JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II ELECTROMAGNETIC THEORY AND TRANSMISSION LINES Previous Question Paper (December - 2017 - R15)
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
Part A
Find Electric field intensity due to the charge distribution ρv.
Answer
The electric field intensity (E) due to a volume charge distribution (ρv) can be found using Gauss's law. For a continuous charge distribution, the electric field at a point P is the vector sum of the electric fields due to all infinitesimal charge elements dQ within the volume.
dE = (1 / 4πε₀) * (dQ / r²) * ar
where dQ = ρv dv. Integrating over the entire volume gives:
E = ∫(ρv dv) / (4πε₀ r²)
This integral calculates the electric field by summing the contributions from each infinitesimal volume element carrying charge density ρv.
Write poisson’s and Laplace equations.
Answer
Poisson's and Laplace's equations are fundamental in electrostatics and are derived from Maxwell's equations under specific conditions.
Poisson's Equation: Relates the electric potential to the charge density. It is derived from Gauss's law (∇ ⋅ E = ρv/ε₀) and the relationship between electric field and potential (E = -∇V).
∇²V = -ρv/ε₀
Laplace's Equation: A special case of Poisson's equation where the charge density is zero (ρv = 0). This applies to charge-free regions.
∇²V = 0
State Biot-Savart’s law.
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Calculate the self inductance per unit length of an infinitely long solenoid.
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Write a wave equation in a lossy, charge free medium based on Maxwell’s Equation.
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What is Brewster angle? Write its equation.
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What is condition for distortion less transmission line?
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Explain how Quarter wave transformer is used for matching?
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What is the value of characteristic impedance and reflection coefficient for an open circuited line?
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What are the characteristics of smith chart?
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Part B
Point charges 5nC and -2nC are located at (2,0,4) and (-3,0,5), respectively. Find the electric field at (1,-3,7).
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Given that E=(3x^2+y)ax+xay kV/m, find the work done in moving a –2µC charge from (0,5,0) to (2,-1,0) by taking the path.
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An electric dipole of 100az pC.m is located at the origin. Find V and E at point (1,π/3,π/2).
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Three point charges -1nC, 4nC, and 3nC are located at (0,0,0),(0,0,1) and (1,0,0) respectively. Find the energy in the system.
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A circular loop located on x^2+y^2=9, z=0 carries a direct current of 10A along aφ. Determine H at (0,0,4) and (0,0,-4).
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In a certain conducting region, H=yz(x^2+y^2)ax-y^2xay+4x^2y^2az mA/m. Determine J at (5,2,-3).
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State Maxwell’s equations in an integral and word form.
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A unit normal vector from region 2 (µ=2µ0) to region 1 (µ=µ0) is an21=(6ax+2ay-3az)/7. If H1 =10ax+ay+12az A/m and H2 =H2xax-5ay+4az A/m. Determine H2x.
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A lossy material has µ=5µ0, ε=ε0. If at 5 MHz, the phase constant is 10 rad/m, calculate the loss tangent, conductivity of the material, complex permittivity attenuation constant and intrinsic impedance.
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Derive the equation for intrinsic impedance in lossless dielectrics.
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Determine the Fresnel coefficients for oblique incidence from lossless medium 1 to lossless medium 2 for parallel polarization.
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Region 1 is a lossless medium for which y ≥ 0, µ=µ0, ε=4ε0, whereas region 2 is free space, y ≤ 0. If a plane wave E=5cos (10^8t+βt)az V/m exists in region 1, find the time average pointing vector.
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A transmission line operating at 500MHz has Z0=80Ω, Propagation constant = 0.04 Np/m, β=1.5 rad/m. Find the line parameters R, L, G and C?
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Find the Zin at any point on the line in terms load impedance starting from voltage and current wave equations on line.
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For a lossless two wire transmission line show that the Characteristic impedance Z0 = 120/sqrt(εr) * cosh^-1(d/2a).
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A lossless transmission line operating at 4.5GHz has L=2.4µH/m and Z0=85Ω. Calculate the phase constant and the phase velocity.
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A 500Ω lossless line has VL = 10e^j250 V and ZL = 50e^j300 Ω. Find the current at λ/4 from the load?
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A 60 Ω air line operating at 20MHz is 10m long. If the input impedance is 90 +j150Ω. Calculate ZL, Γ and S.
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Explain how double stub is used for matching with suitable diagram? Derive equations for its length and location.
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