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e
to
ex
tr
em
ely
lo
w
f
r
eq
u
e
n
cy
elec
tr
ic
an
d
m
ag
n
etic
f
ield
s
(
E
L
F
-
E
MF)
[
1
4
]
–
[
1
8
]
.
T
h
e
e
x
p
o
s
u
r
e
lim
its
im
p
o
s
ed
b
y
t
h
is
co
m
m
is
s
io
n
ar
e
esti
m
ated
o
v
e
r
2
4
h
o
u
r
s
,
f
o
r
th
e
g
e
n
er
al
p
u
b
lic
5
k
V/m
f
o
r
th
e
elec
tr
ic
f
ield
an
d
2
0
0
μ
T
f
o
r
th
e
m
ag
n
etic
f
ield
,
f
o
r
p
r
o
f
ess
io
n
al
ex
p
o
s
u
r
e,
th
ey
ar
e
r
esp
ec
tiv
ely
1
0
k
V/m
an
d
1
m
T
[
1
8
]
.
Sev
er
al
s
tates
o
v
er
th
e
w
o
r
ld
h
av
e
r
elied
th
e
ex
p
o
s
u
r
e
lim
it
v
alu
es
p
r
o
p
o
s
ed
b
y
I
C
NI
R
P
as
n
atio
n
al
s
ta
n
d
ar
d
s
,
wh
ile
o
t
h
er
co
u
n
tr
ies
h
av
e
ta
k
en
m
o
r
e
s
ev
er
e
p
r
ev
e
n
tio
n
th
r
esh
o
ld
s
in
th
e
n
am
e
o
f
t
h
e
p
r
ec
a
u
tio
n
ar
y
p
r
in
cip
le;
aim
in
g
to
p
r
ev
en
t
th
e
ap
p
ea
r
an
ce
o
f
an
y
b
io
lo
g
ical
h
ea
lth
im
p
licatio
n
s
lin
k
ed
to
e
x
p
o
s
u
r
e
to
elec
tr
ic
an
d
m
a
g
n
etic
f
ield
s
,
th
ey
h
av
e
ad
o
p
ted
v
er
y
lo
w
e
x
p
o
s
u
r
e
lim
its
,
n
o
ta
b
ly
in
v
u
ln
e
r
ab
le
z
o
n
es
(
p
o
p
u
la
ted
ar
ea
s
,
h
o
s
p
itals
,
n
u
r
s
er
ies,
s
ch
o
o
ls
)
,
th
ey
co
n
s
id
er
th
at
th
e
lim
it
v
alu
es
r
ec
o
m
m
en
d
e
d
b
y
I
C
NI
R
P
ar
e
r
elativ
ely
h
ig
h
an
d
th
er
ef
o
r
e
a
r
esu
ltin
g
ex
p
o
s
u
r
e
s
itu
atio
n
is
p
o
ten
tially
s
ig
n
if
ican
t
[
1
9
]
,
[
2
0
]
.
As
alter
n
atin
g
cu
r
r
en
t
(
AC
)
elec
tr
ic
tr
an
s
p
o
r
tin
g
p
o
wer
lin
es
ar
e
co
u
n
ted
am
o
n
g
th
e
m
ain
s
o
u
r
ce
s
o
f
elec
tr
ic
an
d
m
a
g
n
etic
f
ield
s
,
wh
ich
ar
e
all
th
e
m
o
r
e
in
ten
s
e
as
th
e
o
p
e
r
atin
g
v
o
ltag
e
o
f
th
e
o
v
er
h
ea
d
p
o
wer
lin
e
is
in
cr
ea
s
ed
an
d
th
e
cu
r
r
en
t
cir
cu
latio
n
th
er
e
is
s
ig
n
if
ican
t.
I
t
b
ec
o
m
es
th
u
s
im
p
er
at
iv
e
to
q
u
an
tif
y
an
d
co
n
tr
o
l
th
e
lev
el
o
f
th
e
elec
tr
ic
an
d
m
ag
n
etic
f
ield
r
ad
iate
d
b
y
th
ese
tr
an
s
m
is
s
io
n
p
o
wer
lin
es,
in
o
r
d
er
to
b
etter
p
r
o
tect
p
u
b
lic
h
ea
lth
an
d
en
v
i
r
o
n
m
e
n
tal
s
af
ety
f
r
o
m
f
ea
s
ib
le
h
az
ar
d
s
r
elate
d
to
t
h
e
p
o
wer
tr
a
n
s
m
is
s
io
n
lin
es
[
2
1
]
.
Giv
en
th
e
o
n
g
o
in
g
co
n
ce
r
n
s
o
f
in
ter
n
atio
n
al
s
o
ciety
ab
o
u
t
th
e
p
o
ten
tially
lo
n
g
-
ter
m
h
ar
m
f
u
l
im
p
ac
ts
o
n
th
e
h
ea
lth
o
f
b
io
l
o
g
ical
s
y
s
tem
s
r
esu
ltin
g
f
r
o
m
ex
p
o
s
u
r
e
to
v
e
r
y
lo
w
f
r
eq
u
e
n
cy
m
ag
n
etic
f
ield
s
p
r
o
d
u
ce
d
b
y
elec
tr
icity
tr
an
s
p
o
r
tin
g
p
o
wer
lin
es;
th
e
latter
i
s
th
u
s
wo
r
k
in
g
to
m
ee
t
t
h
e
ch
allen
g
e
o
f
f
in
d
in
g
s
o
lu
tio
n
s
to
ef
f
ec
tiv
ely
r
ed
u
ce
am
b
ien
t m
ag
n
etic
f
ield
lev
els
.
