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Tuesday, 14 August 2012

Electromagnetic field theory- MSc/PhD model question paper

1(a) What is the basic difference between circuit and field theory? (6Marks)
(b) State and Prove Stokes’ theorem. (6 Marks)
(c) Discuss properties of Dirac-Delta function. (4 Marks)
(d) Given f = xy + yz + xz. Find gradient at (1,2,3) and the directional derivative of f at some point in direction towards the point (3,4,4). (4 Marks)
2 (a) Lines of force and flux can’t cross each other over a single point. Explain. (4 Marks)
(b) Discuss superposition principle with reference to electric potential function. (4 Marks)
(c) Derive expression for field inside parallel plate capacitor. (6 Marks)
(d) The point charges -2 nC, 4 nC and 2 nC are located at (0,0,0), (0,0,1) and (1,0,0) respectively. Find the enrgy in system. (6 Marks)
3 (a) Derive Ampere’s law in differential vector form. (6 Marks)
(b) State and explain Biot-Savart law. (4 Marks)
(c) Relate displacement current and conduction current. (6 Marks)
(d) The toroidal core has r0 = 20 cm and a circular cross section with a = 0.5 cm. If core is made of steel (m = 1000 m0) and has a coil with 100 turns, calculate the amount of current that will produce a flux of 1 mWb in core. (4 Marks)
4 (a) Write Maxwell’s equations in differential and integral form. Explain physical significance. (12 Marks)
(b) Rewrite Maxwell’s equations for harmonically varying field. (4 Marks)
(c) An ac voltage source v = V0 sinwt is connected across a parallel plate capacitor C. Verify that the displacement current in capacitor is same as conduction current wires. (4 Marks)
5 (a) Derive expression for intrinsic impedance. (6 Marks)
(b) Give expressions for circular and elliptical polarization. (6 Marks)
(c) What are Helmholtz equations? (4 Marks)
(d) A parallel polarized wave propagates from air to dielectric at Brewster angle of 8.50. Calculate relative dielectric constant of medium.  (4 Marks)
6 (a) explain the wave propagation in good dielectrics. (6 Marks)
(b) Derive conditions for horizontal and vertical polarization. (6 Marks)
(c) Derive expression for Poynting’s theorem. (4 Marks)
(d) Find skin depth S at frequency of 1.8 MHz in aluminium, where s = 34 MS/m and mr = 1. Also find propagation constant and wave velocity. (4 Marks)
7 (a) explain the characteristics of various types of transmission lines. (6 Marks)
(b) Define artificial lines. What are the applications of artificial lines. (6 Marks)
(c) Obtain expressions for reflection factor and reflection loss. (4 Marks)
(d) A 100 W line feeding the antenna has SWR = 2 and the distance from load to the first minima is 10 cm. Design a single stub matching to make SWR = 1. Given f = 150 MHz.(4 Marks)
8 (a) Discuss types of Bridged T equalizers. (6 Marks)
(b) What is the need of attenuator over a line? (4 Marks)
(c) Write a note on different types of variable attenuators. (6 Marks)
(d) An air line has a characteristic impedance of 75 W and a phase constant of 4 rad/m at 200 MHz.  Calculate the inductance per meter and capacitance per meter of line. (4 Marks)

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