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Pune University - Sem - II : Electrodynamics, April 2010

3 pages, 20 questions, 1 questions with responses, 1 total responses,

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Total No. of Questions : 7] P884 [Total No. of Pages : 3 [3722]-201 M. Sc. PHYSICS PHY UTN - 601 : Electrodynamics (New Course) (2008 Pattern) (Sem. - II) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) Question No. 1 is compulsory and solve any four questions from the remaining. 2) Draw neat labelled diagram wherever necessary. 3) Figures to the right indicates full marks. 4) Use of logarithmic tables and pocket calculator is allowed. Q1) Attempt any four of the following : a) Calculate the intrinsic impedance of an e.m. wave travelling through free space. Given for free space : ~ 0 = 4 10 7 Wb/A-m and = 0 = 8.85 10 12 C2/N-m2. [4] b) Find the ratio of skin depth in copper at 1KHz to that at 100 MHz. [4] c) Two identical bodies move towards each other, the speed of each being 0.9C. Find their speed to each other. [4] d) Calculate the magnitude of Poynting s vector at the surface of the sun. Given : Power radiated by sun is 3.8 1026 Watt and radius of the sun is 7 108 m. [4] e) Calculate the rest mass energy of an electron in eV if it s rest mass is equal to 9.1 10 31 kg. [4] f) Show that the ratio of electrostatic and magnetostatic energy densities ue um is equal to unity. [4] P.T.O. Q2) a) Show that the Maxwell s equations in a charge free region lead to & & KKm 2 E E 2 E b =0 2 2 t C t Explain which term is predominant in metals. & b) [8] && & & j r The magnetic field intensity B at a point is given by B = 0 3 d . 4 r & & Show that Curl B = 0 j . Q3) a) b) [8] Explain the term multipole moments . Derive an expression for potential at a distant point using multipole expansion for a localized charge distribution in free-space. [8] Show that the operator : 2 c 1 2 2 2 is invariant under Lorentz transformations where as C t 2 2 2 2 2 + 2 + 2 is not Lorentz invariant. x y z 2 Q4) a) [8] & If a medium is moving with a velocity u , then show that the Faraday s & & & & law has the form E u B = B . t ( & ) [8] b) Describe 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] Q5) a) Starting from Maxwell s equations, derive inhomogenous wave equations & in terms of scalar potential and vector potential A . Hence explain Lorentz s and coulomb s gauges. [8] b) Prove the relativistic addition theorem for velocities : dx dx u + v x where u = and ux = . x u v dt dt x 1+ 2 c Hence show that any velocity added relativistically to c gives resultant velocity c , which is Lorentz invariant. [8] ux = [3722]-201 -2- Q6) a) Explain the term e.m. field tensor. Hence derive an expression for e.m. field tensor F . [8] b) Describe the term Hertz potential and show that it obeys inhomogenous wave equation. Obtain the electric and magnetic fields in terms of Hertz & potential Z . Q7) a) [8] Calculate the electric field associated with a LASER beam having energy density 106J/cm3. [4] b) Explain Minkowski s space-time diagram. c) Write the expression for force describing magnetic interaction between two current loops and explain it. [4] d) Describe the term Four Vector Potential . rrrr [3722]-201 -3- [4] [4]

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Additional Info : M.Sc. PHYSICS, PHY UTN - 601 : Electronics (New Course) (2008 Pattern) (Semister - II), Pune University
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