Electromagnetic Field Theory(paper no. 3) by SURESH KUMAR.....sureshkumarthegreat@yahoo.com

Electromagnetic Field Theory

PAPER NO. 3

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                                               EC-208
                                  Electromagnetic Field Theory
                                  (B.Tech 4th Semester,1202)
Time : 3 Hours                                                                                        Maximum Marks : 60
NOTE:- This paper consist of Three Sections. Section A is compulsory. Do any Four questions from
                 Section B and any two questions from Section C

                                     Section-A                                         Marks : 20

1(a) Assuming that V is a scalar field and A ia a vector field, classify the following fields as vector, scalar or meaningless:

( X A)
X (²).

(b) Give the statements for stoke Theotm and Divergence Theorm.
(c) A point charge of 50 nc is placed at the centre of a cube. Find the total flux passing through one face of the cube.
(d) Two point charges -1 nc and 4 nc are located at (0, 0, 0) and (0, 0,1). Find the energy in the system.
(e) Justify that the net electric field within a conductor is always zero.
(f) A loop is rotaiting about y axis in a magnetic field B = B_o sui wt a_x Wb/m² (pick the right chois). The voltage induced
    in the loop is due to:
    (i) Transformer Action
    (ii) Generator Action
    (iii) A combination of Transformer and generator action.
    (Jistify your answer).
(g) What is the physical significance of the Poynting vector ?
(h) How reciprocal of a number can be computed using Smith Chart ?
(i) Explain the difference between TE_mn + TM_mn modes.
(j) How many degenerate dominant modes exist in a rectangular resonant cavity for which a = b = c ?

                                              Section-B                                          Marks:5 Each

2. List all the boundary conditions for electric and magnetic fields.
3. If LG = RC condition is satisfied, the transmission line becomes distortionless. Why ?
4. A parallel plate capacitor with a plate area of 10 cm² and plate seperation of 5 mm has a voltage 50 sin 10³ applied
    to its paltes. Calculate the displacement current assuming

= 2

_o. What will be the displacement current, if the
    applied voltage is a d.c. volage of 10 V?
5. Write Maxwell equations in differential and integral form. Also give their word statements.
6. The cut-off frequency of an air filled rectangular waveguide is 2.4 GHz for the TE₁₀ mode. What would be the
    cut-off frequency if the same guide were filled with a lossless nonmagnetic material whose dielectric permitivity
    is six times that of air.

                                               Section-C                                        Marks : 10 Each

7. Consider a rectangular waveguide of dimension a X b. Starting from Maxwell equations and using appropriate
    boundary conditions, find the expression for E and H for TM wave. What is dominant mode ?
8. (a) Show that for a loseless line, every condition on the line is repeated after every λ/2.
    (b) A transmission line with characteristics impedence of 50 Ω is terminated by a load impedence of
         150 - j200 ohms. Determine with the help of Smith Chart or otherwise:
             (i) VSWR,
             (ii) Reflection coefficient.
9. Write notes on any two of the following :
    (a) Double Stub Matching
    (b) Wave Polarisation
    (c) Dielectric Slab Waveguides
    (d) Wave Resonators

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