B
ased
o
n
th
e
ab
o
v
e,
t
h
is
p
ap
e
r
is
p
r
esen
ted
with
th
e
aim
t
o
a
s
s
es
s
an
d
r
e
d
u
ce
t
h
e
m
a
g
n
etic
in
d
u
ctio
n
p
r
o
f
ile
cr
ea
te
d
b
y
an
u
ltra
-
h
ig
h
-
v
o
ltag
e
o
v
e
r
h
ea
d
p
o
wer
lin
e
u
s
in
g
a
m
eth
o
d
o
lo
g
y
o
f
th
e
p
h
y
s
ical
p
r
in
cip
le
o
f
th
e
B
io
t
-
Sav
ar
t
law
an
d
th
e
th
eo
r
y
o
f
v
ec
to
r
m
a
g
n
etic
f
ield
s
s
u
p
er
p
o
s
itio
n
[
2
2
]
–
[
2
4
]
.
Fu
r
th
er
m
o
r
e,
an
ef
f
ec
tiv
e
m
ec
h
a
n
is
m
f
o
r
im
p
r
o
v
in
g
th
e
m
ag
n
etic
in
d
u
ctio
n
m
itig
atio
n
r
esu
ltin
g
f
r
o
m
p
ass
iv
e
an
d
ac
tiv
e
co
m
p
en
s
atio
n
lo
o
p
s
is
p
r
o
p
o
s
ed
,
u
s
in
g
th
e
g
r
ay
wo
lf
o
p
t
im
izer
(
GW
O)
alg
o
r
ith
m
,
wh
ich
ca
n
p
r
o
v
id
e
a
m
in
im
u
m
t
o
tal
m
ag
n
etic
f
iel
d
in
ad
jace
n
cy
o
f
u
ltra
-
h
ig
h
v
o
ltag
e
(
UHV)
AC
o
v
er
h
ea
d
tr
an
s
p
o
r
tin
g
p
o
wer
lin
es.
T
h
e
ef
f
ec
t
o
f
m
ag
n
etic
co
m
p
en
s
atio
n
co
n
s
is
ts
o
f
in
d
u
cin
g
o
r
in
jectin
g
a
c
u
r
r
e
n
t
in
to
a
c
o
n
d
u
ctiv
e
lo
o
p
p
lace
d
in
th
e
im
m
e
d
iate
n
ea
r
n
ess
o
f
th
e
elec
tr
ical
p
o
wer
tr
an
s
m
is
s
io
n
lin
e.
T
h
e
s
ec
o
n
d
ar
y
m
ag
n
etic
f
iel
d
r
esu
ltin
g
f
r
o
m
t
h
e
lo
o
p
cu
r
r
en
t
p
ar
tially
o
r
co
m
p
letely
c
o
m
p
en
s
ates
th
e
a
m
b
ien
t
p
r
i
m
ar
y
m
a
g
n
etic
f
ield
[
2
5
]
–
[
2
9
]
.
Dete
r
m
in
in
g
th
e
s
u
itab
le
lo
ca
tio
n
o
f
th
e
p
ass
iv
e
an
d
ac
tiv
e
c
o
m
p
e
n
s
atio
n
lo
o
p
s
co
o
r
d
in
ates
an
d
th
e
q
u
an
titi
es
r
elate
d
to
th
e
m
itig
atio
n
p
r
o
ce
s
s
r
ep
r
esen
t
im
p
o
s
ed
co
n
s
tr
ain
ts
.
T
o
o
v
er
c
o
m
e
th
ese
d
r
awb
ac
k
s
,
th
e
m
eta
-
h
eu
r
is
tic
alg
o
r
ith
m
s
ca
n
b
e
u
s
ed
to
r
eso
lv
e
s
u
ch
o
p
tim
izatio
n
p
r
o
b
lem
s
.
am
o
n
g
s
t
th
e
m
o
s
t
co
m
m
o
n
alg
o
r
ith
m
s
b
ased
o
n
co
llectiv
e
in
tellig
en
ce
is
th
e
G
W
O.
T
h
is
alg
o
r
ith
m
was
in
itial
l
y
im
p
lem
en
ted
b
y
Mir
jalili
et
a
l.
it
em
u
lates
T
h
e
h
ier
a
r
ch
ical
s
tr
u
ctu
r
e
an
d
co
o
p
er
ativ
e
h
u
n
tin
g
m
e
ch
an
is
m
o
f
a
s
o
ciety
r
ep
r
esen
tin
g
a
g
r
ay
w
o
lf
p
ac
k
in
th
e
wild
life
[
3
0
]
,
[
3
1
]
.
I
n
g
e
n
er
al,
th
e
GW
O
alg
o
r
ith
m
h
as p
r
o
v
e
n
to
b
e
q
u
ite
ef
f
ec
tiv
e
o
n
d
if
f
er
e
n
t
ty
p
es
o
f
f
u
n
ctio
n
s
,
b
o
th
in
ter
m
s
o
f
a
cc
u
r
ac
y
o
f
f
in
d
i
n
g
a
n
e
x
tr
em
u
m
an
d
in
ter
m
s
o
f
co
n
v
er
g
en
ce
s
p
ee
d
.
