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Pune University - Sem - II : Electrodynamics, April 2010 (Old Course)

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Total No. of Questions : 7] [Total No. of Pages : 3 P874 [3722]-21 M. Sc. PHYSICS PHY UT - 601 : Electrodynamics (Old Course) (2005 Pattern) (Sem. - II) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) Question No. 1 is compulsory. Attempt any four questions from the remaining. 2) Draw neat labelled diagrams wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic tables and calculator is allowed. Q1) Attempt any four of the following : a) Calculate the frequency at which the skin-depth in sea water is 1m. Given : = 0 = 4 10 7 Wb/A-m and b = 4.3 b) mho . m [4] If the average distance between the sun and earth is 1.5 1011 m, find the average solar energy incident on the earth. Given P = 3.8 1026W. [4] c) Find the velocity at which the mass of the particle is double it s rest mass. Given C = 3 108 m/s. [4] d) Given the e.m. wave E = i E 0 cos w z t + jE 0 sin w z t , [4] where E0 is constant. Find the corresponding magnetic field. ( ) e) Write Maxwell s equation in differential and integral forms. [4] f) Write and explain the expression for force describing magnetic interaction between two current loops. [4] Q2) a) Obtain Faraday s law of induction for a stationary medium. Hence show that for moving medium it is expressed as - & ( ) & & B , where E is the field observed by a moving E u B = t & [8] observer and u is the velocity of the motion of the medium. & & ( && ) P.T.O. b) Prove that the space interval x2 + y2 + z2 is not invariant under Lorentz transformations, while the combined space-time interval x2 + y2 + z2 c2t2 is Lorentz invariant. [8] Q3) a) Explain Michelson-Morley experiment with reference to the special theory of relativity. Derive the necessary formula for the fringe shift and comment on the result. [8] b) & & && j r The magnetic field intensity B at a point is given by B = 0 3 d . 4 r & && show that B = 0 j . [8] ( ) Q4) a) A plane e.m. wave is incident obliquely on an interface between the two non-conducting dielectric media. Obtain expressions for Fresnell s equations if the electric field vectors are perpendicular to the plane of incidence. [8] b) Explain the term Hertz Potential and show that it obeys inhomogenous wave equation. Obtain the electric and magnetic fields in terms of Hertz & potential Z . [8] Q5) a) What is a linear quadrupole? Derive the expression for potential at a distant point due to a small linear quadrupole. [8] b) Explain the term e.m. field tenser and hence derive the expression for this field tenser F . [8] Q6) a) State and prove Poynting s theorem resulting to the flow of energy at a point in space in an electromagnetic field. [8] b) Solve the inhomogeneous wave equation : 2 c (x , t) = g (x , t) by Fourier analysis. Use Dirac-delta function G (x , x ) to obtain the solution. Q7) a) [3722]-21 [8] Two identical bodies move towards each other, the speed of each being 0.9C. What is their speed relative to each other? [4] -2- b) Find the phase velocity of a plane e.m. wave at a frequency of 10 GHz in polyethelene material. Given : ~ 0 = 4 10 7 Wb/A-m, r = 2.3, 2 0 = 8.85 10 12C /N-m2 and b = 2.56 10 4 mho/m. [4] c) Explain the term Four Vector Potential . [4] d) Describe and explain the Minkiowski s space-time diagram. [4] rrrr [3722]-21 -3-

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Additional Info : M.Sc. PHYSICS, PHY UT - 601 : Electrodynamics (Old Course) (2005 Pattern) (Semister - II), Pune University
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