JNTU
JNTU B.Tech II ELECTROMAGNETIC THEORY AND TRANSMISSION LINES Previous Question Paper (March - 2022 - R13)
Answer any five questions. All questions carry equal marks.
Main
Point charges 5nC and -2nC are located at (2,0,4) and (-3,0,5), respectively. Find the electric field at (1,-3,7).
Answer
The electric field intensity E at a point due to a point charge q is given by E = (q / (4πε₀R²)) * aR, where R is the distance vector from the charge to the point and aR is the unit vector. Given ε₀ = 8.854 × 10⁻¹² F/m.
For charge q₁ = 5nC at P₁(2,0,4) and point P(1,-3,7):
R₁ = (1-2)ax + (-3-0)ay + (7-4)az = -ax - 3ay + 3az
|R₁| = sqrt((-1)² + (-3)² + 3²) = sqrt(19) ≈ 4.359
E₁ = (5 × 10⁻⁹ / (4π * 8.854 × 10⁻¹² * 19)) * ((-ax - 3ay + 3az) / 4.359) ≈ 2.365 * (-ax - 3ay + 3az) V/m.
For charge q₂ = -2nC at P₂(-3,0,5) and point P(1,-3,7):
R₂ = (1-(-3))ax + (-3-0)ay + (7-5)az = 4ax - 3ay + 2az
|R₂| = sqrt(4² + (-3)² + 2²) = sqrt(29) ≈ 5.385
E₂ = (-2 × 10⁻⁹ / (4π * 8.854 × 10⁻¹² * 29)) * ((4ax - 3ay + 2az) / 5.385) ≈ -0.621 * (4ax - 3ay + 2az) V/m.
Total field E = E₁ + E₂ ≈ (-2.365 - 2.484)ax + (-7.095 + 1.863)ay + (7.095 - 1.242)az = -4.849ax - 5.232ay + 5.853az V/m.
Derive Poisson’s and Laplace equation from Gauss Law.
Answer
From Gauss's Law in differential form, the divergence of the electric flux density D is equal to the volume charge density ρv:
Since D = εE and E = -∇V (where V is the electric potential), we substitute these into the equation:
Assuming a homogeneous medium (ε is constant), we obtain Poisson's equation:
In a charge-free region where ρv = 0, this simplifies to Laplace's equation:
Derive the relationship between the E and V.
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Determine the capacitance of each of the capacitors in Figure. Take εr1 = 4, εr2 = 6, d = 5 mm, 51 = 30 cm.
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Derive the expression of Electric field at a point due to an infinite sheet of charge.
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Summarize the Maxwell’s equations for Static Electro-Magnetic fields with remarks.
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State and explain the Biot-Savart’s Law.
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What is the inconsistency in Ampere’s law? How is it rectified by Maxwell?
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Describe the boundary conditions at the interface between Dielectric-Dielectric and Dielectric-conductor.
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What is Poynting theorem? Derive the expression for Poynting vector.
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Derive Wave Equations for conducting and perfect dielectric Media.
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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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A transmission line operating at 500MHz has Z0=80Ω, Propagation constant = 0.04Np/m, β=1.5 rad/m. Find the line parameters R, L, G and C?
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Derive the expression for input impedance of a transmission line when it is terminated by a load.
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A 500Ω lossless line has V_L = 10e^(j250) V and Z_L = 50e^(j300) Ω. Find the current at λ/4 from the load?
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Explain how double stub is used for matching with suitable diagram?
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A 50Ω loss less line connects a signal of 50 KHz to a load of 140Ω. The load power is 75Mw. Calculate (i) Voltage Reflection coefficient (ii) VSWR.
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