Ultim
atel
y
,
th
e
s
im
u
latio
n
r
esu
lts
r
ea
c
h
ed
will
b
e
co
m
p
ar
ed
to
th
o
s
e
id
en
tifie
d
b
y
th
e
p
o
lar
izatio
n
ellip
s
e
tech
n
iq
u
e
f
o
r
th
e
m
ag
n
etic
in
d
u
ctio
n
a
n
a
ly
s
is
[
3
2
]
.
2.
M
O
DE
L
I
NG
M
E
T
H
O
DO
L
O
G
Y
T
h
is
s
tu
d
y
p
r
o
p
o
s
es
a
q
u
asi
-
s
tatic
m
o
d
elin
g
tech
n
iq
u
e
to
q
u
an
tify
an
d
m
itig
ate
m
ag
n
etic
in
d
u
ctio
n
lev
els
n
ea
r
an
o
v
er
h
ea
d
v
er
y
h
ig
h
v
o
ltag
e
p
o
wer
lin
e
at
p
o
wer
f
r
eq
u
e
n
cy
.
T
h
e
id
ea
b
eh
i
n
d
o
u
r
ap
p
r
o
ac
h
is
to
co
m
b
in
e
t
h
e
f
u
n
d
am
e
n
tal
p
r
i
n
cip
le
o
f
B
io
t
-
Sav
ar
t'
s
law
w
ith
th
e
u
s
u
al
th
e
o
r
em
o
f
s
u
p
e
r
p
o
s
itio
n
o
f
v
ec
to
r
f
ield
s
f
r
o
m
m
u
ltip
le
o
v
er
h
ea
d
co
n
d
u
cto
r
s
with
th
eir
im
ag
es
r
elativ
e
to
th
e
g
r
o
u
n
d
.
T
h
e
p
o
s
itio
n
in
g
o
f
th
e
d
e
-
en
er
g
ized
elec
tr
ic
wir
es
o
f
t
h
e
p
ass
iv
e
an
d
ac
tiv
e
atten
u
atio
n
lo
o
p
s
an
d
th
e
ass
o
ciate
d
p
a
r
am
eter
s
was
d
eter
m
in
ed
th
r
o
u
g
h
an
o
p
t
im
izatio
n
p
r
o
ce
s
s
u
s
in
g
th
e
GW
O
alg
o
r
ith
m
to
en
s
u
r
e
h
ig
h
m
ag
n
etic
co
m
p
en
s
atio
n
.
T
h
e
n
o
v
elty
o
f
th
is
s
tu
d
y
lies
in
th
e
co
m
b
i
n
e
d
ap
p
licatio
n
o
f
th
ese
ap
p
r
o
ac
h
es
to
s
ig
n
i
f
ican
tly
an
d
ef
f
ec
tiv
el
y
r
ed
u
ce
th
e
ef
f
e
cts o
f
m
ag
n
etic
in
d
u
ctio
n
d
u
e
to
th
e
p
r
o
p
o
s
ed
o
v
er
h
ea
d
tr
a
n
s
m
is
s
io
n
lin
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
1
4
4
-
5
1
6
1
5146
2
.
1
.
M
a
g
net
ic
ind
uct
io
n c
a
lcula
t
i
o
n
I
n
m
a
g
n
eto
s
tatics,
th
e
B
io
t
-
Sa
v
ar
t
is
lar
g
el
y
a
p
p
lied
to
e
v
alu
ate
th
e
m
ag
n
etic
in
d
u
ctio
n
at
an
y
p
o
in
t
in
s
p
ac
e,
cr
ea
ted
b
y
a
cu
r
r
en
t
elem
en
t
in
a
s
tr
aig
h
t
co
n
d
u
cto
r
o
f
in
f
in
ite
len
g
th
,
as
d
e
p
icted
in
Fig
u
r
e
1
.
Acc
o
r
d
in
g
to
th
e
s
u
p
er
p
o
s
itio
n
p
r
in
cip
le,
th
e
r
esu
ltin
g
m
ag
n
etic
f
lu
x
d
en
s
ity
at
p
o
in
t
(
)
is
t
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[
3
3
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[
3
4
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=
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(
1
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w
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r
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etic
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f
th
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p
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m
is
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e
am
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litu
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th
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cu
r
r
en
t
t
h
at
p
ass
es
th
r
o
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g
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ea
ch
p
h
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co
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r
is
d
is
tr
ib
u
ted
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n
if
o
r
m
ly
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t
h
e
to
tal
n
u
m
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f
elem
en
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d
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r
s
c
o
n
s
titu
tin
g
ea
c
h
p
h
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co
n
d
u
cto
r
[
3
5
]
.
I
n
UHV
th
r
ee
p
h
ase
p
o
wer
lin
e
cir
c
u
its
,
a
s
im
p
le
ap
p
licatio
n
o
f
B
io
t
–
Sav
ar
t
law
allo
ws
d
eter
m
in
in
g
th
e
o
v
er
all
m
ag
n
etic
f
lu
x
d
e
n
s
ity
B
d
u
e
to
all
cu
r
r
en
ts
p
ass
in
g
th
r
o
u
g
h
th
e
p
h
ase
co
n
d
u
cto
r
s
o
f
th
e
p
o
we
r
tr
an
s
m
is
s
io
n
lin
e
at
an
y
o
b
s
er
v
atio
n
p
o
in
t
[
3
3
]
,
[
3
4
]
.
