Visvesvaraya Technological University (VTU) 2004 B.E Electrical and Electronics Engineering 4th SEM Y/UST FIELD THEORY - Question Paper
5. fa) Explain the nature of the force when a charged particle is moving through
EC 44.
steady electric and magnetic fields.
Find an expression for force on differential current element moving in a steady magnetic field.
Deduce the result to a straight conductor in a uniform magnetic field.(8 Marks)
(b) A conductor 4m long lies along the y-axis with a current of 10.0A in the - ay direction. Find the force on the conductor if the field in the region is
B = 0.05 ax Tesla. (10 Marks)
(c) Discuss the magnetic boundary conditions to apply to B,H and M at the interface between two different magnetic materials. (8 Marks)
6. (a) Discuss the physical significance of displacement current and justify that for
the case of a parallel plate capacitor the displacement current is equivalent to conduction current.
Comment on the ratio of magnitudes of conduction current density to displacement current density.
A circular cross-section conductor of radius 1.5mm carries a current
i = 5.5 sin(4 x 1010i)A Find the amplitude of the displacement current
density if cr = 35 mhojm and e r = 10. (10 Marks)
(b) Derive Maxwell's equations in point form Gauss law for electric and magnetic fields. - -
*
Given E -- Em'sin(ujt - j3I)ay in free space, calculate D,B and H. uo Marks)
7. (a) Discuss i_:e propagation of uniform plane waves in a lossless medium.
A uniform plane wave Ey = 10sm(27r x 10s t-(3x) is traveling in ?-direction in free space. Find i) Phase constant , ii) Phase velocity and iii) the expression
for Hz. Assume Ez = 0 = Ey. aoMarks)
(b) Define Poynting vector and explain the power flow associated with it.
The electric field intensity at a distance of 10 km in free space from a radio station was found to be 2.2 mv/m. Calculate
i) the power density and ii) The total power radiated from the station. Assume rhe radiation to be spherically symmetric. do Marks)
8. Write notes on :
a) Gauss5 divergence theorem (5 Marks)
b) Equation of continuity. (5 Marks)
c) Solution of Laplace's equation (5 Marks) d> Magnetic circuits. (5 Marks)
EC44
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Fourth Semester B.E. Degree Examination, July/August 2004
BM/E C/E E/TE/ML/IT
[Max.Marks : 100
Time: 3 hrs.J
Note: Answer any FTVE full questions.
1. (a) Explain Coulombs law. Justify that the force field in the region of an isolated
charge Q is spherically symmetric. (4 Marks)
(b) Develop an expression for the electric field intensity when charge is distributed uniformly over a surface. (8 Marks)
A line charge of 2 nc/m lies along y-axis while surface charge densities of 0.1 and -0.1 nc/m2 exist on the plane Z=3 and Z=-4m respectively. Find the electric field intensity at a point (1, -7,2).
(c) State and explain Gauss' law and verify it for a point charge.
A point charge Q=30nc is located at the origin in Cartesian coordinates. Find the electric flux density D at (l,3,-4)m. (8Marks)
2. (a) Find an expression establishing the relationship between electric field intensity
and gradient of potential.
Find the electric field strength E at the point (1,2, 1) given the potential V = 3x2y -|- 2yz2 + 3xyz. (10 Marks)
(b) Derive an expression for the energy stored in a region of continuous charge distribution.
A parallel plate capacitor for wrhich C = A/d has a constant voltage V applied across the plates. Find the stored energy in the electric field. do Marks)
3. * (a) Discuss the three basic principles that apply to conductors in electrostatic
fields. Indicate how these principles with a given knowledge of potential field help to calculate certain field quantities.
%
If the potential field V is V = 100(zr - y2) find E, V at a point (2,-1,3) and the equation representing the locus of all points having a potential of 300V.
(6 Marks)
(b) Discuss the behaviour of fields at the interface between a perfect dielectric and
a conductor. (8 Marks)
(c) State and discuss uniqueness theorem. (6 Marks)
4.. (a) State and discuss Amperes circuital law and apply it to the case of an infinitely long co-axial transmission line carrying a uniformly distributed current, to calculate the magnetic field intensity. ' (8 Marks)
(b) If the magnetic field intensity in a region is H = x2ax + 2yzay + (-x2)az, find the current density at the origin. (4 Marks)
(c) Discuss the concept of vector magnetic potential and arrive at an expression for it.
Given the vector magnetic potential A = x2ax + 2yz ay + (-x2)az, find the magnetic flux density. (8 Marks)
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