LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

FIRST SEMESTER – NOVEMBER 2010

    PH 1812  – ELECTRODYNAMICS

 

 

 

Date : 30-10-10                 Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART-A

Answer all questions                                                                                                 10 x 2 = 20

1. State two properties of lines of force.
2. Distinguish between polar and non-polar dielectrics.
3. Define magnetic vector potential?
4. Using Ampere’s circuital law find the magnetic field near infinitely long current carrying conductor
5. What is motional e.m.f.?
6. Write down any two Maxwell’s equations and give significance.
7. Write second order Wave equations for E and B
8. What is Brewster’s angle?
9. What is an acceleration field?
10. Is charge Lorentz invariant? Justify?

 

PART-B

Answer any four questions                                                                                      4 X 7.5 = 30

11. Derive the integral and differential forms of Gauss’s law
12. Derive the Neumann’s formula for mutual inductance between two pair of coils
13. a) State Biot-Savart’s law. Find the magnetic field at a distance z above the centre of a circular loop of radius R carrying a steady current I
14. b) List any three properties of Ferro and Para magnetic materials. [2+2.5+3]
15. Find the charge and current distributions that would give rise to the potentials V= 0, with

A =

Where  is a constant and

15. Derive the expressions for electric and magnetic fields of a point charge with constant velocity.

 

PART-C

Answer any four questions                                                                                     4 x 12.5 = 50

16   a. Obtain the general expression for energy of a point charge distribution

1. Find the energy of a uniformly charged shell of total charge q and radius R
2. Discuss the theory of multipole expansion of vector potential and derive an expression for the magnetic vector potential.
3. State and prove Poynting’s theorem?
4. Discuss with necessary theory, the case of oblique incidence of electromagnetic wave at the interface of two non-conducting media and hence obtain Fresnel’s equations.
5. Obtain an expression for the power radiated by an oscillating electric dipole

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

FIRST SEMESTER – APRIL 2012

PH 1812 – ELECTRODYNAMICS

 

 

Date : 25-04-2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART A

Answer all questions                                                                                                                (10 x 2 = 20 )

1. Explain why electrostatic energy does not obey superposition principle?
2. What is a non polar dielectric? Give an example
3. Mention any two differences between para and ferro magnets
4. How are the bound and the free charges related to each other in linear media?
5. What is motional e.m.f.?
6. Give the expressions for Maxwells stress tensor
7. Define skin depth
8. Calculate the degree of polarization for ordinary light reflected from glass with refractive index 1.5 at an angle of incidence of 45.
9. Write the boundary conditions for reflection of electromagnetic wave at the boundary of a conducting surface
10. Define radiation reaction.

Part B

Answer any four questions                                                                                                     (4 x 7.5 = 30)

11. i) Derive Gauss’s law in differential form. (4)
12. ii) Find the capacitance per unit length of two co-axial metal cylindrical tubes of radii a
    and b (3.5)
13. Derive the theory of multipole expansion of magnetic vector potential
14. Obtain the Neumann’s formula for mutual inductance between a pair of coils.
15. Establish the wave equations for E and B. Derive the expression for energy and momentum of electromagnetic waves
16. Derive the Abraham-Lorentz formula for the radiation reaction? Obtain the Lienard-Wiechart potentials for a moving point charge

Part C

Answer any four questions                                                                                                  (4 x 12.5 = 50)

16. Show that the electrostatic potential in a charge free region satisfies the Laplace’s equation. Find a charge distribution that would produce a potential   ф=
17. i) A spherical shell of radius R, carrying a uniform surface charge σ, is set spinning at angular velocity. Find the vector potential it produces at a point P outside the sphere.
18. ii) State Biot-Savart law. Find the volume current density when current I is uniformly distributed over a wire of circular cross section, with radius R.
19. Explain the concept of potential formulation of electrodynamics. Elucidate the difference between Coluomb and Lorentz gauge?
20. Discuss the phenomenon of reflection and transmission of electro- magnetic waves at the boundary between two linear dielectric media in the case of oblique incidence and hence find expressions for the reflection and transmission coefficients
21. Explain the theory of magnetic dipole radiation to obtain expression for power radiated.

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

FIRST SEMESTER – NOVEMBER 2012

PH 1818 – ELECTRODYNAMICS

 

 

Date : 05/11/2012            Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

Answer ALL questions:                                                                                                                   (10×2=20)

1. Obtain the differential form of Gauss’s law from the integral form.
2. For volume currents, show that ∇. B = 0.
3. What is a gauge transformation? Give an example.
4. Write down the momentum conservation equation in electrodynamics.
5. State the criteria under which electric dipole radiation dominates as compared to the magnetic dipole radiation.
6. Define radiation zone.
7. Write down the Lorentz transformation of a four vector.
8. Write down the relativistic Lagrangian for a free particle.
9. What are the boundary conditions on E and B for a wave guide?
10. Write down the continuity equation in magneto hydrodynamics.

PART – B

Answer any FOUR questions:                                                                                                        (4×7.5=30)

11. The electric potential of some configuration is given by the expression V(r)=A() where A and λ are constants. Find the electric field E(r), the charge density ρ(r) and the total charge Q.
12. Explain the phenomena of reflection at a conducting surface using suitable boundary conditions on the Maxwell’s equations.
13. Arrive at an expression for proper velocity four vector and hence establish its transformation equations.
14. Obtain Leinard-Wiechert potentials for a moving point charge.
15. Describe the non-relativistic motion of charged particle in a slowly space varying magnetic field.

PART – C

Answer any FOUR questions:                                                                                                      (4×12.5=50)

16. Outline the theory of multipole expansion of electrostatic potential in powers of (1/r).
17. Obtain expressions for reflection and transmission coefficients for oblique incidence of EM wave at an interface.
18. Derive an expression for F_μν, the electromagnetic field tensor in the covariant form. Also find the contravariant form of the electromagnetic field tensor.
19. Derive an expression for the power radiated from an arbitrary source.
20. Obtain the general expression for electric and magnetic field components for an EM wave propagating along the z-axis of a waveguide. Hence derive an expression for the cut off wavelength for a TE mode of propagation in a rectangular waveguide.

 

 

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