ELECTROMAGNETIC FIELD THEORY

ELECTROMAGNETIC FIELD THEORY
(EMFT)
SEM-IV, 2011
B TECH QUESTION PAPERS
UTTARAKHAND TECHNICAL UNIVERSITY
(UTU)

Time: 3 hours

Total marks:100

Attempt any four part of the following

1. State and explain Divergence theorem in detail.
2. Explain the cylindrical coordinate system with the concept of incremental length.
3. Two charges of similar sign and magnitude 1×10^-12 C are located one meter apart. What is the potential at a point that is midway between the two charges and 50cm from the line connecting the charges?
4. Find the divergence of A? If A = rsinΦI_r+2rcosΦI_Φ+2Z²I_z
5. Find the field of a sheet of charge in which symmetry is about plane?
6. Find the constant a, b, c so that V = i(x + 2y + az) + j(bx – 3y – z) + k(4x + cy + 2z) is irrational.

Attempt any four part of the following

1. Calculate the capacitance of a two wire line or two cylindrical conductors.
2. The electrical field between two concentric cylindrical conductors at r= 0.01m and r= 0.05m is given by E = (10⁶/r)I_r v/m. Find the energy stored in 1 meter length.
3. Write a short note on Boundary relations in two perfect dielectric media.
4. Explain the solution of Laplace equation in cylindrical coordinates.
5. Use Poisson equation to find V in the region between two concentric right circular cylinders containing a uniform charge density ρ.
6. Given V = cosΦ/ρ in free space.
   (i)Determine the volume charge density at p(0.5, 60^o, 1)
   (ii) Find the electric field intensity, E at p(0.5, 60^o, 1)

Attempt any two part of the following

1. Find the magnetic of a circular current carrying loop.
2. (i) Explain the magnetic torque and moment in detail.
   (ii) Find the magnetization in a magnetic material where
   (a)    m = 1.8 x 10^-5 h/m, H = 120 A/M
   (b) B= 300µT and X_m=15
3. (i) Explain Biot-savart law and Ampere circuital law.
   (ii) The field B = (-2I_x ­+ 3I_y + 4I_z)mT is present in free space. Find vector force exerted on straight wire carrying 12A in I_AB direction, given A(1, 1, 1) and B(2, 1, 1).

Attempt any two part of the following

1. (i) Explain Faraday law and Maxwell’s equations.
   (ii) Explain Wave propagation in lossy dielectrics.
2. Explain Poynting theorem in detail. A plane wave propagating in free space with a peak electric field intensity of 0.75 v/m. Find average power through the square area 120 cm on a side perpendicular to the direction of propagation ƞ=377.
3. Explain the Brewster angle. It is given Explain the Brewster angle. It is given two dielectric medium one is free space and other has Ɛ₂= 4Ɛ_o and µ₂= µ_o. Determine reflection coefficient for Oblique incidence θ₁= 30^o for a (i) perpendicular polarisation, (ii) parallel polarisation.

Attempt any two part of the following

1. Derive transmission line equations. As open wire transmission line with Z_o= 300 Ω is terminated by Z_L= 600 Ω. Find the reflection coefficient and standing wave ratio.
2. Derive input impedance of transmission line. Define standing wave ratio.
3. Calculate the cut-off frequencies for the TE₀₁, TE₁₁, TE₁₂ modes in a rectangular metal wave guide of dimensions 2 cm × 1 cm.

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