Wave Theory & Propagation - May 2012

Electronics & Telecomm. (Semester 4)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.

Explain any four of the following:-

1 (a) Continuity equation.(5 marks) 1 (b) Boundary Conditions for Electrostatics.(5 marks) 1 (c) Polarization of Electromagnetic waves.(5 marks) 1 (d) Ampere's Circuital law.(5 marks) 1 (e) Magnetic Vector Potential.(5 marks) 2 (a) Two conducting cones at θ =π/10 and θ = π/6 of infinite sheet extent are separated by an infinitesimal gap at r=0.
If V (θ= π/10)=0V and V(θ= π/6)=50V.
Find potential V and electric field intensity Ē between the cones. Neglect the fringing effect.(10 marks) 2 (b) Find the electric field intensity Ē due to an infinite line charge.(10 marks) 3 (a) A circuit carrying a current I amp form a regular polygon of 'n' side inscribed in circumscribing circle of radius R. Calculate the Magnetic flux at the centre of the polygon and show that B approaches that for a loop if 'n' tends to infinity. (10 marks) 3 (b) Given the potential V=10/r² sinθcos θ,:-
(i) Find the Electric flux density D at (2, π/2, 0).
(ii) Calculate the work done in moving a 5 μC charge from point A(1, 30⁰, 120⁰) to B(3, 90⁰, 60⁰). (10 marks) 4 (a) A vector field is given by:
A(r, ϕ, z) = 30e^-r a_r - 2za_z.
Verify Divergence theorem for the volume enclosed by r = 2m, z = 0m, and z = 5m. (10 marks) 4 (b) Define Poynting Vector. Obtain the integral form of Poynting theorem and explain each term. (10 marks) 5 (a) Verify Stokes's theorem for portion of a sphere r = 4m, 0 ≤ θ ≤ 0.1 π, 0 ≤ ϕ≤ 0.4 π.
Given: H = 6r sin ϕa_r + 18rsin θ cos ϕa_ρ.(10 marks) 5 (b) Derive Maxwell's equation in point form and integral form for free space.(10 marks) 6 (a) Derive the expression for the potential energy stored in a static electrical field. (10 marks) 6 (b) A charge distribution with spherical symmetry has density:
ρ_v = (ρ₀r)/a for 0 ≤ r ≤ a
ρ_v= 0 for r > a,  Determine E everywhere.(10 marks) 7 (a) Prove that static charge field is irrotational and the static magnetic field is solenoidal.(10 marks) 7 (b) Derive general wave equations for E and Efields. Give solution to the wave equation in perfect dielectric for a wave travelling in z-direction which has only x-component of E field. (10 marks)