Visvesvaraya Technological University (VTU) 2006 B.E Electrical and Electronics Engineering 4th SEM FIELD THEORY - Question Paper
Page No. 1 EC 44
USN
Fourth Semester B.E Degree Examination, July 2006 EE / EC / TE / IT / ML / BM Field Theory
Time: 3 hrs.] [Max. Marks: 100
Note: 1. Answer any FIVE full questions.
2. Assume any missing data.
1 a. State and explain coulombs law in the vector form. Mention the units of each term
involved. (06 Marks)
b. Explain the terms i) Electric field intensity and ii) Electric potential. Also bring out the relation between them. (06 Marks)
c. Point charges of 50nc each are located at A(l. 0, 0), B(-l, 0, 0), C(0, 1, 0) and D(0, -1, 0)m. Find the total force on the charge at A. Also find the electric field intensity at A. (08 Marks)
2 a. Explain the concept of work and potential as applied to an electric field and hence
obtain an expression for the potential difference between two points in an electric field produced by a point charge. (06 Marks)
b. Find electric field intensity at P(0, -h, 0)m due to a line charge of finite length along Z axis between A(0, 0, Zi)m and B(0, 0, Z2)m. (06 Marks)
c. A line charge of total charge lp.c is placed between A(0, 0, 1) and B(0, 0, 2)m. Find electric field intensity at (i) Pi(0, 0, 0)m and (ii) p2(0, 1, l)m. (08 Marks)
3 a. Starting from Gausss law, arrive at Poissons equation and Laplace equation. Write
Laplace equation in explicit form in
i) Cartesian co-ordinate system and
ii) Cylindrical co-ordinate system. (06 Marks)
b. Obtain an expression for the electric field intensity due to an infinite line charge along z axis having a uniform charge of Pi c/m. using Gausss law. (06 Marks)
c. Using Laplace equation, find an expression for the electric potential at any point in an infinitely long co-axial cable with inner radius am and outer radius bm. (08 Marks)
4 a. Discuss the boundary conditions at the interface between two dielectrics of different
permitivies. (06 Marks)
b. Find the stored energy in a system of four identical charges of 4nc at the corners of a square of side lm. What is the stored energy if only two charges are placed at the corners of the square. (06 Marks)
c. Find the potential and volume charge density at P(0.5, 1.5, l)m in free space given the potential field as under
i) V = 2x2 - y2 - z2 volt ii) V = 6p(j)Z volt. (08 Marks)
5 a. State and explain Biot Savarts law. Using this, find the magnetic field intensity in the
vicinity of an infinitely long, straight, filamentary current I Ampere along Z-axis.
(10 Marks)
b. State and discuss Amperes circuital law. Write also in point form. Determine H for a solid cylindrical conductor of radius a where current I is uniformly distributed over the cross section. (1 Marks)
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Page No.2 EC 44
6 a. Discuss the boundary conditions at the interface between two media of different
permeabilities. (06 Marks)
b. State and explain Faradays law of electromagnetic induction. Write also in point form. (06 Marks)
c. Calculate the inductance of a solenoid of 200 turns wound tightly on a cylindrical tube of length 60cm and of diameter 6cm, given that medium is air. Derive the expression used. (08 Marks)
7 a. Starting from Maxwells equations derive the wave equation for sinusoidal waves in a
good dielectric medium. (08 Marks)
b. Derive the wave equation for a wave in conducting medium and hence explain the terms Skin depth. (06 Marks)
c. State and prove Poyntings theorem. (06 Marks)
8 Write short notes on:
a) Energy density in an electrostatic field
b) Continuity equation
c) Force between two differential current elements,
d) Vector magnetic potential. (20 Marks)
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