boundary conditions
energy, momentum, angular momentum and radiation pressure
geometrical optics limit
polarisation
Radiation of EM waves [16,17,18][F2,L2,B3]
example: field of a current sheet
radiation from a point charge
Feynman formula for radiation
angular distribution, relativistic beaming
spectral distribution
oscillating charges and QM
examples: origin of refractive index, plasma frequency
A "self-test" of problems in electrodynamics is available in the form of
a PS file. You can download/view this by clicking
here.
The questions in this ``self-test'' are based on standard Electromagnetic Theory Courses at M.Sc level which you should be familiar with. Go through the questions, mentally checking whether you know the answer; when in doubt, try working out the answer explicitly. Some questions require knowledge of a certain ``standard'' formula. You are, of course, expected to look up these formula in the usual textbooks.
If you find majority of these questions nontrivial please let me know.
You need not turn in the solutions to these problems.