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Code No: R21029
R10
SET - 1
II B. Tech I Semester Supplementary Examinations Dec - 2013
ELECTRO MAGNETIC FIELD
(Electrical and Electronics Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1.
Three equal positive charges of 6 x10-9 C each are located at three corners of a square of sides
15cm each. Determine the magnitude and direction of electric field at the vacant corner.
2.
a) Derive the expression for electric field intensity due to an electric dipole.
b) Verify whether the potential fields given below satisfy Laplace’s equation,
10 sin  sin 
i) V 
2
ii) V cos 4 z
r
3. a) State and explain Continuity equation of current in integral form and point form.
b) A capacitor consists of two metal plates each of 140cm2, placed in parallel and 3mm apart
The whole of space between the plates is filled with a dielectric having a relative
permittivity of 4. A Potential difference of 500V is maintained between the plates.
Determine i) the capacitance
ii) the charge on the capacitor
iii) the electric flux density and
iv) the potential gradient.
4.
Derive an expression for magnetic field intensity due to a finite length of current carrying
filament.
5.
a) State and explain Ampere’s circuit law.
b) A current sheet k1=5ax A/m flows on y=10, while k2= -10ax A/m flows on y= -4. Find H at
the origin.
6.
a) Derive an expression for the torque on current loop placed in a magnetic field.
b) A distribution line consists of two straight parallel conductors supported on the cross arms
of wooden poles spaced 80m apart. The normal spacing between the two conductors is
15cm, suppose a current of 10,000A flows down one conductor and back the other during a
fault. Determine the force on each 100m section of conductor.
7.
a) Derive the expression for energy stored in a magnetic field.
b) A toroidal coil of 1400 turns has a mean radius of 30cm and a radius for the winding of 3cm.
What is the average self-inductance?
i) With air core
ii) With an iron core of relative permeability µr =800?
8.
a) Explain about induced e.m.f and derive the expressions for statically and dynamically
induced e.m.fs.
b) Write Maxwell’s equations in: i) Point form
ii) Integral form. Explain the significance of
each equation.
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R10
Code No: R21029
SET - 2
II B. Tech I Semester Supplementary Examinations Dec - 2013
ELECTRO MAGNETIC FIELD
(Electrical and Electronics Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1.
a) Derive the concept of electric field intensity from Coulomb’s Law
b) The concentrated charge of 0.35µC is located at the vertices of an equilateral triangle of 8m
of side. Find the magnitude and direction of force on charge due to other two charges.
2.
a) Prove that the potential due to an electric dipole satisfies Laplace equation.
b) Calculate the potential due to a dipole moment of 50x10-10 C/m at a distance 1 m from it,
i) On its axis.
ii) On its perpendicular bisector.
3.
a) Derive the Ohms Law in point form.
b) A spherical condenser has capacitance of 60 pF. It consists of two concentric spheres differ
in radii by 4cm and having air as dielectric. Find the radius of inner and outer spheres.
4.
Derive an expression for magnetic field intensity due to a circular coil.
5.
a) Derive the Maxwell’s third equation.
b) Using Ampere’s circuit law, obtain an expression of the magnetic field intensity at any point
due to a concentric cylindrical conductor, the inner and outer conductors carrying equal and
opposite currents.
6.
a) Derive the expression for force on a straight current carrying conductor placed in a magnetic
field.
b) Two long parallel wires separated 8m apart carry currents of 50A and 60A respectively in
the same direction. Calculate the magnitude and direction of the force between them per unit
length.
7.
a) Derive the expression for mutual inductance with Neuman’s formula.
b) A solenoid with 400 turns is 200mm long and 25mm in diameter. If the current is 450mA
determine, i) Inductance and
ii) Energy stored in solenoid. Assume µr =1.
8.
a) State and Explain Poynting theorem.
b) Derive the expression of one of the Maxwell’s equation curl (E) = - B
t
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Code No: R21029
R10
SET - 3
II B. Tech I Semester Supplementary Examinations Dec - 2013
ELECTRO MAGNETIC FIELD
(Electrical and Electronics Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1.
a) Derive the expression for the field due to a surface charge.
b) Two point charges -4µC and 5µC are located at (2,-1, 3) and (0, 4,-2) respectively. Find the
potential at (1, 0, 1) assuming zero potential at infinity.
