Visvesvaraya Technological University (VTU) 2006 B.E Electrical and Electronics Engineering 4th SEM / FIELD THEORY - Question Paper
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Reg. No
Fourth Semester B.E. Degree Examination, January/February 2006
(Max.Marks : ICO
Time: 3 hrs.)
Note: 7. Answer any FIVE full questions.
2. Assume the missing data, if any.
1. (a) Explain electric field intensity at a point in an electric field produced by a point charge. Show that the electric field intensity at any point due to an infinite sheet of charge- is independent of the distance to the point from the sheet. (8 Marks)
(b) Explain the concept of work and potential as applied to an electric field and henc obtain an expression for the potential difference between two points in an electri field produced by a point charge. (6 Marks)
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(c) Find the electric field at the origin due to a point charge of 6.44 x 10~C located at (-4,2, -3)77? in the Cartesian coordinate system. (6 Marks)
2. (a) State and prove Gauss law cna determine the field due to an infinite 'ine charge
using the same. (10 Marks)
(b) With usual notaiions establish tne relationship between elecrric field intensity and the electric potential. (4 Marks)
(c) Given the potential field V = 50 x X-YZ -j- 20y2Volts in free spcce, find the voltage at a point P(1.2, -3) and the field strength at P. (6 Marks)
3. (a) Using Laplace's equation, prove that the electric potential at any point distanT
r in the space between 2 charged concentric spheres of radii and R0 as
l l
(8 N._,ks)
V = V
o
(b) With usual notations derive boundary conditions at the boundary between a , dielectric and a conductor in an electric field. (8 Marks)
(c) Prove that the potential field given by V = 2x2- 3y2 + z2 satisfies Lapicce equation.
(4 Marks)
4. (a) Using the concept of volume energy density in an electric field, find the total energy stored in :
i) A parallel plate system
ii) Two concentric spherical conductors. Hence find their capacitcnces.
(8 Marks)
(b) Show that the magnetic field intensity at the end of a long solenoid is one half of that at the center. (6 Marks)
(c) Derive an expression for the equction of continuity. (6 Marks)
Contd.... 2
5. (a) State and prove Ampere's circuitai.law and apply it to a straight solid cylindricc! conductor to calculate the magnetic field intensity. . (8 Marks)
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(b) Discuss the concept c- vector magnetic potential and hence show that * i t # ;
'A = ' j ~r dv; where A is the vector magnetic potential and J is the
current density.
(6 Marks)
(c) Find the magnetic field inrensity at the center of a square of sides equal to 5m and carrying current of 10A. (6 Marks)
6. (a) Derive an expression for the force on a differential current element placed in a magnetic field. Also obtain an expression for the emfjnduced between the two ends of a conductor due to its motion in a steady magnetic field. (8 Marks)
(b) Find the frequency at which the conduction current density and the displacement current density are equal in a medium with
a = 2 x 10-4 mho/m and eT= 81 (6 Marks)
(c) Starting from Faraday's law' of electromagnetic induction derive the Maxwell's equation y x & = ~r
(6 Marks)
7. (a) State and prove Poyniing's theorem. v (10 Marks)
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(b) A radio station transmits power radially c'ound the spherical region. The desired electrical field intensity c: a distance of 10 km from the station is ImV/m. Calculate the corresponding H, P cr.d the station power. (10 Marks)
8. Write explanatory note on :
(a) Divergence theorem
(b) Biot-Savart's law
(c) Wave propagation in a good conducting medium
(d) Inductance of a co-axlc! cable. (5x4=20 Marks)
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| Earning: Approval pending. |