I
n
f
ield
co
n
d
itio
n
s
,
th
e
h
eig
h
t
o
f
th
e
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v
er
h
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d
co
n
d
u
cto
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is
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ea
tly
in
f
lu
en
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d
b
y
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h
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v
ar
iab
ilit
y
o
f
th
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ter
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ain
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d
th
e
ef
f
ec
t
o
f
atm
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s
p
h
er
ic
c
o
n
d
itio
n
s
(
tem
p
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at
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r
e,
win
d
an
d
ice
lo
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n
t
h
e
co
n
d
u
cto
r
’
s
s
ag
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e.
Gen
er
ally
,
t
o
s
im
p
lify
in
g
th
e
ca
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latio
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t
h
e
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r
h
ea
d
tr
an
s
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tin
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elec
tr
ical
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as
s
tr
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t,
p
ar
allel
to
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o
th
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an
d
p
ar
allel
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ass
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Fig
u
r
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2
,
an
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it
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ca
lcu
lated
u
s
in
g
th
e
f
o
llo
win
g
r
elatio
n
s
h
ip
[
3
6
]
,
[
3
7
]
:
ℎ
=
ℎ
(
2
3
)
(
2
)
w
h
er
e,
ℎ
r
ep
r
esen
ts
th
e
m
a
x
im
u
m
h
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h
t
o
f
th
e
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o
n
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r
at
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e
s
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o
f
t
o
wer
;
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th
e
m
ax
i
m
u
m
s
ag
o
f
th
e
co
n
d
u
cto
r
at
th
e
m
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le
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o
in
t o
f
th
e
c
o
n
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u
cto
r
s
p
an
.
Fig
u
r
e
1
.
Descr
ip
tiv
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s
ch
em
a
o
f
B
io
t
-
Sav
ar
t la
w
f
o
r
m
ag
n
etic
f
ield
ca
lcu
latio
n
Fig
u
r
e
2
.
Simp
lifie
d
g
eo
m
etr
y
o
f
an
o
v
er
h
ea
d
co
n
d
u
ct
o
r
s
u
s
p
en
d
e
d
b
etwe
en
two
s
u
p
p
o
r
ts
I
t
is
im
p
o
r
tan
t
t
o
n
o
te
th
at
t
h
ese
ca
lcu
latio
n
p
r
o
c
ed
u
r
es
tak
e
in
to
co
n
s
id
er
atio
n
th
e
e
f
f
ec
t
o
f
th
e
in
d
u
ce
d
cu
r
r
e
n
t
in
th
e
g
r
o
u
n
d
wir
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an
d
th
e
g
r
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u
n
d
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ec
t,
wh
ich
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e
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r
esen
ted
b
y
th
e
im
ag
es
o
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t
h
e
cu
r
r
en
ts
p
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in
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th
r
o
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g
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th
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co
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d
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itu
ated
at
a
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b
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g
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s
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ce
,
as d
e
p
icted
in
Fig
u
r
e
3
[
3
6
]
,
[
3
7
]
.
I
n
a
two
-
d
i
m
en
s
io
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(
2
D)
r
ec
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g
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e
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ten
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r
iz
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tal
an
d
v
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tical
co
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cu
r
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th
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two
eq
u
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s
ex
p
r
ess
ed
in
th
e
f
o
llo
win
g
[
3
8
]
–
[
4
0
]
:
r
e
r
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dl
r
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dB
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P
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ro
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I
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&
C
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8
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lcu
late
th
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m
ag
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(
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as
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in
Fig
u
r
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3
;
D
e
r
ep
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th
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co
m
p
lex
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e
n
etr
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d
e
p
th
o
f
th
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tr
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cu
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d
,
it
is
esti
m
ated
b
y
th
e
f
o
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win
g
ex
p
r
ess
io
n
[
3
6
]
,
[
3
7
]
:
=
√
2
√
0
−
4
(
4
)
wh
er
e,
is
th
e
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esi
s
tiv
ity
o
f
th
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ex
p
r
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in
(
Ω
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m
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r
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e
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e
AC
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p
p
ly
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e
f
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n
d
am
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ag
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ar
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n
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Fig
u
r
e
3
.
Ma
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f
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ip
[
3
6
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[
3
7
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:
|
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2
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2
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5
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I
n
th
e
ca
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e
o
f
a
s
in
u
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4
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
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0
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I
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t J E
lec
&
C
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m
p
E
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g
,
Vo
l.
15
,
No
.
6
,
Decem
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25
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1
4
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1
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1
5148
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]
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[
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6
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etic
f
lu
x
d
en
s
ity
;
Bt
is
th
e
p
h
ase
an
g
le
o
f
th
e
m
ag
n
etic
f
lu
x
d
en
s
ity
,
it
i
s
ca
lcu
lated
as
(
8
)
:
=
(
)
(
8
)
Sin
ce
th
e
in
f
lu
en
ce
o
f
th
e
v
alu
e
o
f
th
e
i
n
d
u
ce
d
cu
r
r
en
ts
in
th
e
g
r
o
u
n
d
wir
es
d
er
iv
in
g
f
r
o
m
th
e
o
v
er
h
ea
d
tr
an
s
m
is
s
io
n
lin
e
cu
r
r
en
ts
is
tak
en
i
n
to
ac
c
o
u
n
t
in
m
ag
n
etic
f
lu
x
d
e
n
s
ity
ca
lcu
lat
in
g
;
th
e
q
u
an
tity
o
f
th
ese
cu
r
r
en
ts
ca
n
b
e
f
o
u
n
d
as
[
3
6
]
,
[
3
7
]
:
[
]
=
-
[
−
1
]
[
]
[
]
(
9
)
w
h
er
e,
in
d
icate
th
e
AC
elec
tr
ic
in
d
u
ce
d
cu
r
r
en
ts
in
th
e
g
r
o
u
n
d
wir
es;
r
ep
r
esen
t
t
h
e
n
o
m
in
al
cu
r
r
en
ts
o
f
th
e
p
h
ase
co
n
d
u
cto
r
s
;
d
escr
ib
e
th
e
s
elf
-
im
p
ed
an
ce
s
o
f
g
r
o
u
n
d
wir
es;
r
ep
r
esen
t th
e
m
u
tu
a
l im
p
ed
an
ce
s
b
etwe
en
th
e
p
h
ase
co
n
d
u
ct
o
r
s
an
d
th
e
g
r
o
u
n
d
wir
es.
