MSc Physics (Electronics I) SEM II 2018 19 May 2018-19 PHYSICS PAPER II ELECTRODYNAMICS Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 (a) Attempt any one:
   • (i) Starting with the 4-force = Jy show that can be written as f, = 8
   • (ii) State and prove Poynting theorem. Explain the terms Poynting vector and 8
   • (b) Attempt any one:
   • (i) the components of the electric and magnetic fields in terms of the 4 scalar and vector potentials. Define the field tensor in terms of the scalar and vector potentials. Express the field tensor in terms of the electric and
   • (ii) Show that and are invariant under a Lorentz 4 transformation. (note: You are NOT being asked to find the expressions in terms of the electric and magnetic fields)
2. Q2 (a) Attempt any one:
   • (i) . Derive an expression for frequency dependence of conductivity. What is 8 plasma frequency? Show that under the limit mt <<1 the conductivity is constant and is equal to oo
   • (ii) Explain the terms phase and group velocity. For the superposition of two 8 waves of equal amplitudes and distinct but neighboring frequencies and U obtain the expressions for group velocity and phase velocity
   • (b) Attempt any one:
   • (i) For plane harmonic waves in matter obtain the relations, 4
   • (ii). Discuss the classifications of fields in wave guides 4
3. Q3 (a) Attempt any one:
   • (i) The LW electric field for a point charge is given by: 8 Using this relation show that the power P radiated, per unit solid angle for a collection of charges under non relativistic limit, having electric dipole moment p is given by
   • (ii) The retarded scalar potential is given by 8 Show that it satisfies the equation
   • (b) Attempt any one:
   • (i) | Show that the Lorentz force law takes the form 4 Where P = 4A and U =q = = A) with p is linear momentum and and A are scalar and vector potential respectively
   • (ii) The LW Potentials are 4 Where the square bracket indicates that the quantities are measured at retarded time. If is constant, show that
4. Q4 (a) Attempt any one:
   • (i). Write the expression for field tensor {F} .Form energy momentum tensor 8 {T}.Obtain the term Tjx. What does the term represent?
   • (ii). Write the Lagrangian for a non relativistic charge particle in electromagnetic 8 field. Write the same for relativistic particle. Express it in terms of four velocity and four vector potential and apply Hamilton’s Principle
   • (b) Attempt any one: Obtain the continuity equation from the equation —— = —J ,
   • (ii) For a charge particle in external electromagnetic field the Lagrangian 4
5. Q5 Attempt any four:
   • (a) For a uniform wire of radius ‘a’ carrying de current ‘I’ Determine the 3
   • (b) Show that the 4-volume element defined by d*x = where 3 = X,/i is an invariant under proper Lorentz transformation
   • (c) Show that for insulators anomalous dispersion is disregarded. 3
   • (d) Write Maxwell’s equation in vacuum with p=0 and obtain the wave 3 Suppose we have two sets potentials, A) and A’) which 3 corresponds to same electric and magnetic fields. By how much can they
   • (f) do you understand by the term retarded potential? 3
   • (g) Comment on the symmetry property of energy momentum tensor {T}. What 3
   • (h) Write down the components of 3

Read from the scan above, so a character or two may differ. The scan is the original.