Electromagnetic Field Theory - 2013 (A)

2013•Semester 3•Civil-CA•End Semester
Bihar Engineering University, Patna
2013 (A)

Electromagnetic Field Theory

Time: 3 hoursCode: 103307Full Marks: 70

Instructions:

  1. The marks are indicated in the right-hand margin.
  2. There are TEN questions in this paper.
  3. Attempt any FIVE questions.
Q.1 Solve both questions :[14]

  1. Find the potential distribution due to a long pair of parallel wires of negligible cross-section and having equal and opposite line charge density. Also obtain equipotential surfaces produced by them.

  2. Find the capacitance of two parallel cylindrical conductors having their radii as a and separation between their axes as b.

Q.2 Solve all questions :[14]

  1. State uniqueness theorem and prove it.

  2. Explain conductor properties and obtain boundary conditions.

  3. For a two-dimensional system in which \( r=\sqrt{x^2+y^2} \) determine \( \nabla^2V \) when \( V=\frac{1}{r} \).

Q.3 Solve all questions :[14]

  1. Find the energy density in the magnetic field.

  2. Find the magnetic field inside a solid conductor carrying a direct current, and hence obtain total magnetic flux per unit length within the conductor.

  3. Prove Stokes' theorem.

Q.4 Solve both questions :[14]

  1. Obtain two Maxwell's equations which deviate from steady-state field.

  2. The electric field of electromagnetic wave is given by \( E_x=0=E_z \), \( E_y=A\cos\omega(t-\frac{z}{c}) \). Using Maxwell's equation in free space, find the magnetic vector \( \vec{H} \).

Q.5 Solve both questions :[14]

  1. Find the ratio of \( \vec{E} \) and \( \vec{H} \) in a uniform plane wave.

  2. Discuss the wave propagation in conducting medium and obtain the value of \( \alpha \) and \( \beta \).

Q.6 Solve this question :[14]

  1. Derive the reflection coefficient of perfect dielectric for oblique incidence in the case of parallel polarization. Obtain Brewster angle.

Q.7 Solve both questions :[14]

  1. State Poynting theorem and prove it.

  2. A short vertical transmitting antenna erected on the surface of a perfectly conducting earth produces effective field strength \( E_{\text{eff.}} = E_{\theta \text{eff.}} = 100\sin\theta \frac{\text{mu}}{\text{m}} \) at points at a distance of one mile from the antenna. Compute the Poynting vector and total power radiated.

Q.8 Solve both questions :[14]

  1. Discuss UHF line as circuit element and hence find the input impedance of short-circuited quarter-wave line.

  2. Discuss quarter-wave line as transformer.

Q.9 Solve both questions :[14]

  1. Discuss Smith chart and its uses.

  2. Design a necessary matching unit to join without impedance mismatch the two different sections of transmission line whose impedances are 75 ohm and 50 ohm.

Q.10 Solve this question :[14]

  1. Find the field component of TM wave in parallel plane guide and hence discuss TEM wave.