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KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS
Electrical Engineering Department
EE 340 MAJOR EXAM I
Fall 2017/2018 (171)
TIME: 6:00-7:30 PM
DATE: TUESDAY 24-October-2017
Instructors: M. Sharawi, M. Khan and H. Masoudi
Name: ___________________________________________________________________________
ID # _____________________________________________________________________________
Section:__________________________________________________________________________
Maximum Score
Total
15
o = 8.854×10-12 [F/m]
o = 4×10-7 [H/m]
Score
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Cricle one letter corresponding to the correct (or most appropraite) answer to the following
qustions (Each one point)
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1- In an electrostatic field which of the following is not correct:
a) The circulation of the electric field around a closed path is zero
b) The potential difference between any two points is zero
c) A material that has a very short relaxation time of the order of 10-19 s is considered as a Good
Conductor
d) The field is said to be conservative
e) Electrical susceptibility of the medium is the source of linear dielectric polarization.
f) None of the above
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2- An infinitely long straight line is placed along the y- axis and charged with a uniform line charge
density  l  10 [C/m]. Given that the medium has a relative permittivity of r = 5, the electric flux
density vector, in [C/m2] at  1, 0, 1 m , is given as:
a)
b)
c)
d)
e)
5  a x
5ax
 az 
2
 az 
2
5  a x  a z 
2  o
5  a x
 az 
2  o
 a x  az 
2
f) None of the above
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3- Consider the electrostatic field E  2ax  2ay  az [V/m] which exists in free space. Also consider the
cylindrical volume V of height h  2 m and base radius a  2 m . The electrostatic energy (in Joule)
stored inside the volume V equals:
a) 2.8 1010
o
b) 0.5 109
c) 18o
1
d)  10 9
6
e) 109
f) None of the above
z
h
a
y
x
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4- In free space, the charge distribution that generates the electric field E 
a)
3  osin 3r
b)
r2
3 osin 3r
d)
3  osin 3r
C / m 2 


 mC / m3 


r2
3 osin 3r
 mC / m3 
c)
4


r
4
r
3 osin 3r
 mC / m 3 


C / m 3 


r
f) None of the above
e)
4
1
r2
1  cos 3r  ar  mV / m is
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5- In free space, a semi-circle ring with radius ‘a’ is carrying a uniform line charge distribution
l  o C / m . The semi-circle ring is located in the x-y plane with its center being the origin as shown
in the side figureThe electric field intensity vector in [V/m] at the origin is:
a)
b)
c)
d)
e)
f)
o
 ax  a y 
4 o a
o
ay
2 o a 2
o
ay
2 o a
 o
ay
2 o a
o
ay
4 o a
None of the above
y
.
o
x
a
l  o
-------------------------------------------------------------------------------------------------------------------------------------------------4 2 y
2
[sin(2 x ) a x +cos(2x ) a y ]  kA/m  , the total current crossing
through the surface 0  x  1 m and 0  z  2 m at the plane y  1 m is:
6- Given the current density J  10 e
a)
b)
c)
d)
e)
f)
0.615 mA
1.23 MA
2.46 MA
1.23 MA
2.46 kA
None of the above
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7- In free space, an infinitely long line with a uniform charge distribution is placed at y = 0, z =-2 m and
parallel to the x-axis, and an infinite uniformly charged sheet is located at the x-y plane with a charge
density of s  5 nC / m2  . If the electric field vector E at point (-1, 0, -1) is ZERO, then the charge


density of the infinite line  l in  n C / m is:
a) 15.71
b) 31.42
c) 5
d) -15.71
e) -31.42
f) None of the above
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8- For an electric Dipole with a dipole moment P  6  10 12 a z C m  located at (6, 0, 0) m, the resulting
electric potential in free space at the point (0, 0, 4) m is
a) 5.75 mV
b) 0.575 mV
c) 0.671 mV
d) -0.575 mV
e) -0.671 mV
f) None of the above
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9- Two concentric spheres are shown in the figure. The inner sphere is of radius a, and the outer sphere
has an inner radius b. The material between the two spheres has a dielectric constant  r  2.25 . If the
inner sphere of r = a has a charge density v  4 nC / m3  , the expression for the electric field in [V/m]


between the two spheres in region (1) is:
a2
ar
r2
a3
b) 66.96 2 ar
r
a) 66.96
c) 66.96
b  a 
d) 150.59
e) 150.59
3
r2
ar
a3
ar
r2
b  a 
3
ar
r2
f) None of the above
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10- The electric field intensity vector in [V/m] generated from an electric potential V  5 r 2 sin 2  V 
o
o
at the point 1, 45 , 45  is:
a) 5 ar  5 a
b) 5ar  5a
c) 5 ar  7.07 a
d) 7.07 ar  7.07 a
e) 7.07 ar  7.07 a
f) None of the above
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11- In free space, a straight line of uniform line charge density l  o C / m  is placed on the z- axis
such that one of its ends is at z  a and the other end is at z  b  b  a  . Assuming the potential to be
zero at infinity, the electrostatic potential in [V] at the origin is
a)
 o
b
ln  
 o  a 
o
a
ln  
2  o  b 
o
c)
b  a 
4  o
o
b
ln  
d)
4  o  a 
z
b)
o  b 
 
4  o  a 
f) None of the above
e)
b
l  o
o
a
.
x
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12- In a medium with a relative permittivity of 2, the cylindrical volume 0    a has a uniform volume
charge distribution v  o C / m3  , the electric field intensity vector in [V/m] at (b, 0, 0) with b > a,


is:
a)
o a3
a
4 o b
b)
o a 2
a
2 o b
c)
o a 2
a
4 o b
d)
o a 2
a
4 ob 2
e)
o a 2
a
2b
f) None of the above
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13- Given that 𝐸1 = 100 [V/m] at a charge–free dielectric free space interface shown, with 1 =30o and
2 =60o. Then the magnitude of E2 and the dielectric constant of medium 2, respectively, are
a)
b)
c)
d)
e)
f)
57.735 [V/m], 3
73.54 [V/m], 3
36.34 [V/m], 2
83.56 [V/m], 2.25
66.44 [V/m], 4.5
None of the above
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14- In free space, an infinitely large plane sheet of uniform surface charge density  S  2  nC / m 2  , is
placed on the y  z plane. Considering the two points a (7, 5, 0) and b (-5, 0, 0) shown, the electrostatic
potential difference V ba equals:
a)
b)
c)
d)
e)
f)
451.977V
225.988 V
225.988 V
451.977 V
151.977V
None of the above
y
.
0
.
b
.
z
 S  2 n C / m 
2
a
x
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15- A homogenous dielectric with r = 3 fills region 2 (z ≤ 0) while region 1 (z ≥ 0) is free space. If the
interface is charge free and the electric field in medium 1 is given as E1  10 a x  2 a y  6 a z [V/m], then
the angle of field E 2 in medium 2 that it makes with the normal to the interface, is
a) 11.1o
b) 22.3o
c) 39.45o
d) 78.9o
e) 50.55o
f) None of the above