PHYSICS MAGADH UNIVERSITY QUESTION POST- GRADUATE

PHYSICS MAGADH UNIVERSITY QUESTION POST- GRADUATE 

                                                                              2015-2017
                                                                          Time: 3 hours
                                                                         Full Marks: 80
                                           Candidates are required to give their answers in
                                                 their own words as far as practicable.
                                                     The questions are of equal value.

                                             Answer five questions, selecting two from each
                                                 Group , in which Q. No. 1 is compulsory.

1. Answer any four questions:
   (a). Explain Lorentz transformation as orthogonal transformation.
   (b). What is Lienard- Wiechert potential?
   (c). Explain principle of equivalence.
   (d). Outline the consequence of Einstein field equation.
   (e). What is Debye Shielding?
   (f). Explain Lawson's criterion.
   (g). Explain Magnetic diffusion.
   (h). What are Reynolds number?

                                                                     Group- A

2. (a) Prove that the four dimensional volume element ds =  dsdydgdt is invariant under Lorentz transformation.

    (b). Prove D' Alemberation Operator is invariant under Lorentz transformation.

3. Obtain the covariant equation of motion of particles in an electromagnetic fields.

4. Obtain Schwarzschild's exterior solution for the gravitational field of a single mass at rest and explain on the field of a single mass at rest and explain on the basis of this solution the advance of perihelion of Planet Mercury.

5. Discuss the physical properties of de- sitter model of Universer and compare it with those of the actual universe.

                                                                     Group- B

6. Obtain Boltzmann- Vlasov Kinetic equation for plasma. Using this equation, obtain the dispersion relation for electron plasma oscillation.

7. Derive Appleton- Heartress Formula for the ionospheric plasma. Outline the importance of this formula.

8. Explain the following terms:
    (a). Whistler mode of wave propagation
    (b). Measurement of plasma number density

9. Derive expression for the velocity of Alfven waves. Discuss their Physical importance.

10. Write short notes on any two of the following:
      (a). Magnetohydrodynamic  (MHD) equation of  plasma
      (b). Fusion reactor at high temperature
      (c). Landau damping
      (d). Determination of Plasma parameters
      (e). Black holes