## 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} = ρ^{2} z^{2} 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=V_{0} 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} = (ρ_{0}r)/a for 0 ≤ r ≤ a

ρ_{v} = 0 for r > a, Determine E everywhere.(10 marks)