2.
a) Derive the Poisson’s and Laplace’s equation.
b) In a cylindrical co-ordinates, V=80V at ρ=6mm and V=0 at ρ=66mm. Find the voltage at
ρ=150mm, if the potential depends only on ρ.
3.
a) Derive the expression for capacitance with multiple dielectrics between two plates.
b) A capacitor is composed of two plates separated by a sheet of insulating material 5mm thick
and εr1 =8. The distance between the plates is increased to allow the insertion of second
sheet 8mm thick and of relative permittivity of εr2. If the capacitance of the capacitor so
formed is one-half of the original capacitance. Determine the value of εr2.
4.
a) State and explain Biot-Savart’s Law.
b) A circular loop of wire of radius ‘a’, laying in XY plane with its centre at the origin carries a
current ‘I’ in the +Ø direction. Using Biot-Savart’s law find the H (0,0,z) and H (0,0,0).
5.
a) Using Ampere’s circuit law, find H due to an infinite sheet of current.
b) Find the magnetic field intensity at a centre of a square of sides equal to 15m and carrying a
current equal to 80A.
6.
a) State and explain Lorentz’s force equation.
b) A conductor of 400cm long carries a current of 15A at right angles to a uniform field
produced by the pole core of an electrical machine. Now
if core has a circular cross
section of 90 mm diameter and total flux in core is 15 mWb, then determine i) force
developed on the conductor and ii) power required to move conductor at a speed of 40
m/sec in a plane at right angles to the field ?
7.
Derive an expression for mutual inductance between a straight long wire and a square long
wire in the same plane.
8.
a) Derive the Maxwell’s equations in point and integral form for time varying fields.
b) State and prove Poynting theorem.
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Code No: R21029
R10
SET - 4
II B. Tech I Semester Supplementary Examinations Dec - 2013
ELECTRO MAGNETIC FIELD
(Electrical and Electronics Engineering)
Time: 3 hours
Max. Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
1.
a) State and explain Gauss’s law as applied to electro-static fields in differential form.
b) Point charges of 50 nC each are located at A(1,0,0), B(-1,0,0), C(0,1,0) and D(0,-1,0) in free
space. Find the total force on the charge at A.
2.
a) Derive the expression for torque on an electric dipole in an electric field.
b) Verify whether the potential fields given below satisfy Laplace’s equation.
1
i) V1 = x2+y2-2z2+10
ii) V2 = 2
2
2
x y z 

3.
a) Derive the expression for capacitances of the spherical condenser.
b) A parallel plate capacitor contains three dielectrics with εr1 =1, d1=0.3mm; εr2=3, d2=0.4mm;
εr3=4, d3=0.5mm. The surface area is 15cm2.
i) Find total capacitance.
ii) Find total energy stored.
4.
a) Derive the expression for Maxwell’s second equation.
b) A uniform solenoid 150mm in diameter 500mm long has 150 turns of wire and a current of
I=2A. Find the magnetic field on the axis of the solenoid,
i) At the centre
ii) At one end and
iii) Half way from the centre to one end.
5.
a) Derive the equation for point form of Amperes current law.
b) Find the field intensity of a point on the axis, 4m from the centre of a circular coil of area
200cm2 and carrying a current of 80A.
6.
a) What is a magnetic di-pole? How a magnetic dipole does differs from an electric dipole.
b) What is the maximum torque on a square loop of 200 turns in a field of uniform flux density
is 1Wb/m2. The loop has 15cm side and carries a current of 5A.
7.
Obtain an expression for the self-inductance, with N closely spaced turns.
8.
a) Show that the displacement current in the dielectric of a parallel plate capacitor is equal to
the conduction current in the leads.
b) State the faradays laws of electro-magnetic induction and derive the expression for the
transformer and motional e.m.fs.
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