Wave Theory & Propagation - May 2013

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) Derive the equation of electric potential due to Electric dipoles.(5 marks) 1 (b) A point charge of 100μC is located at origin. Find electric potential at (1,2,3)m. (5 marks) 1 (c) State and Explain Gauss's Law. (5 marks) 1 (d) Find out the total charge present in the closed surface defined by
0 ≤ x ≤ 1 , 0 ≤ y ≤ 1, 0 ≤ z ≤ 1
if ρ_v = (10x²)/4 C/m³.(5 marks) 1 (e) State and Explain divergence theorem.(5 marks) 2 (a) Derive Poisson's and Laplace's Equations.(10 marks) 2 (b) Derive the equation for Electric field intensity due to infinite surface charge or plane charge. (10 marks) 3 (a) Show that -
(i) ∇.D = 0 for the field of point charge.
(ii) ∇.E = 0 for the field of uniform line charge.(10 marks) 3 (b) Evaluate both sides of divergence theorem for the field
D = 2xyzâ_x2zâ_y + x â_z
for the region defined by -1 ≤ x ≤ 1 , -1 ≤ y ≤ 1 and -1 ≤ z ≤ 1. (10 marks) 4 (a) State and explain continuity equation and displacement current. (10 marks) 4 (b) Derive the equation for Magnetic field intensity due to finite straight line current carrying conductor. (10 marks) 5 (a) Explain Stokes's theorem and Ampere's circuital law.(10 marks) 5 (b) Find 'H' inside and outside of a solid cylindrical conductor of radius 'a' metre where I is uniformly distributed over the cross section.(10 marks) 6 (a) State and derive the equations for Poynting theorem. (10 marks) 6 (b) Derive the Electromagnetic wave equation for good conductor.(10 marks)

Write short notes on (any two):-

7 (a) Boundary Condition in Electrostatic and Magnetostatic.(10 marks) 7 (b) Reflection of uniform plane wave.(10 marks) 7 (c) Wave Impedance for free space.(10 marks)