Download VTU BE 2020 Jan ECE Question Paper 17 Scheme 3rd Sem 17EC36 Engineering Electromagnetics

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Note: Answer any FIVE full questions, choosing ONE full question from each module.
ai
U
. _
Module-1

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1
1 a. Obtain an expression for electric field intensity at any given point due to 'n' number of point
:,
P
charges. (04 Marks)

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-
.
b. Four 10 nC positive charges are located in the z = 0 plane at the corners of a square 8 cm on
a side. A fifth 10 nC positive charge is located at a point 8 cm distant from the other charges.
... .

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Calculate the magnitude of the total force on this fifth charge for e = e
o
. (08 Marks)
to ,,,
m C.

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Find the total charge contained in a 2 cm length of the electron beam for 2 cm < z < 4 cm,
,-
. =
.,
p = 1 cm and p

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v
= ?5 e
-100
PII.ic/m
3

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. (08 Marks) ,
1:) ;',,
,
....
4,

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ch
1,

OR

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..._ (
-
-1
ce
,-

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1
-
2 a. Define electric flux and electric flux density, and also, obtain the relationship between
2 ?_) electric flux density and electric field intensity. (06 Marks)
b. Infinite uniform line charges of 5 nC/m lie along the (positive and negative) x and y axes in

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:. - ...
free space, Find E at P(1, 2, 3).
-.., ,.. ,. ,
(10 Marks)
- ?

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c. Given a 60 JAC point charge located at the origin, find the total electric flux passing through:
. r
t

E' =.

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c.) I.)
(i) That portion of the sphere r = 26 cm bounded by 0 < 0 < ?
Tr
and 0 < l4)r < ?
Ir

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.
i8
2 2
"Z
el) c

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(ii) The closed surface de fined by p = 26 cm and z = ?26 cm. (04 Marks) . CZ CZ
-E1 t
Module-2
27 ce
>, t

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l of G i l l f 3 a. State and obtain mathematical o auss law. (07 Marks)
4- 0
0 ?-' --)
ri:
c_

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.? CZ
i
l
0 CD b. Given D = 6p sin ? a,
0

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+ p cos ? a
m
C/m
2
. Evaluate both sides of divergence theorem

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0..
P 0.
2
l
2

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)

00
0J
for the region bounded by p = 2m, sir = 0, (1) = 7C rad, z = 0 and z = 5m. ,.).

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0
(08 Marks)
a) 174
c. Derive the point form of current continuity equation.
3 0

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(05 Marks)
.47.
.?
{% a.
L 0

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OR
PD
72

>, t.? - *

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tu)
C eJ) 4
a.
Given the non-uniform field E = y
,

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x + x a'
y
+ 2 'a, V/m, determine the work expended in
carrying 2C from B(1, 0, 1) to A(0.8, 0.6, 1), along the shorter arc of the circle; x
2

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+ y
2
=1,
P >
iI.J.

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Z = 1. (07 Marks) t.)
?,
8
,
b. Derive the expression for potential field resulting from point charge in free-space. (07 Marks)

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._: c.i
c.
Find the value of volume charge density at p(r = 1.5 in, 0 = 30?, (I) = 50?), when
0
,

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A A ',
0
z
D= 2rsin Ocos4;lar+reosecos(1)au?rsin4la, C/m
2

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. (06 Marks)
P
0
Module-3 .
E

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5 a. Using Gauss law derive Poisson and Laplace equations. (05 Marks)
b. State and prove uniqueness theorem. (10 Marks)
c. Calculate A 1-12 at P
2
(4, 2, 0) resulting from I,A LI = 2rc

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i
az1.1Am at P1(0, 0, 2). (05 Marks)
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17EC36

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USN
Third Semester B.E. Degree Examination, Dec.2019/Jan.2020
Engineering Electromagnetics
Time: 3 hrs. Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.

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ai
U
. _
Module-1
1

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1 a. Obtain an expression for electric field intensity at any given point due to 'n' number of point
:,
P
charges. (04 Marks)
-

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.
b. Four 10 nC positive charges are located in the z = 0 plane at the corners of a square 8 cm on
a side. A fifth 10 nC positive charge is located at a point 8 cm distant from the other charges.
... .
Calculate the magnitude of the total force on this fifth charge for e = e

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o
. (08 Marks)
to ,,,
m C.
Find the total charge contained in a 2 cm length of the electron beam for 2 cm < z < 4 cm,

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,-
. =
.,
p = 1 cm and p
v

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= ?5 e
-100
PII.ic/m
3
. (08 Marks) ,

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1:) ;',,
,
....
4,

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ch
1,

OR
..._ (

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-
-1
ce
,-
1

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-
2 a. Define electric flux and electric flux density, and also, obtain the relationship between
2 ?_) electric flux density and electric field intensity. (06 Marks)
b. Infinite uniform line charges of 5 nC/m lie along the (positive and negative) x and y axes in
:. - ...

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free space, Find E at P(1, 2, 3).
-.., ,.. ,. ,
(10 Marks)
- ?
c. Given a 60 JAC point charge located at the origin, find the total electric flux passing through:

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. r
t

E' =.
c.) I.)

