LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M. Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2003

PH 3802 / PH 922 – ELECTRODYNAMICS II

07.11.2003                                                                                             Max.   : 100 Marks

1.00 – 4.00

 

PART – A

 

Answer ALL questions.                                                                               (10 x 2 = 20)

 

1. Write down the real electric and magnetic fields for a plane monochromatic wave of amplitude E_o, frequency w, and phase angle that is travelling in the negative y – direction and polarised in the z – direction

 

2. What is anomalous dispersion?

 

3. Why are the ‘retarded potentials’ so called?

 

4. State the Larmor formula for the power radiated by a moving point charge.

 

5. Define Contra – and Covariant tensors of rank – 2 by their transformation properties.

 

6. What is the Darwin Lagrangian? Give an expression for the same.

 

7. Write down the electrodynamic boundary conditions near the surface of a perfect conductor.

 

8. Distinguish between TM and TE waves.

 

9. How are the electric and the magnetic fields, in a perfectly conducting fluid, related?

 

10. State the principle of the ‘pinch’ effect.

 

PART – B

 

Answer any FOUR questions                                                                     (4 x 7.5 = 30)

 

11. Derive expressions for the reflection and the transmission Coefficients for normal incidence of a plane em wave at the boundary between two linear media.

 

12. An in finite straight wire carriers the current

 

 

 

0, for t £ 0

I(t)  =                           .     Find the resulting electric field.

I_o, for t > 0

 

-2-

 

13. a) Prove that  the charge  density  transforms  like  the  time  component  of  the  4 – vector.                                                                                                       (2)

 

1. b) Obtain an expression for the relativistic Lagrangian for a charged particle.

(5.5)

 

14. Assuming a sinusoidal time dependence for the em fields inside a cylindrical wave guides establish the Maxwells equations in terms of transverse and parallel components.

 

15. Use the necessary em equation’s to explain the role played by the ‘magnetic Reynolds number’ to distinguish between the diffusion of magnetic lines of force and the freezing – in of the magnetic lines of force.

 

PART – C

 

Answer any FOUR questions                                                                   (4 x 12.5 = 50)

 

16. Explain the dispersion phenomenon in nonconductors and hence obtain the Cauchy’s equation.

 

17. Derive expressions for the electric and magnetic fields of an oscillating electric dipole.

 

18. Write down the field-strength tensors explicitly in matrix form and establish the covariance of the Maxwell’s equations

 

19. Discuss the propagation of TE Waves in a rectangular wave guide with inner dimensions a, b (with a = 2b) and find the frequencies of the first four modes.

 

20. Discuss the magneto hydrodynamic flow between boundaries with crossed electric and magnetic fields and bring out the role played by the Hartmann number.

 

 

 

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