# BE EE 5th Semester Field Theory July 2009

EE 503 Field Theory

(2006 Scheme)

PART – A

(Answer ALL questions)

(All questions carry EQUAL marks)

1. (a) Transform the Cartesian Vector A = x ax + y ay + z az to cylindrical and spherical coordinates.

(b) Derive the expression for the capacitance of an isolated sphere.

(c) Derive the continuity equation and hence define the felaxation time.

(d) State and explain :

(i) Biot – Savart Law

(ii) Ampere’s Circuital Law

(e) Can TEM waves propagate in a rectangular wave guide? Justify your answer.

(f) Define wave polarization. Differentiate between different types of polarization.

(g) What is Smith Chart? What are its applications?

(h) Differentiate between Critical angle and Brewster angle.

PART-B

2. (a) Derive the boundary conditions across a dielectric – dielectric boundary.

(b) Derive the Poisson’s and Laplace’s Equations. Also highlight the significance of the Uniqueness theorem.

OR

3. (a) If J = -y ^ COS 0 ar + sin 6 a0 j A! m2; find the current passing through a sphere of radius 1.0 m.

(b) Determine the self inductance of a coaxial cable of inner radius ‘a’ and outer radius ‘b’.

4. (a) Define uniform plane wave. Prove its transverse nature.

(b) Derive the wave equations for a wave propagating in free space.

OR

5. (a) Distinguish between group velocity and phase velocity,

(b) State and derive Poynting’s Theorem. Explain its significance.

5. (a) State Maxwell’s equations in integral and differential form. Give proper interpretation to each equation, indicating the law / theorem / postulate form which each equation is derived.

OR

6. (a) Define -. (i) Magnetic Vector Potential (ii) Displacement Current.

(b) Calculate the total magnetic flux crossing the surface

= ;z7 2; \ < p <2m\ 0 < z < 5 m; given A — ~p/{ az wb/m.

7. (a) Derive an expression for the input impedance of a transmission line.

(b) Explain the principle of stub matching.

OR

8. (a) Discuss the reflection of plane waves incident normally on a boundary between a dielectric and a perfect conductor.

(b) Write notes on :

(i) Total internal reflection

(ii) Characteristic impedance of a transmission line.