JNTU
JNTU B.Tech III ELECTROMAGNETIC THEORY AND TRANSMISSION LINES Previous Question Paper (March - 2021 - R16)
Answer any five questions. All questions carry equal marks.
Main
State and prove Gauss’s Law in both point and integral forms, defining all the terms involved, and establish the Poisson’s and Laplace’s equations.
Answer
Gauss's Law states that the total electric flux passing through any closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space. Mathematically, in integral form:
where D is the electric flux density, S is the closed surface, Qenc is the enclosed charge, and ρv is the volume charge density. Applying the divergence theorem to the left side:
This yields the point form (differential form):
Since D = εE and E = -∇V, substituting these into the point form gives Poisson's equation:
For a homogeneous medium where ε is constant, this simplifies to:
In a charge-free region (ρv = 0), this reduces to Laplace's equation:
Derive an expression for the field in the dielectric region of a cylindrical capacitor, and hence estimate its capacitance, assuming the length as 5 cm, diameter ratio of conductors as 2.50, and
Answer
For a cylindrical capacitor with inner radius a and outer radius b, the electric field E in the dielectric region is derived using Gauss's Law. Assuming a charge Q on the inner conductor of length L:
The potential difference V is the integral of E from a to b:
Capacitance C is defined as Q/V:
Given L = 0.05 m, b/a = 2.50, ε = ε0εr = (8.854 × 10-12) × 2.10 ≈ 1.859 × 10-11 F/m:
Find the Electric Field and Potential due to a single shell of radius R, having a uniform surface charge density
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Two point charges of 5 nC and -5 nC are located at (3, 0, 0) and (-3, 0, 0) respectively. Find the resultant force on a 1 nC charge located at the origin, and also the electric field at the same point.
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Explain the utility and significance of Ampere’s Force Law, and obtain an expression for the force between two current loops.
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Establish the expressions for the Maxwell’s curl equations in differential and integral forms, for time-varying fields.
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Given
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State the Biot-Savart’s Law, and hence list out the expressions for the magnetic field due to the three different current distributions.
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Derive the wave equations for a medium having conductivity σ. Hence list out the same for free space.
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State and prove Poynting Theorem, and explain its significance.
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A UPW with
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A UPW is normally incident from free space onto a perfect conductor medium. Find the resultant reflection coefficients for electric and magnetic fields.
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Using the lossy line equivalent circuit model, derive the transmission line equations in terms of load parameters.
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Using necessary approximations, find the attenuation and phase constants, characteristic impedance and phase velocity for a HF transmission line, having R = 5Ω/m, L = 1.2 μH/m, G ≈ 0, C = 120 pF/m at 50 MHz.
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Establish the relations for the input impedances of - (i) SC and OC lines, (ii) lines of length λ/4 and λ/2, terminated with a load of ZR at UHF.
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Design a quarter wave transformer section to match a 75 ohm cable to a load of 150 ohms at 300 MHz, and illustrate the connectivity with a neat sketch. What are its limitations ?
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