# CUSAT Previous Year Question Papers BE EE 5th Sem Field Theory Nov 09

**EE 503 Field Theory**

**(2006 Scheme)**

**PART-A**

(Answer all questions)

I. a. Show that the D field due to a point charge has a divergence of zero.

b. Find the capacitance of an isolated spherical shell of radius ‘a’.

c. In a perfect dielectric will there be any attenuation of the E and H waves? Give reasons.

d. Write down the Maxwell’s equations in Differential and Integral form for free space.

e. Which kind of materials have both conduction current and displacement current? Derive the relation between J_{c} and Jo

f. Give the significance of poyntings’ theorem in electromagnetic wave propagation.

g. Find the skin depth ‘S’ at a frequency of 1.6 MHz in aluminum, where a = 38.2M; / m and fir = \. Also find u .

h. What is a Smith Chart? Differentiate between single stub and double stub matching.

**PART B**

II. a. State Divergence Theorem. Given that D ^{=}j in cylindrical coordinates. Evaluate both the sides of the divergence theorem for the volume enclosed by r -1 m, r — 2m, -Z~ = 0,-2- = 10m.

b. Derive the Laplace’s equation and Poission’s equation starting from one of the Maxwell’s equations.

**OR**

III. a. A parallel plate capacitor has a surface charge of + p_{s} {^/ _{2} J on the lower side of the copper plate and —p, {^/_{m}2 j ^{0,1} the upper side of the lower plate. Use Gauss’s Law to find ‘D’ and ‘E’ in the region between the plate.

b. Use cylindrical coordinates to find the area of the curved surface of a right circular cylinder of radius ‘a’.

c. In spherical coordinates and relative to infinity the potential in the region r > 0 surrounding a point charge ‘Q’ is V = Find E.

V. a. State and explain Biot-Savant Law.

b. Show that ‘H’ on the axis of a circular current loop of radius ‘a’ is Specialize the result to the centre of the loop.

**OR**

VI. (a)Explain the boundary conditions for magnetic fields across the interface between two materials.

(b)Show that the inductance per unit length of a coaxial conductor of inner radius ‘a^{1} and outer radius 1)’ can be given by L = ^-lu(bja). Verify the above equation by using the formula for the energy stored in a magnetic field.

VII. (a) Derive the wave equation for free space and hence prove that uniform plane waves will not have field components in the direction of propagation.

(b)Starting from Maxwell’s equation derive an expression for the poynting vector. Also give its significance in wave propagation.

**OR**

Given E = E_{m}Sin(a>t – fSz)ay in free space, Find D, B, and H.

Write short notes on:- (i) Elliptic polarization

(i) propagation modes in rectangular wave guides

Show that for normal incidence of a travelling wave at the interface between two regions, are the intrinsic impedance of medium (1) and medium (2) respectively.

VIII. (a) Give Snell’s law of refraction. A wave is incident at an angle of 30° from air to teflon with E_{r} = 2.1. Calculate the angle of transmission.

(b)For a parallel polarized wave travelling from air into glass having e_{r} — 500, Find the brew star angle.

**OR**

IX. (a)Derive an expression for the characteristic impedance of a Loss less Transmission Line. What is VSWR? Give its mathematical expression.

(b) When are standing waves produced? A wave propagates from a dielectric medium to the interface with free space. If the angle of incidence is the critical angle of 20°, find the relative permittivity.