Electromagnetic Field Theory 2009-10

Note : (I) Attempt all questions.

(2)    All questions cany equal marks.

1. Attempt any four parts of the following :

(a) Express vector B = —ar + r cos 0 aQ + in cartesian coordinates.

(b)    Given point P{-2,6,3) and vector

A = yav + ( x +. Express P and A in spherical system.

(c) Explain the gradient of a scalar field.

(d) State and explain the divergence theorem

(e) Given A— 5a ^ — 2av find the expression of a unit vector E such that B |) A .

(f)  State and explain the Stokes theorem.

2. Attempt any four parts of the following :

(a) The cable shown in Fig. 1, is 10 km long. If ?1=10 mm, /*2 =15 mm, r3 = 20 mm, £^=2.0, € i’2 = 4.0. Find the capacitance of the cable.

(b) If the current density ,/ = ~(cos0<ir + sin0ae),r A/m2, find the current passing through a sphere radius of 1.0 m.

(c) If a potential v = x2yz + Ay^z, (i) find A so that

Lapace’s equation is satisfied (ii) with the value of A, determine electric field at (2,1, -1)

(d) State and explain the poisson’s and Laplace’s equation

(e) State and explain the coulomb’s law.

(f)  A sphere of volume 0.1 m- has a charge density of 8.0 pc/m3. Find the electric field at a point (2, 0, 0) if the centre of the sphere is at (0, 0, 0)

3.  Attempt any two parts of the following :

(a) State and explain the Biot-Savrat law. What is. the magnetic field, H in cartesian coordinates due to Z-directed current element ? Find J if I = 2 A.

(b) State and explain the Stokes theorem. When vector magnetic potential is given by

A = —(2.0 cos 0 ar + sin0 fjncj the magnetic flux density.

(c) An isotropic material has a magnetic susceptibility of 3 and the magnetic flux density, B – 1 0yax

mwb/nr. Determine ,u, pn, ./, M and H. Define

inductance, mutual inductance and coefficient of coupling.

4. Attempt any two parts of the following :

(a) State and explain the Maxwell’s equation in differential and integral form. Also define the displacement currrent and depth of penetration.

(b) Derive the relation between E and H in uniform plane wave.

(c) Derive the expression for oc and (3 in a conducting medium.

5. Attempt any two parts of the following :

(a) By using Smith chart, find the input impedance of 7? Q lossless transmission line of length 0.1 X. when the load is a short.

(b) The short circuit and open circuit impedance of 10 km long open wire transmission line are ZsC = 2930 Z 26° and Znc =260 Z – 32° at a frequency of i kHz. Calculate the characteristics impedance and phase velocity.

(c) Define reflection loss, transmission loss and return loss. The 600 Q lossless transmission line is feeded

by 50 fl generator. If the line is 200 meter long and

termintated by load 500 fi. Determine in db

(i) Reflection loss

(ii) Transmission loss (iii) return loss.