JNTU
JNTU B.Tech III ELECTROMAGNETIC THEORY AND TRANSMISSION LINES Previous Question Paper (October - 2020 - R16)
Answer any five questions. All questions carry equal marks.
Main
An infinitely long uniform line charge is located at y=3, z=5. If ρl = 30 nC/m, find electric field intensity E at (i) origin (ii) P(5,6,1).
Answer
The electric field intensity E due to an infinitely long line charge with charge density ρl is given by the formula:
Here, the line is parallel to the x-axis at y=3 and z=5. The radial distance ρ from the line to a point (x, y, z) is ρ = √((y-3)2 + (z-5)2). The unit vector aρ is ((y-3)ay + (z-5)az) / ρ.
(i) At the origin (0, 0, 0): ρ = √((0-3)2 + (0-5)2) = √(9+25) = √34. aρ = (-3ay - 5az) / √34. With ρl = 30 × 10-9 C/m and 1/(2πε0) ≈ 18 × 109, E = (30 × 10-9 × 18 × 109 / 34) × (-3ay - 5az) / √34 ≈ -2.76ay - 4.60az V/m.
(ii) At P(5, 6, 1): ρ = √((6-3)2 + (1-5)2) = √(32 + (-4)2) = 5. aρ = (3ay - 4az) / 5. E = (30 × 10-9 × 18 × 109 / 52) × (3ay - 4az) / 5 ≈ 12.96ay - 17.28az V/m.
Derive the expression for point form of Gauss law.
Answer
Gauss's Law states that the total electric flux Ψ passing through any closed surface is equal to the total charge enclosed by that surface:
The charge enclosed can be expressed as the volume integral of the volume charge density ρv:
Applying the Divergence Theorem to the surface integral, we convert it to a volume integral:
Equating the two expressions for charge:
Since this holds for any arbitrary volume, the integrands must be equal, resulting in the point form of Gauss's Law:
Develop an expression for potential due to dipoles.
Answer
Sign in to view the complete answer paper.
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
Sign in to view the complete answer paper.
State Ampere's law in integral form and derive the derivative form from it. Derive the continuity equation.
Answer
Sign in to view the complete answer paper.
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° with the x axis, find the force on the conductor.
Answer
Sign in to view the complete answer paper.
Starting with Ampere's law, derive Maxwell's equation in integral form based on this law and obtain the corresponding differential equation by applying Stoke's theorem.
Answer
Sign in to view the complete answer paper.
State and prove the boundary conditions for E and H fields for dielectric-conductor interface.
Answer
Sign in to view the complete answer paper.
Derive the relationship between E and H field and show that E/H = 120π.
Answer
Sign in to view the complete answer paper.
Write briefly about instantaneous, average and complex poynting vectors.
Answer
Sign in to view the complete answer paper.
What is Brewster angle? What is its significance?
Answer
Sign in to view the complete answer paper.
Discuss the significance of the Poynting theorem and Poynting vector for energy relations in an electromagnetic field.
Answer
Sign in to view the complete answer paper.
For a 10 MHz travelling wave with Eo=6 V/m find (i) Average poynting vector (ii) Peak energy density.
Answer
Sign in to view the complete answer paper.
Derive an expression for input impedance at any point in a transmission line.
Answer
Sign in to view the complete answer paper.
Derive the secondary constants for a loss less transmission line.
Answer
Sign in to view the complete answer paper.
Explain the basis for construction of Smith chart. Illustrate as to how it can be used as an Admittance chart.
Answer
Sign in to view the complete answer paper.
Sketch input impedance versus line length for shorted and open circuited line with 0 < l < λ.
Answer
Sign in to view the complete answer paper.