I
t
is
p
o
s
s
ib
le
to
e
s
tim
ate
th
e
s
elf
an
d
m
u
tu
al
im
p
ed
an
ce
s
p
er
u
n
it
len
g
th
u
s
in
g
th
e
an
aly
tical
ap
p
r
o
ac
h
o
f
th
e
s
im
p
lifie
d
C
ar
s
o
n
-
C
lem
th
eo
r
em
;
as
s
h
o
wn
in
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
s
r
esp
ec
tiv
ely
[
3
6
]
,
[
3
7
]
:
=
+
0
8
+
0
2
[
1
4
+
(
)
]
=
0
8
+
0
2
(
)
(
1
0
)
w
h
er
e,
is
th
e
AC
r
esi
s
tan
ce
o
f
g
r
o
u
n
d
wir
e
in
[
Ω
/m
]
;
is
t
h
e
d
is
tan
ce
s
ep
ar
atin
g
th
e
p
h
ase
co
n
d
u
cto
r
f
r
o
m
th
e
g
r
o
u
n
d
wir
e
in
[
m
]
is
th
e
g
eo
m
etr
ical
r
a
d
iu
s
o
f
g
r
o
u
n
d
wir
e
in
[
m
]
.
T
h
e
C
ar
s
o
n
-
C
lem
's
p
r
in
cip
le
ca
n
b
e
u
s
ed
wh
en
th
e
s
ep
ar
atio
n
d
is
tan
ce
b
etwe
en
p
h
ase
co
n
d
u
cto
r
s
is
litt
le
th
en
1
5
%
o
f
co
r
r
esp
o
n
d
in
g
s
o
i
l
r
ec
o
v
er
y
lo
ca
tio
n
D
e
.
2
.
2
.
M
a
g
net
ic
ind
uct
io
n m
it
i
g
a
t
io
n
T
h
e
b
io
lo
g
ical
im
p
ac
ts
o
f
l
o
w
-
f
r
eq
u
en
cy
elec
tr
o
m
ag
n
etic
f
ield
s
o
n
th
e
p
o
p
u
latio
n
h
ea
lth
h
av
e
r
em
ain
ed
a
m
ajo
r
p
r
e
o
cc
u
p
ati
o
n
o
f
th
e
in
ter
n
atio
n
al
s
o
ciet
y
f
o
r
s
ev
er
al
d
ec
ad
es.
T
h
e
elec
tr
ic
f
ield
is
ea
s
ily
s
to
p
p
ed
b
y
all
ty
p
es
o
f
m
ater
ials
;
wh
ile
th
e
m
ag
n
etic
f
ield
is
ab
le
to
p
as
s
th
r
o
u
g
h
m
o
s
t
m
ater
ials
,
ev
en
th
e
h
u
m
an
b
o
d
y
,
an
d
ca
n
n
o
t
b
e
s
t
o
p
p
ed
.
Pr
o
tectio
n
co
n
s
is
ts
o
f
s
tay
in
g
awa
y
f
r
o
m
th
e
s
o
u
r
ce
o
r
u
s
in
g
s
h
ield
in
g
s
tr
ateg
ies
[
4
2
]
.
I
n
o
r
d
er
to
m
in
im
ize
p
o
ten
tia
l
ef
f
ec
ts
ass
o
ciate
d
with
v
er
y
lo
w
f
r
eq
u
en
cy
m
a
g
n
etic
f
ield
r
ad
iatio
n
,
th
e
m
o
s
t
co
m
m
o
n
r
e
d
u
ctio
n
te
ch
n
iq
u
e
in
m
a
g
n
etic
f
ield
s
h
ield
in
g
o
f
UHV
o
v
er
h
ea
d
tr
an
s
m
is
s
io
n
lin
es
i
s
th
e
im
p
lem
en
tatio
n
o
f
an
e
f
f
ec
tiv
e
co
m
p
e
n
s
atio
n
s
y
s
tem
.
T
h
e
p
r
in
cip
le
o
f
th
is
tech
n
iq
u
e
is
b
a
s
ed
o
n
th
e
in
s
er
tio
n
o
f
a
co
n
d
u
ctiv
e
lo
o
p
m
a
d
e
u
p
o
f
two
co
n
d
u
cto
r
s
co
n
n
ec
ted
to
g
eth
er
;
an
d
is
in
s
talled
n
ea
tly
u
n
d
e
r
th
e
p
h
ase
co
n
d
u
ct
o
r
s
in
an
ap
p
r
o
p
r
iate
p
o
s
itio
n
o
f
th
e
ar
ea
o
f
in
ter
es
t
to
b
e
p
r
o
tecte
d
.
