Bharathiar University 2004 M.Sc Physics Electromagnetic Theory and Electrodynamics - Question Paper
Degree
(b) Define the electromagnetic field four tensor
and write its components explicitly. Stow how they can be used to write the Maxwells equathsas in eovariant form,
27. (a) Derive an expression for Thomson Cross-section in terms of classical electromapietic radius of the charge,
. Or
(b) What is normal and momolms dispersion? Derive Sellmeier's equation for the refractive index of a dielectric medium.
28. (a) Derive the equations of Telegraphy.
Or
(b) Discuss the phenomenon of total internal , reflection on the basis f electromagnetic theory. -
/ 29, (a) In a parallel plate capacitor, show that the
u / rate at which energy flow into the capacitor from the surrounding space is equal to the rate at which the stored electric energy increases. -
(i.e.) P E~.
dt
Or
(b) Show that
{i) The momentum of charge! particle in an electromagnetic field is given by
J
P=mV + A ; ' !
(ii) The Lagrangian ftmclien of the charged'' particle in an electromagnetic field is given by
30. (a) Calculate the scalar and vector functions j
which characterise the electric Mi of a dipole of ). : moment P at a position r. . 1 j
--V-
lb)- Derive m exjlue magnatic vest?r * t-O
potential and verify whether it satisfies Poissons equation. v" HP
fc
<$-
0
7
ss arti.iw1-
{For thfe candidates admitted from 2002 and onwards) . M.Sc. DEGREE EXAMINATION, APRIL 2004. Second Semester
3159
Part III Physics
Paper V ELECTROMAGNETIC THEOBY AND ELECTRODYNAMICS
Time: Three hours Maximum: 100 marks
Answer ALL questions.
SECTION A(20x1 = 20 marks)
Choose the correct answer.
1. The normal component of dielectric displacement
cross a charge free boundary.
is
(b) Continuous te ' (d) Infinite.
(a) Zero
(c) Discrete
2, Rr of half-wave antenna is
(a) 178,5 . (b) 78,5 O Cc) ' 1731 Q (d) 73.1 a. .
3, In anisotropic medium, the direction of K and S
are-.
(a) same (b) zero
(c) not same (d) infinite.
4, The electrons are bound to the-in
an atom by linear restoring force.
Ca) Nucleus (b) Protons
Cc) Hydrogen (d) Oxygen,
5, The- of light is a universal constant
iaj phase (b) amplitude. *
Cc) velocity (d)" wavelength.
Fill up the blasts : _,
6, , Maxwelji equations invariant under
transformation,
7, The factor ~ Cl ~ cos2 f) is called degree of
2
8. Electromagnetic wave are --
nature.
9. Po*er radiated by an electric---_
proportional Is the fourth power of the frequency.
10. Hi# total bound . charge m a dielectric
Match the foiowing:
11. Xt (a) Impedance of the medium
12. t (b) Scattering angle
13. Z (c) Relaxatioa time
14. # (d) Electromagnetic field tensor
15. fe> Electric sasceptibiltj.
Answer the following in 1 or 2 sentences;
18. * What is meant'by Cerenkov-radiation?
17. What is meant by Bayleigh Scattering?
18. Dtfiae currest density,
20. Define the electromagnetic field tensor.
SECTION B {5x8 30 marks)
Answer All. questions, choosing either (a) or fib),
21. (a) If in a certain region of space the electric
field vector S is given by
4*re0 V Calculate the curl of the field.
(b) Derive an expression for electric intensity,
22. (a) Deduce the equation of continuity.
Or
(b) Find the power radiated by as osrilllcmg electric dipole.
23. (a) Show that in case of plasma and saper conductors
a = i and curl J ~-as with a -
m ' m
W
Cb) A hollow rectangular wave guide has a a 6
cm and 6-4 cm, 'The frequency of the Impressed signal is 8 Gz. Compute for TEJ0 mode.
ii) Cut off wavelength (ii) Guide wavelength.
24. (a) Explain. the parameters of scattering.
Or
<b) What is meant by resonance scattering?
25. (a) Prove that the space interval x2 +y2 +22 is
not invariant under Lorentz transformation while the space-time interval x* -f- y2 +z2 -cHs is invariant.
Or': -
, \h) '"Mention the properties' of 4-vertors as-d ~... _ it with that of S-vectors,
SECTION C (5x10* SO marks)
Answer ALL questions, choosing either (a) or (b),
26 (a) Writing Maxwells equations is 4-vector form and prove that they are invariant under Lorentz traasiommiiwu.
Or
5 3159
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