Wave Theory & Propagation - Dec 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) State and Explain Coulomb's Law. (5 marks) 1 (b) Method of Images.(5 marks) 1 (c) Gauss's Law. (5 marks) 1 (d) Poynting Vector. (5 marks) 1 (e) Polarization of Electromagnetic Waves. (5 marks) 2 (a) Find Electric field intensity due to a volume charge.(10 marks) 2 (b) Calculate the total charge within the volume 0 ≤ ρ ≤ 0.1, 0 ≤  ϕ ≤ π, 2 ≤ z ≤ 4. Given ρ_v = ρ² z² sin (0.6ϕ). (10 marks) 3 (a) A total charge of 40/3 nC is uniformly distributed over a circular ring of radius 2m placed on z=0 plane with centre at origin. Find electric potential at (0,0,5). (10 marks) 3 (b) A vector field is given by:
A(r, ϕ, z) = 30e^-r â_r - 2zâ_z.
Verify Divergence theorem for the volume enclosed by r = 2m, z = 0m, and z = 5m. (10 marks) 4 (a) Explain Maxwell's equations in differential and Integral form for time-varying field.(10 marks) 4 (b) Derive V and E for a dipole situated at the origin on z axis. (10 marks) 5 (a) Derive an expression for magnetic field intensity due to finite long straight element.(10 marks) 5 (b) Prove that static electric field is irrotational and static magnetic field is solenoidal.(10 marks) 6 (a) Derive Poisson's and Laplace's equation. (10 marks) 6 (b) Use Laplace's equation to find capacitance of a coaxial cable of inner radius 'a' and outer radius 'b'. Given V=V₀ at r=a and V=0 at r=b. (10 marks) 7 (a) Derive general wave equations for E and H fields. (10 marks) 7 (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)