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Tuesday, 7 July 2015

Field theory-Model question paper for B.E/B.Tech



1(a)  A uniform volume charge distribution exists in a spherical volume of radius a. Using the concept of  energy density or otherwise, find the total energy of the system.  (6 Marks)
(b) Three charges -1(µC), 4(µC) and 3(µC) are located in free space at (0,0,0), (0,0,1) and (1,0,0) respectively. Find the energy stored in the system. (4 Marks)
(c) Transform the vector A = y ax – x ay + z az into cylindrical co-ordinates. (4 Marks)
(d) The electric potential in the vicinity of the origin is given as V = 10x2 + 20 y2 + 5 z2 (V). What is the electric field intensity? Can this potential function exist? (6 Marks)
2(a) Determine the capacitance of a parallel-plate capacitor consisting of  two parallel conducting plates of area A and separation d. (6 Marks)
(b) Using Laplace’s equation, obtain the potential distribution between two spherical conductors separated by a single dielectric. The inner spherical conductor of radius ‘a’ is at a potential ‘V0’ and the outer conductor of radius ‘b’ is at potential 0. Also find variation of E. (8 Marks)
(c) A cubical region of space is defined by the surfaces x=1.8, y=1.8, z=1.8,x=2, y=2 and z=2. If D=3y2ax+3x2yax (C/m2);
(i) Find the exact value of the total charge enclosed within the cube by surface integration.
(ii) Find an appropriate value for the enclosed charge by evaluation of derivatives at the centre of the cube.  (6 Marks)
3(a) State Ampere’s circuital law. (4 Marks)
(b) State Stoke’s theorem. (4 Marks)
(c) Show that the magnetic flux density B set up by an infinitely long current-carrying conductor satisfies the Gauss’s law. (4 Marks)
(d) A cylinder of radius ‘b’ and length ‘L’ is closely and tightly wound with N turns of a very fine conducting wire. If the wire carries a dc current I, find the magnetic flux density at any point on the axis of the cylinder (solenoid). What is the magnetic flux density at the centre of the cylinder? Also, find B at the ends of the cylinder. (8 Marks)
4(a) Write a note on magnetic torque and moment on a closed circuit. (6 Marks)
(b) What are magnetic circuits? Distinguish between linear and non-linear magnetic circuits. (10 Marks)
(c) Through a suitable experiment on a magnetic material, the magnetic flux density B is found to be 1.2 T when H=300 A/m. When H is increased to 1500 A/m, the B field increased to 1.5 T. What is the percentage change in the magnetization vector? (4 Marks)
5(a) Find the self-inductance per unit length of an infinitely long solenoid. (6 Marks)
(b) A steady state current is restricted to flow on the outer surface of the inner conductor (ρ=a) and the inner surface of the outer conductor (ρ=b) in a coaxial cable. If the coaxial cable carries a current I, determine the energy stored per unit length in the magnetic field in the region between the two conductors. Assume that the dielectric is non-magnetic. (8 Marks)
(c)  Consider two coupled circuits having self-inductances L1 and L2 that carry currents I1 and I2 respectively. The mutual inductance between the two coupled circuits is M12. Find the ratio I1/I2 that makes the stored magnetic energy Wm a minimum. (6 Marks)
6(a) State Faraday’s law. Derive Maxwell’s equation in point form from faraday’s law. (8 Marks)
(b) Show that for a sinusoidally varying field, the conduction current and the displacement current are always displaced by 900 in phase. (4 Marks)
(c) The dry earth has a conductivity 10-8 S/m, and a relative permittivity 4. Find the frequency range on which the conduction current dominates the displacement current. (4 Marks)
(d) Write Maxwell’s equations in integral form. (4 Marks)
7(a) Derive the differential form of continuity equation from the Maxwell’s equations. (4 Marks)
(b) Write the set of four Maxwell’s equations in terms of eight scalar equations in Cartesian coordinates. (12 Marks)
(c) Consider the wet earth with the following properties: ε = 30 ε0 μ = μ0  σ = 10-2 S/m. Determine the ratio of amplitudes of conduction and displacement currents at 100 MHz. (4 Marks)
8(a) Write the phasor and time-domain forms of a uniform plane wave having a frequency of 1 GHz, that is traveling in the +x=direction in a medium of ε = 12ε0
μ = μ0. ( 6 Marks)
(b) Define skin depth. Prove that high frequency resistance is very much greater than dc resistance. (6 Marks)
(c) State and explain Poynting’s theorem. (5 Marks)
(d) Determine the critical angle if the refractive index of the medium is 1.77. (3 Marks)

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