T
h
is
clo
s
ed
lo
o
p
is
in
ten
d
ed
to
p
r
o
d
u
ce
an
au
x
iliar
y
m
a
g
n
eti
c
f
ield
wh
ic
h
o
p
p
o
s
es
th
e
o
r
ig
in
al
m
ag
n
etic
f
ield
,
in
o
r
d
e
r
to
c
o
m
p
e
n
s
ate
it
p
ar
tially
o
r
to
tally
,
as
ex
p
lain
ed
in
Fig
u
r
e
4
.
T
h
is
co
m
p
en
s
atio
n
o
f
m
ag
n
etic
f
lu
x
d
e
n
s
ity
is
p
r
o
d
u
ce
d
eith
er
b
y
an
in
d
u
ce
d
c
u
r
r
en
t
b
y
th
e
p
h
ase
co
n
d
u
cto
r
s
(
p
ass
iv
e
co
m
p
en
s
atio
n
)
,
o
r
b
y
an
in
j
ec
ted
cu
r
r
en
t
b
y
a
s
ec
o
n
d
ar
y
p
o
wer
s
o
u
r
ce
(
ac
tiv
e
co
m
p
e
n
s
atio
n
)
[
2
5
]
–
[
3
1
]
.
I
t
is
im
p
o
r
tan
t
to
m
en
tio
n
th
at
th
is
co
m
p
en
s
atio
n
s
y
s
tem
d
o
es
n
o
t
o
n
ly
a
p
p
ly
t
o
n
ew
lin
es,
b
u
t
ca
n
also
b
e
u
s
ed
f
o
r
e
x
is
tin
g
lin
es;
th
ey
ca
n
b
e
u
s
ed
s
ep
ar
ately
o
r
to
g
eth
e
r
if
n
ec
ess
ar
y
.
2
.
2
.
1
.
P
a
s
s
iv
e
lo
o
p c
o
m
pens
a
t
io
n
T
h
is
s
tr
ateg
y
in
v
o
lv
es
in
s
tallin
g
a
p
ass
iv
e
lo
o
p
co
n
s
is
tin
g
o
f
two
co
n
d
u
ct
o
r
s
f
o
r
m
in
g
a
cl
o
s
ed
cir
cu
it
p
r
o
p
er
l
y
estab
lis
h
ed
b
etwe
en
th
e
p
h
ase
co
n
d
u
cto
r
s
o
f
th
e
o
v
er
h
ea
d
p
o
wer
lin
e
a
n
d
th
e
g
r
o
u
n
d
lev
el.
Acc
o
r
d
in
g
to
Far
ad
a
y
'
s
law
o
f
m
ag
n
etic
i
n
d
u
ctio
n
,
th
e
latte
r
,
r
esu
ltin
g
f
r
o
m
th
e
m
a
g
n
etic
f
ield
o
f
th
e
p
o
wer
lin
e,
p
r
o
d
u
ce
s
a
m
ag
n
etic
f
lu
x
,
th
e
tem
p
o
r
al
v
ar
iatio
n
o
f
th
is
m
ag
n
etic
f
lu
x
th
r
o
u
g
h
th
e
p
a
s
s
iv
e
lo
o
p
p
r
o
d
u
ce
an
elec
tr
o
m
o
tiv
e
f
o
r
ce
(
E
MF)
,
wh
ich
ca
u
s
es
th
e
cir
cu
latio
n
o
f
an
in
d
u
ce
d
c
u
r
r
en
t
wh
ich
i
n
tu
r
n
will
p
r
o
d
u
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
timiz
ed
p
a
s
s
ive
a
n
d
a
ctive
s
h
ield
in
g
o
f m
a
g
n
etic
in
d
u
ctio
n
g
en
era
ted
b
y
…
(
S
a
la
h
-
E
d
d
in
e
Ho
u
ich
er
)
5149
an
in
d
u
ce
d
m
ag
n
etic
in
d
u
ctio
n
o
p
p
o
s
ite
to
th
at
o
f
th
e
co
n
d
u
cto
r
s
o
f
th
e
lin
e,
in
o
r
d
er
to
p
ar
tially
co
m
p
en
s
ate
f
o
r
it
[
4
3
]
–
[
4
9
]
.
T
h
e
E
MF
in
d
u
ce
d
in
th
e
co
m
p
en
s
atio
n
lo
o
p
is
r
ep
r
esen
ted
as
th
e
o
p
p
o
s
ite
d
er
iv
ativ
e
with
r
esp
ec
t to
tim
e
o
f
th
e
m
ag
n
etic
f
lu
x
th
r
o
u
g
h
th
is
clo
s
ed
lo
o
p
; it
is
ex
p
r
ess
ed
b
y
th
e
r
elatio
n
[
4
3
]
–
[
4
9
]
:
(
)
=
−
(
1
1
)
Fig
u
r
e
4
.
I
n
s
tallatio
n
o
f
a
c
o
n
d
u
ctiv
e
co
m
p
en
s
atio
n
lo
o
p
u
n
d
er
th
e
UHV
o
v
e
r
h
ea
d
t
r
an
s
m
is
s
io
n
lin
e
T
h
e
n
e
g
ativ
e
s
ig
n
(
-
)
d
escr
ib
e
s
th
e
b
e
h
av
io
r
o
f
L
en
z'
s
law,
th
e
elec
tr
o
m
o
tiv
e
f
o
r
ce
ten
d
s
to
o
p
p
o
s
e
th
e
v
ar
iatio
n
in
m
ag
n
etic
f
lu
x
,
it
id
en
tifie
s
th
e
d
ir
ec
tio
n
o
f
th
e
AC
in
d
u
ce
d
cu
r
r
en
t
cir
cu
latio
n
in
th
e
co
m
p
en
s
atio
n
lo
o
p
.
