Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B. Tech III ELECTROMAGNETIC FIELDS AND WAVES Previous Question Paper (September - 2021 - R18)
Answer any five questions. All questions carry equal marks.
Main
Define Electric Field intensity. Three identical point charges of 10 nC are located at the vertices of an equilateral triangle of side 10 cm. Calculate the magnitude of the force on each charge and the electric field intensity at the center of the triangle.
Answer
Electric Field Intensity (E) is defined as the force experienced by a unit positive test charge placed at a point in an electric field. It is given by E = F/q, measured in V/m or N/C.
For the equilateral triangle with side length a = 0.1 m and charges q = 10 × 10⁻⁹ C:
The force on one charge due to the other two is the vector sum of the individual Coulomb forces. The distance between any two charges is 0.1 m. The angle between the two force vectors is 60°. The magnitude of each individual force is:
The resultant force magnitude is:
At the center of an equilateral triangle, the electric field vectors produced by three identical charges are equal in magnitude and separated by 120°. By symmetry, their vector sum is zero. Thus, the electric field intensity at the center is 0 V/m.
State and derive the expression for Equation of Continuity.
Answer
The Equation of Continuity states that the divergence of current density is equal to the negative rate of change of volume charge density, expressing the principle of conservation of charge.
Derivation:
- The total current I leaving a closed surface S is the rate of decrease of charge Q inside the volume V: I = -dQ/dt.
- Expressing current in terms of current density J: ∮ J · dS = -d/dt ∫ ρ dv.
- Applying the Divergence Theorem to the surface integral: ∫ (∇ · J) dv = -∫ (∂ρ/∂t) dv.
- Since this holds for any arbitrary volume, the integrands must be equal: ∇ · J = -∂ρ/∂t.
Derive an expression for the capacitance of a parallel plate capacitor having two dielectric media.
Answer
Sign in to view the complete answer paper.
With necessary explanation, derive the Maxwell’s two equations for electrostatic fields.
Answer
Sign in to view the complete answer paper.
Derive general field relation for time varying electric and magnetic fields using Maxwell’s equations.
Answer
Sign in to view the complete answer paper.
A hollow conducting cylinder has inner radius a and outer radius b which carries current I along the positive z-direction. Find H everywhere.
Answer
Sign in to view the complete answer paper.
A wire in the form of a parabola carries a current 3A. Calculate the magnitude of the magnetic field intensity at its focus if the distance from the focus to the apex is 20cm.
Answer
Sign in to view the complete answer paper.
Explain about scalar and vector magnetic potentials.
Answer
Sign in to view the complete answer paper.
What are the different ways of EMF generation? Explain with the governing equations and suitable practical examples.
Answer
Sign in to view the complete answer paper.
Assuming that sea water has 𝜇 = 𝜇o, 𝜖 = 81𝜖o, 𝜎 = 20S/m, determine the frequency at which the conduction current density is 10 times the displacement current density in magnitude.
Answer
Sign in to view the complete answer paper.
What do you mean by displacement current? Write down the expression for the total current density.
Answer
Sign in to view the complete answer paper.
Derive the boundary conditions of the normal and tangential components of electric field at the interface of two media with different dielectrics.
Answer
Sign in to view the complete answer paper.
Derive the expression for the attenuation constant, phase constant and intrinsic impedance for a uniform plane wave in a good conductor.
Answer
Sign in to view the complete answer paper.
Discuss about the plane waves in lossy dielectrics.
Answer
Sign in to view the complete answer paper.
Derive an expression for transmission of TE waves between parallel perfectly conducting planes for the field components.
Answer
Sign in to view the complete answer paper.
For a frequency of 10GHz and plane separation of 5cm in air, find the cutoff frequency, cutoff wavelength, phase velocity and group velocity of the wave.
Answer
Sign in to view the complete answer paper.