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Saturday, 8 October 2016

Field theory- model question paper for MSc Physics/ B.E/B.Tech Electronics

1(a) transform the vector A = yax – xay + zaz into cylindrical coordinates. (04 marks)
(b) Determine the electric field intensity on the axis of a circular conductor (ring) of linear charge density ρL.(06 Marks)
(c) Determine using gauss’s law, the electric field due to a sphere of charge of radius, a. The charges are uniformly distributed over a spherical surface with a distribution ρs. (06 Marks)
(d) An infinitely long line charge of uniform density, ρL produces an electric field. Show that the divergence of this electric field is zero everywhere except at the line. (04 marks)
2(a) Write a note on equipotential surface. (04 Marks)
(b) Three identical line charges with ρL= 10 nC/m are placed on each of the coordinate axes of a rectangular coordinate system. Given the points A(1,2,3) and B(8,6,10), find VAB due to all the three line charges. (06 Marks)
(c) Show that the gradient of the scalar field, V (x,y) = x-y (V) is normal to the planes of constant V. (05 Marks)
(d) What is an electric dipole? Mention one application. (05 marks)
3(a) Ina cylindrical electron beam of radius R and unit length, the volume charge density is given by, ρv = Kρ, where K is some arbitrary constant. Determine the energy stored in the beam. (08 Marks)
(b) Distinguish between convection current and conduction current. (06 Marks)
(c) A copper wire of cross sectional area, 10 -4 m2 carries a uniformly distributed current of 200 A. If the electron density in copper is 4.25×1028 electrons/m3, determine the average drift velocity of the electrons. What is the electric field in the wire? If the length of the wire is 105 m, calculate the potential difference between its ends. What is the resistance of the wire? (06 Marks)
4 (a) Write a note on boundary conditions for perfect dielectric materials. (06 Marks)
(b)  Determine the capacitance of a parallel plate capacitor consisting of two parallel conducting plates of area A and separation d. (06 Marks)
(c) Find the capacitance of an isolated conducting sphere of radius a. (04 Marks)
(d) What is Poisson’s equation? Explain. (04 Marks)
5 (a) State and explain Uniqueness theorem. (06 Marks)
(b) In a charge free region of free space, the potential field is given as V (x,y) = x3-f(x)-y2. Find f(x) if E and V are zero at (0,0,0). (06 marks)
(c) Determine magnetic field due to a current, I flowing in a straight conductor of length 2L. (08 Marks)
6(a) Explain Ampere’s circuital law. (04 Marks)
(b) Write down Maxwell’s equations. (04 Marks)
(c) Show that the magnetic flux density B set up by an infinitely long current carrying conductor satisfies the Gauss’s law. (06 Marks)
(d) Write a note on scalar and vector magnetic potentials. (06 Marks)
7 (a) Explain the terms magnetic susceptibility and relative permeability. (04 marks)
(b) Find the self inductance per unit length of an infinitely long solenoid. (04 Marks)
(c) A steady 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. (06 Marks)
(d) 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. Determine the ratio I1/I2 that makes the stored magnetic energy, Wm a minimum. (06 Marks)
8 (a) From Faraday’s law, derive Maxwell’s equation in point form. (04 marks)
(b) The dry earth has a conductivity 10-8 S/m and a relative permeability 4. Find the frequency range on which the conduction current dominates the displacement current. (04 Marks)
(c) Write the phasor and time-domain forms of a uniform plane wave having a frequaency of 1 (GHz), that is traveling in the +x direction in a medium of ε = 12ε0 and µ = µ0 (06 Marks)
(d) What are Snell’s laws? Explain. (06 Marks)

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