T
h
e
in
d
u
ce
d
elec
tr
ical
v
o
ltag
e
ac
r
o
s
s
th
is
co
m
p
en
s
atio
n
clo
s
ed
lo
o
p
ca
n
b
e
esti
m
ated
u
s
in
g
th
e
f
o
ll
o
win
g
[
4
3
]
–
[
4
9
]
:
=
−
ℓ
(
1
2
)
w
h
er
e,
is
th
e
AC
in
d
u
ce
d
v
o
ltag
e;
ex
p
r
ess
es
th
e
an
g
u
lar
f
r
eq
u
e
n
cy
in
(
r
a
d
/s
)
;
ℓ
is
th
e
p
ass
iv
e
lo
o
p
len
g
th
;
is
th
e
m
ag
n
etic
f
lu
x
i
n
th
e
clo
s
ed
lo
o
p
co
n
d
u
cto
r
s
.
As
th
e
p
ass
iv
e
co
m
p
en
s
atio
n
lo
o
p
is
ar
r
an
g
ed
h
o
r
izo
n
tally
u
n
d
er
th
e
p
h
ase
c
o
n
d
u
ct
o
r
s
o
f
th
e
p
o
we
r
lin
e,
a
n
d
c
o
n
s
eq
u
en
tly
,
o
n
ly
th
e
v
er
t
ical
co
m
p
o
n
en
t
o
f
th
e
m
ag
n
etic
in
d
u
ctio
n
wh
ich
is
p
er
p
en
d
icu
lar
t
o
th
e
p
la
n
e
o
f
th
is
p
ass
iv
e
lo
o
p
co
n
tr
i
b
u
tes
to
t
h
e
v
al
u
e
o
f
t
h
e
m
ag
n
etic
f
lu
x
.
T
h
e
m
ag
n
etic
f
lu
x
th
r
o
u
g
h
th
e
p
ass
iv
e
lo
o
p
c
an
b
e
ca
lcu
lated
u
s
in
g
th
e
f
o
r
m
u
la
[
4
3
]
–
[
4
9
]
:
=
∫
⃗
⃗
⃗
2
1
(
1
3
)
T
h
e
two
co
n
d
u
cto
r
s
co
n
s
titu
tin
g
th
e
p
ass
iv
e
lo
o
p
ar
e
lo
ca
te
d
at
th
e
co
o
r
d
i
n
ates
(
1
,
2
)
an
d
(
1
,
2
)
as
in
d
icate
d
in
Fig
u
r
e
5
.
B
y
i
n
teg
r
atio
n
o
f
th
e
v
e
r
tical
m
ag
n
etic
f
ield
th
r
o
u
g
h
th
e
c
o
o
r
d
i
n
ates
o
f
th
e
clo
s
ed
lo
o
p
co
n
d
u
ct
o
r
’
s
,
th
e
m
a
g
n
eti
c
f
lu
x
is
ex
p
r
ess
ed
as
[
4
3
]
–
[
4
9
]
:
=
−
0
ℓ
4
∑
=
1
[
(
2
−
)
2
+
(
−
2
)
2
]
[
(
1
−
)
2
+
(
−
1
)
2
]
[
(
1
−
)
2
+
(
+
1
+
)
2
]
[
(
2
−
)
2
+
(
+
2
+
)
2
]
(
1
4
)
w
h
er
e,
(
,
)
ar
e
th
e
o
r
th
o
g
o
n
al
co
o
r
d
in
ates
o
f
th
e
co
n
d
u
cto
r
s
o
f
th
e
p
o
wer
lin
e;
p
r
esen
ts
t
h
e
cu
r
r
en
ts
cir
cu
latin
g
in
th
e
c
o
n
d
u
cto
r
s
o
f
th
e
p
o
wer
lin
e.
T
h
e
to
tal
im
p
ed
an
ce
v
alu
e
o
f
t
h
e
p
ass
iv
e
l
o
o
p
is
p
r
esen
ted
b
y
a
r
esis
tan
ce
in
s
er
ies
with
an
in
d
u
ctan
ce
an
d
an
elec
tr
ical
ca
p
ac
itan
ce
;
it
is
g
iv
en
b
y
th
e
f
o
llo
win
g
f
o
r
m
u
l
a
[
5
0
]
,
[
5
1
]
:
=
√
2
+
(
−
1
)
(
1
5
)
I
n
g
en
er
al,
th
e
ca
p
ac
itan
ce
in
th
e
p
ass
iv
e
lo
o
p
is
in
teg
r
ated
in
s
er
ies
with
th
e
in
d
u
ctan
c
e
i
n
o
r
d
e
r
to
ca
n
ce
l
p
ar
t
o
f
th
e
in
d
u
ctiv
e
r
e
ac
tan
ce
,
aim
in
g
to
in
cr
ea
s
e
th
e
cu
r
r
en
t
in
ten
s
ity
p
ass
in
g
th
r
o
u
g
h
th
e
c
o
n
d
u
cto
r
s
o
f
th
e
clo
s
ed
lo
o
p
;
wh
ich
p
r
o
v
id
es
ef
f
ec
tiv
e
m
ag
n
etic
f
ield
co
m
p
en
s
atio
n
.
