Engineering electromagnetics - model question paper for B.Tech / M.Tech

1(a) Transform the vector B = y a_x – x a_y + z a_z into cylindrical co-ordinates. (4 Marks)

(b) Derive an expression for electric field due to an infinite sheet of electric charge. (6 Marks)

(c) Explain Gauss’s law. Mention one application. (6 Marks)

(d) Find div D at the origin if D = e^-x sin y a_x – e^-x cos y a_y + 2 Z a_z. (4 Marks)

2 (a) Write notes on potential gradient and electric field due to dipole. (8 Marks)

(b) Deduce a relation for the work done in moving a point charge in an electric field. (4 Marks)

(c) Write a note on ‘the method of images’. (4 Marks)

(d) The electron and hole mobilities of a semiconductor are 0.43 and 0.21 m²/volt.sec at a particular temperature. If the electron and hole concentrations are both 2.3× 10¹⁹ m^-3, find the conductivity at this temperature.  (4 marks)

3 (a) What are the boundary conditions for perfect dielectric materials? (6 Marks)

(b) Deduce the capacitance of a two-wire line. (10 Marks)

(c) Determine the dielectric constant of a material in which the electric flux density is 4 times the polarization. (4 Marks)

4 (a) Derive Poisson’s and Laplace’s equations. (6 Marks)

(b) Explain how Laplace’s equation can be solved through numerical iteration. (8 Marks)

(c) The four sides of a square trough are held at potentials 0, 20, -30 and 60 volt. The highest and lowest potentials are kept on opposite sides. Determine the potential at the centre of the trough. (6 Marks)

5 (a) What is Ampere’s circuital law. (4 Marks)

(b) Write a note on Stoke’s theorem. (4 Marks)

(c) Differentiate between scalar and vector magnetic potentials. (8 Marks)

(d) A filamentary conductor is formed into an equilateral triangle with sides of length ‘l’ carrying current ‘I’. Determine the magnetic field intensity at the centre of the triangle. (4 Marks)

6 (a) Explain self inductance and mutual inductance. (6 Marks)

(b) What are retarded potentials? (4 Marks)

(c) Write Maxwell’s equations in point form and in integral form. (6 Marks)

(d) A ferrite material is operating in a linear mode with B = 0.05 T. If m_r=50, calculate M, H and c_m. (4 Marks)

7 (a) Write a note on lossless propagation of sinusoidal voltages. (6 Marks)

(b) What is skin effect? Derive a relation for skin depth. (6 Marks)

(c) Write a note on wave polarization. (4 Marks)

(d) A 50 Ω lossless transmission line is terminated by a load impedance, Z_L = 50 – j75 Ω. If the incident power is 100 mW, find the power dissipated by the load.  (4 marks)

8(a) What is chromatic angular dispersion? (4 Marks)

(b) Write a note on planar dielectric waveguides. (6 marks)

(c) Write a note on radiation of electromagnetic energy from a simple dipole antenna. (6 Marks)

(d) An optical fiber link is known to have dispersion β₂=20ps²/km. A Gaussian light pulse at the input of the fiber is of initial width T = 10 ps. Determine the width of the pulse at the fiber output if the fiber is 15 km long. (4 Marks)