Tuesday, 16 April 2013

ELECTROMAGNETIC FIELD THEORY


ELECTROMAGNETIC FIELD THEORY
SEM-IV, 2012
B.TECH
UTTARAKHAND TECHNICAL UNIVERSITY
utu question paper

Time: 3 Hours
Total Marks: 100
SECTION A
Attempt any four questions
  1. Suppose an electric field

    is as given then determine the following:
    (i) E at P if P (r = 0.8, Ø=30o, θ=45)
    (ii) |E| at p.
    (iii) A unit vector in direction of E at P.
  2. State and prove Gauss-Divergence theorem. Also comment on its physical significance with respect to flux in flow in a spherical conductor?
  3. A solenoid 50 cm long, 2 cm in diameter and contains 1500 turns. The cylindrical core has a diameter of 2 cm and a relative permeability of 75. This coil being coaxial with a second solenoid, also 50cm long, but with a 3 cm diameter and 1200 turns. Calculate
    (i) L for the inner solenoid
    (ii) L for the outer solenoid
    (iii) M between the two solenoid?
  4. Discuss the problem wave propagation in free space and also obtain the value for intrinsic impedance?
  5. Given a non-magnetic material with
    Er = 3.2, σ = 1.5 x 10-4 S/m. Evaluate the values of
    (i) loss-tangent (ii) attenuation constant (iii) phase constant (iv) intrinsic impedance?
  6. Discuss pointing vector and pointing theorem. Also describe its significance with respect to power calculate for plane wave propagation? 
SECTION B
Attempt any four questions
  1. Given that
    B.TECH UTTARAKHAND TECHNICAL UNIVERSITY (UTU)
    in free space, find the average power passing outward through the surface r =106, 0<ϕ <π/3, 0<θ < 2π?
  2. A good conductor planar in form carries a uniform plane wave of wavelength 0.3mm and a velocity of 3 x 10 m/s assuming that the conductor is non-magnetic, determine.
    (i) Frequency (ii) conductivity?
  3. Establish the conversion relationships among three coordinate system used in electromagnetics. Thus, represent given vector P= 4ax + 5ay + 7az of Cartesian system in to cylindrical system?
  4. State & prove Biot-Savart's law & also explain its physical significance with respect to a current carrying conductor being infinitely long?
  5. Explain how Gauss's law is significant in respect to divergence theorem & also explain the physical interface linking the two laws with the help of mathematical or geometrical artifacts?
  6. Discuss all the forms of Maxwell's equation & justify the analogy persisting between the various forms in electrostatics & magnetostatics. What does this signifies physically?
SECTION C
Attempt any two questions
  1. Discuss Transmission lines structure with respect to wave propagation along with transit-time effect & its significance to transmission line analysis
  2. What do you understand by skin-depth? Explain with the help of graphs & equations. List down some implicit applications of this depth with respect to communications under the sea?
  3. Explain & discuss each step of Smith-chart generation & calculation. Also throw some light on importance of it?
SECTION D
Attempt any two questions
  1. Discuss some of the applications involved for the Gauss's law in work? Derive a relationship for electric field E in a hollow cylindrical conductor & depict its variation along with the distance from the conductor?
  2. Prove that standing waves are generated in a transmission line with complete expressions along with electrical equivalent of transmission line? Also, graphically depict the forward & backward wave components?
  3. Explain the propagation of plane wave in a loss-less transmission line & compare the result with low-loss transmission line. Justify your observations mathematically?
SECTION E
  1. Write short note on any two?
  • Poisson and Laplace equations.
  • Helmholtz wave equation.
  • Curl, Divergence & Gradient.
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