JNTU
JNTU B.Tech III ELECTROMAGNETIC THEORY AND TRANSMISSION LINES Previous Question Paper (August - 2022 - R16)
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Main
Evaluate the electric field intensity at a point P (-5, 7, -4) in free space due to a charge of 0.2 milli coulombs placed at point R(2, -1, -2).
Answer
The electric field intensity E at a point P due to a point charge Q is given by Coulomb's Law:
Given: Q = 0.2 mC = 0.2 × 10⁻³ C, R = P - R = (-5 - 2)aₓ + (7 - (-1))aᵧ + (-4 - (-2))a₂ = -7aₓ + 8aᵧ - 2a₂. The distance vector magnitude is |R| = sqrt((-7)² + 8² + (-2)²) = sqrt(49 + 64 + 4) = sqrt(117) ≈ 10.817 m. The unit vector is aᵣ = R / |R|. Substituting values with ε₀ ≈ 8.854 × 10⁻¹² F/m:
Calculating the magnitude factor: 1 / (4π * 8.854 × 10⁻¹² * 1265.59) ≈ 7105.8. Thus, E ≈ 0.2 × 10⁻³ * 7105.8 * (-7aₓ + 8aᵧ - 2a₂) ≈ -9.95aₓ + 11.37aᵧ - 2.84a₂ kV/m.
Derive the expression for point form of Gauss law.
Answer
Gauss's Law in integral form states that the total electric flux passing through a closed surface is equal to the total charge enclosed by that surface:
Using the Divergence Theorem, the surface integral of the electric flux density D over a closed surface can be converted to a volume integral of its divergence:
Equating the two expressions for the total charge:
Since this equality holds for any arbitrary volume, the integrands must be equal, resulting in the point form of Gauss's Law:
This equation indicates that the divergence of the electric flux density at any point is equal to the volume charge density at that point.
Define Electric field intensity at a point. Derive the expression for E for a line charge.
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An infinitely long uniform line charge is located at y=3, z=5 of PL = 30 nc/m. Find E at the origin.
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State Ampere's law in integral form and derive the derivative form from it. Derive the continuity equation.
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A 3 meter long straight conductor carries a current of 100A in the +x direction. If the flux density is uniformly 2 Tesla and is parallel to xy plane, making an angle of 30 degrees with the x axis, find the force on the conductor.
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Starting with Ampere's law, derive Maxwell's equation in integral form based on this law and obtain the corresponding differential equation by applying Stroke's theorem.
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State and prove the boundary conditions for E and H fields.
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Derive the relationship between E and H field and show that E/H = 120π.
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Write briefly about instantaneous, average and complex poynting vectors.
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Discuss the wave propagation in good conductor and good dielectrics.
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For a 20 MHz travelling wave with Eo=6 V/m find:
i) Average poynting vector
ii) Peak energy density.
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Derive an expression for input impedance at any point in a transmission line.
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Derive the secondary constants for a low loss transmission line.
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Explain the basis for construction of Smith chart. Illustrate as to how it can be used of an Admittance chart?
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Sketch input impedance versus line length for shorted and open circuited line with 0 < l < λ.
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