## Electromagnetic Engineering - Dec 2015

### Electronics Engineering (Semester 5)

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.

### Solve any four:

**1 (a)** State and explain Coulomb's law.(5 marks)
**1 (b)** Derive Poisson's and Laplace equation.(5 marks)
**1 (c)** What is intrinsic impedance of free space?(5 marks)
**1 (d)** Define directive gain and directivity with respective antenna. An antenna has a directivity of 20 and a radiation efficiency of 90% compute the gain in dBs.(5 marks)
**1 (e)** Find out the divergence and curl of the following function. $$ \overline{A}=2xy\overline{ax}+(x^2z)\overline{ay}+z^3 \overline {az} $$(5 marks)
**2 (a)** Given the potentials V=2x^{2}y-5xz and a point P(-4, 3, 6) find V,E,D and e, at point P.(10 marks)
**2 (b)** Derive boundary conditions for electric fields at the boundary of two dielectric media.(10 marks)
**3 (a)** Derive Maxwell's integral and point form equations for time varying fields.(10 marks)
**3 (b)** Prove $\nabla, \overline{D} = e_v.$(10 marks)
**4 (a)** In a media characterized by σ=0, μ=μ_{0} and ε=ε_{0} $$ \overline{E}=20 \sin (10^8 t-\beta z)\overline {ay} \ \text{v/m.} \text{ find}\beta \text{ and }\overline {H}. $$(10 marks)
**4 (b)** Derive the expression for the reflection and transmission coefficients in case of reflection from perfect dielectric at oblique incidence.(10 marks)
**5 (a)** Explain in detail MOM method also state advantage and drawback of it.(10 marks)
**5 (b)** State and derive the Poynting theorem and describe the significance of each term.(10 marks)
**6 (a)** What is line of sight propagation? Obtain the expression for range of line of sight for space wave propagation in terms of antenna's transmitting and receiving heights.(10 marks)
**6 (b)** Explain ground wave, space wave propagations.(10 marks)
**6 (c)** Derive an expression for radiation resistance of an small loop antenna. Explain its significance.(10 marks)