## 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} = (10x^{2})/4 C/m^{3}.(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_{x}2zâ_{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)