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(i) That portion of the sphere r = 26 cm bounded by 0 < 0 < ?
Tr
and 0 < l4)r < ?
Ir
.

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i8
2 2
"Z
el) c
(ii) The closed surface de fined by p = 26 cm and z = ?26 cm. (04 Marks) . CZ CZ

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-E1 t
Module-2
27 ce
>, t
l of G i l l f 3 a. State and obtain mathematical o auss law. (07 Marks)

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4- 0
0 ?-' --)
ri:
c_
.? CZ

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i
l
0 CD b. Given D = 6p sin ? a,
0
+ p cos ? a

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m
C/m
2
. Evaluate both sides of divergence theorem
0..

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P 0.
2
l
2
)

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00
0J
for the region bounded by p = 2m, sir = 0, (1) = 7C rad, z = 0 and z = 5m. ,.).
0

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(08 Marks)
a) 174
c. Derive the point form of current continuity equation.
3 0
(05 Marks)

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.47.
.?
{% a.
L 0
OR

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PD
72

>, t.? - *
tu)

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C eJ) 4
a.
Given the non-uniform field E = y
,
x + x a'

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y
+ 2 'a, V/m, determine the work expended in
carrying 2C from B(1, 0, 1) to A(0.8, 0.6, 1), along the shorter arc of the circle; x
2
+ y

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2
=1,
P >
iI.J.
Z = 1. (07 Marks) t.)

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?,
8
,
b. Derive the expression for potential field resulting from point charge in free-space. (07 Marks)
._: c.i

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c.
Find the value of volume charge density at p(r = 1.5 in, 0 = 30?, (I) = 50?), when
0
,
A A ',

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0
z
D= 2rsin Ocos4;lar+reosecos(1)au?rsin4la, C/m
2
. (06 Marks)

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P
0
Module-3 .
E
5 a. Using Gauss law derive Poisson and Laplace equations. (05 Marks)

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b. State and prove uniqueness theorem. (10 Marks)
c. Calculate A 1-12 at P
2
(4, 2, 0) resulting from I,A LI = 2rc
i

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az1.1Am at P1(0, 0, 2). (05 Marks)
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17EC36
OR
6 a.

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Show that V
2
V = 0 , for V = (5p
4
? 6p

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-4
)sin44). (05 Marks)
b. Evaluate both sides of Stoke's theorem for the field H = 6xy 3y
2
a

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y
A/m and the
rectangular path around the region, 2 x S 5, ?1 y 1, z = 0. Let positive direction of
d; be a, . (08 Marks)
c. State and explain Ampere's circuital law. Using the same, obtain the expression for H at

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any given point due to the infinite length filamentary conductor, carrying current I.
(07 Marks)
Module-4
7 a. Obtain an expression for Lorentz force equation. (05 Marks)
b. Obtain the relationship between magnetic fields at the boundary of two different magnetic

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media. (09 Marks)
c. Derive the expression for force between two infinitely long. Straight, parallel filamentary
conductors, separated by distance d, carrying equal and opposite currents, I. (06 Marks)
OR
8 a. Given a ferrite material which operates in a linear mode with B = 0.05 T, calculate value.,:::

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for magnetic susceptibility, magnetization and magnetic field intensity. Given J. = 50.
(05 Marks)
b. Obtain expressions for magneto motive force (mmf) and reluctance in magnetic circuits by
making use of analogy between electric and magnetic circuits. (08 Marks)
- >

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c. Two differential current elements, l
i
A LI = 3(10
-6
) a

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y
Am at P
1
(1, 0, 0) and
I,AL2 =3(10

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-6
)(-0.5ax+ 0.4a, + 0.3az) Am at P2(2, 2, 2) are located in free space. Find
vector force exerted on 1
1
01,2 by 1, 4 L, . (07 Marks)

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Module-5
9 a. Explain the inadequacy of Ampere's circuital law for time-varying fields. Obtain a suitable
correction for the same, which will remain consistent for both time and non-time-varying
fields. (05 Marks)
b.

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Let pt = 10
-5
H/m, E = 4 x le F/m, 6 = 0 and p, = 0. Find K (including units) so that the
A
following pair of fields satisfy Maxwell's equations: E = (20y ?Kt)ax V/m

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;
?
H =(y + 2x 10
6
t) , A/m. (05 Marks)

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e. Starting from Maxwell's curl equation, obtain the equation of Poynting's theorem and
interpret the same. (10 Marks)
OR
10 a. Express Maxwell's equations in phasor form as applicable to free-space. Using the same,
obtain vector Helmholtz equation in free space. (09 Marks)

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b. Obtain an expression for skin depth when an electromagnetic wave enters a conducting
medium. Also, calculate the skin depth when a 160 MHz plane wave propagates through
aluminum of conductivity 10
5
U/m, E

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r
= M
r
= 1 (05 Marks)
c. Starting from equation of Faraday's law, obtain the point form of Maxwell's equation

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concerning spatial derivative of E and time derivative of H .
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