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End-Term Examination

Fourth Semester [B.Tech] - May 2005

Paper Code : ETEC – 205 Subject : Electromagnetic Field Theory

Time : 3 Hours

Maximum Marks : 75

Note : Attempt any 5 questions in all.

Q1

( a )

Explain the physical interpretation of:

  1. Gradient
  2. Curl
  3. Divergence

6

( b )

 Give the expression of
  1. Elementary length
  2. Surface area
  3. Volume

in cylindrical and spherical coordinates.

3

( c )

 If A(r,q,f) = 2r2 sin(q) ar , find (i) Ñ.A (ii) Ñ´A

6

Q2

( a )

Find electrostatic potential V and electric field intensity E for a dipole.

8

( b )

 A point charge Q is placed at a height 'h' above an infinite conducting sheet. Using method of images, show that the total charge induced on the conducting sheet is -Q.

7

Q3

( a )

Derive boundary relations for electric field across a common boundary separating two different media.

8

( b )

 Two concentric spherical shells of radii 'a' and 'b' with b>a are charged with equal and opposite charges +-Q. Find

(i) Total energy of the system    (ii) Total capacitance of the system

7

Q4

( a )

A volume current distribution is given by:

J(r,f,z) = J0 az ; r<a
            =0 ; r>a

using Ampere's circuital law, find the magnetic flux density at all  points.

7

( b )

 Explain  (i) Ampere's law of force  (ii) Faraday's law.
give their typical applications in electromagnetism.

8

Q5

( a )

Give Maxwell's equations in time varying form in

(i) Integral form    (ii) Differential form

7

( b )

 Derive wave equation and find its solution when E = Ex ax and the direction of propagation is along +z direction.

8

Q6

( a )

For a uniform plane wave in sea water with
σ = 4 S/m, ε = 80 ε0, µ = µ0 find

  1. attenuation constant α
  2. phase constant β
  3. intrinsic impedance η
  4. wavelength λ

at a frequency of  f = 25 KHz

5

( b )

Derive relations for reflection and transmission coefficients for electric field when an electromagnetic wave is incident normally on the surface separated by two different media η1  and η2 .

5

Q7

( a )

Derive transmission line equation.

6

( b )

Derive an expresion for input impedance Zin  of a lossless line having length 'l' and a characteristic impedance of Z0 .

5

( c )

Give the difference between distortion less and lossless line.

4

Q8

 ( a ) Find the (i) input impedance (ii) reflection coefficient (iii) VSWR on the line when ZL =0; ZL = infinity; ZL =Z0 .

9

( b )

 For a line with L = 3.5 mH/Km, C = 0.008 uF/Km and R = G = 0, find Z0 and γ at frequency of 1KHz.

6

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