KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS
ELECTRICAL ENGINEERING DEPARTMENT
COURSE
SECTION
EXAM
PLACE
DATE
TIME
INSTRUCTORS
EE # 340
ALL
FINAL
7/121(3,4),122(2) and 124(1)
June 3, 2006
7:00 P.M.
Drs: E. Hassan, H. Jamid and H. Ragheb
________________________________________________________________________
STUDENT NAME
--------------------------
STUDENT I.D.
---------------------------
Student Lab.
---------------------------
ATTEMPT ALL FIVE QUESTIONS
PROBLEM 1
PROBLEM 2
PROBLEM 3
PROBLEM 4
PROBLEM 5
TOTAL
Q1-(a)- In the configuration shown, Region 1 is defined
by 0≤ ρ ≤ a and region 2 is defined by a≤ ρ ≤ ∞
Given that:




E1  z 2 sin a   z 2 cos a  2 z sin a z
Region 2
Region 1
a
and  r1  6 ,  r 2  3 Find:

i- E 2 in region 2 at the boundary : ρ = a.
ii- Find Vpq where p(a/4,30o,5) and q(3a/4,60o,10).
Q1-(b)- A vertical plane (perpendicular to the z=0 plane) and intersects the z=0 plane at
the line 2y+x=4, is charged with surface charge density ρs = 4 C/m2 . Find the
electric field at the origin.
Q2- The diagram below shows an infinitely long filamentary wire, which carries the
sinusoidal current:
i(t )  I o cos t
The rectangular loop of dimensions b  h shown in the diagram lies entirely in the y  z
plane. This loop moves away from the filamentary wire with the constant velocity
u  a y uo . At t  0 , the left hand side of the rectangular loop is located at a distance a
from the filamentary wire. Assume the medium is air.
Derive an expression for the EMF induced in the rectangular loop for t  0 .
z
N  turns
i(t )  I o cos t
u  a y uo
h
 EMF 
b
y
Q-3 The diagram below shows an infinitely long filamentary wire that passes through
the center of an N  turn toroidal coil having a rectangular cross-sectional area. The core
of the toroidal coil has a relative permeability  r . The inner and outer radii of the coil are
a and b , respectively. As seen in the diagram, the filamentary wire carries D.C. current
I and no current flows in the toroidal coil.
a) Derive an expression for the magnetic flux through one turn of the toroidal coil.
b) Derive an expression for the mutual inductance between the filamentary wire and the
toroidal coil.
c) Using the following set of values: N  500 , a  3 cm , b  8 cm , h  0.05 m ,
r  100 , and I  2 A , calculate:
i) The mutual inductance in Henry.
ii) The magnetostatic energy stored in the core of the toroidal coil (Hint: Wm  0.5MI 2
and also Wm  0.5 LI 2 ).
z
z
I
I
N  turns
h
h
a
a
b
b
Q-4- A lossy non-magnetic dielectric has an intrinsic impedance 10015 o at ω  10 8
rad/sec. If a plane wave is propagating through this medium having a magnetic field
given by
H  15e  ay cos(108 t  y)aˆ z
Find:
(a) the electric field E ,
(b) the attenuation constant α and the skin depth δ ,
(c) the relative permittivity ε r ,
(d) the conductivity σ .
(e) The phase velocity.
A/ m
Q-5- A uniform plane wave in free space ( z  0 ) with the electric field component,
E  10 cos(ωt  3 z ) aˆ x V/m
hits normally a dielectric surface at z  0 as shown below. Assuming that the dielectric
surface is smooth and ε r  4 ,  r  1 and σ  0 , determine
(a) ω
(b) The wavelength of the wave in air.
(c) Calculate the reflection and transmission coefficients.
(d) Write expressions for the total electric and magnetic fields in mediums 1 & 2.
(e) Calculate the average reflected power over a rectangular area of 3 2 m2 inclined
by an angle 60 with respect to z-axis as shown.
3  2 m2
rectangular plane
H
E
z
60 o
Dielectric
Medium (2)
Free space
Medium (1)
x
 D  ds   q
Gauss’s law :
dE  
enclsed
b
D  εE ,
Vab    E  dl ,
C
a
dq
4 o  r r 2
1
we  ε E 2 ,
2
Q
,
V
D1n  D2 n   s
Biot-Savart law : dH  I
We   we dv
v
l
an
2d
E Field of infinite line and infinite plane: E 
Boundary conditions:
ar
E
E1t  E2t
dl  aˆ r
, Ampere’s Law
4πr 2
O 
 H  dl  I
s
an
2
1
X 109 F/m
36
enclosed
o  4 x 107 H/m
H Field of infinite line and infinite plane: H 
Boundary conditions:
inductance M 
BN 1  BN 2 ,
 
1 
Kxan , F   IdlX B
2
Φ
I
vp 
jωμ(σ  jωε)
 [ {1  (
(ai xan ) , H 
aˆ12  ( H 2  H1 )  K , mutual
S
γ
2d
emf   (v  B )  dl  
Faraday’s law :
phase velocity:
I
ω
,
β
λ
,
 2
) }  1]

,
2
For good conductor :
B
 ds
t
wm 
1
H2
2
2π
β
Z
 
jωμ
,
σ  jωε
1/ 4
Z   /  [1  (  ) 2 ]
 [ {1  (
α  β  πμσf
 2
) }  1]

, Tan(2 z )   
2
, Z
1
μπf
(1  j ) , δ 
α
2σ
 1  σ 2 
σ μ
For good Dielectric: α 
, β  ω με 1     ,
2 ε
 8  εω  
Z
μ 
σ 
1  j

ε 
2ωε 
Reflection and Refraction: For normal incidence take all angles to be ZEROS.
η 2 cos θ i  η1 cos θ t
η 2 cos θ i  η1 cos θ t
η cos θ t  η1 cos θ i
Γ//  2
η 2 cos θ t  η1 cos θ i
Γ 
 cos θ t
1  Γ//  Τ// 
 cos θ i



2η 2 cos θ i
, 1  Γ  Τ
η 2 cos θ i  η1 cos θ t
2η 2 cos θ i
, Τ// 
,
η 2 cos θ i  η1 cos θ t
,
Τ 
θi  θ r ,
sin θ t 
β1
sin θ i
β2