T
h
e
s
elf
-
in
d
u
ct
an
ce
o
f
th
e
p
ass
iv
e
clo
s
ed
lo
o
p
is
d
eter
m
i
n
ed
as
[
4
3
]
–
[
4
9
]
:
p
I
r
B
r
m
i
t
B
r
m
i
t
I
I
n
t
e
r
e
st
a
r
e
a
UHV
o
v
e
r
h
e
a
d
p
o
w
e
r
l
i
n
e
C
o
mp
e
n
s
a
t
i
o
n
l
o
o
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
1
4
4
-
5
1
6
1
5150
=
4
×
1
0
−
7
×
ℓ
×
(
)
(
1
6
)
w
h
er
e,
r
l
is
th
e
r
ad
i
u
s
o
f
p
ass
iv
e
lo
o
p
co
n
d
u
cto
r
;
s
l
is
th
e
d
is
tan
ce
s
ep
ar
atin
g
th
e
two
co
n
d
u
cto
r
s
o
f
t
h
e
co
n
d
u
ctiv
e
lo
o
p
.
T
h
e
cu
r
r
en
t
i
n
ten
s
ity
th
r
o
u
g
h
th
e
co
n
d
u
ct
o
r
s
o
f
th
e
co
m
p
e
n
s
atio
n
l
o
o
p
is
d
eter
m
in
e
d
b
y
th
e
f
o
r
m
u
la
as [
4
3
]
-
[
4
9
]
:
=
(
1
7
)
T
h
is
in
d
u
ce
d
cu
r
r
en
t
will
cr
ea
te
a
m
ag
n
etic
in
d
u
ctio
n
wh
ic
h
o
p
p
o
s
es
th
at
g
en
e
r
ated
b
y
t
h
e
cu
r
r
e
n
ts
o
f
th
e
s
o
u
r
ce
,
ac
co
r
d
in
g
to
(
3
)
m
en
tio
n
ed
a
b
o
v
e
.
T
h
e
r
esu
l
tin
g
m
ag
n
etic
in
d
u
ctio
n
is
o
b
t
ain
ed
b
y
s
u
m
m
i
n
g
th
e
v
ec
to
r
s
o
f
th
e
in
itial
m
ag
n
etic
in
d
u
ctio
n
an
d
th
at
o
f
th
e
co
m
p
en
s
atio
n
l
o
o
p
,
as
in
d
icat
ed
in
th
e
f
o
llo
win
g
r
elatio
n
[
4
3
]
–
[
4
9
]
:
⃗
⃗
=
⃗
⃗
+
⃗
⃗
(
1
8
)
Fig
u
r
e
5
.
Or
th
o
g
o
n
al
co
o
r
d
in
a
tes o
f
th
e
p
o
wer
lin
e
co
n
d
u
cto
r
s
an
d
p
ass
iv
e
clo
s
ed
lo
o
p
2
.
2
.
2
.
Act
iv
e
lo
o
p c
o
m
pens
a
t
io
n
I
n
th
is
co
m
p
en
s
atio
n
p
r
o
ce
d
u
r
e,
a
cu
r
r
en
t
is
g
en
er
ate
d
f
r
o
m
an
ex
ter
n
al
p
o
wer
s
o
u
r
ce
c
o
n
s
is
tin
g
o
f
an
ac
tiv
e
f
ee
d
b
ac
k
lo
o
p
g
u
i
d
e
d
b
y
a
m
ea
s
u
r
in
g
s
en
s
o
r
th
at
co
n
tr
o
ls
th
e
cu
r
r
en
t
v
al
u
e
cir
c
u
latin
g
in
th
e
b
o
th
lo
o
p
co
n
d
u
cto
r
s
an
d
d
etec
ts
th
e
v
ar
iatio
n
o
f
t
h
e
co
m
p
e
n
s
atin
g
m
ag
n
etic
in
d
u
ctio
n
cr
ea
t
ed
wh
ich
in
ter
ac
ts
with
th
at
g
en
er
ated
b
y
th
e
cu
r
r
en
ts
o
f
th
e
p
o
wer
lin
e
in
o
r
d
e
r
to
p
ar
tially
o
r
p
er
f
ec
tly
c
o
m
p
en
s
ate
in
th
e
zo
n
e
to
b
e
p
r
o
tecte
d
[
5
1
]
–
[
5
6
]
.
T
h
e
v
alu
e
o
f
th
e
cu
r
r
en
t
to
b
e
in
jecte
d
m
u
s
t
b
e
ca
r
ef
u
lly
ca
lcu
lated
in
o
r
d
er
t
o
o
b
tain
s
ig
n
if
ica
n
t
co
m
p
en
s
atio
n
.
T
h
er
e
ar
e
two
d
if
f
er
en
t
m
eth
o
d
s
to
d
eter
m
in
e
th
e
cu
r
r
e
n
t
o
f
t
h
e
s
o
u
r
ce
to
b
e
in
jecte
d
,
eith
er
u
s
in
g
em
p
ir
ica
l
f
o
r
m
u
las,
o
r
b
y
a
ca
lcu
latio
n
alg
o
r
ith
m
wh
ich
m
ak
es
it
p
o
s
s
ib
le
to
ad
ju
s
t
th
e
co
il c
u
r
r
en
t a
n
d
c
o
m
p
en
s
ate
th
e
am
b
ien
t m
ag
n
etic
in
d
u
ctio
n
[
5
1
]
–
[
5
6
]
.
Fo
r
a
d
esig
n
in
g
lo
o
p
,
ac
c
o
r
d
in
g
to
th
e
em
p
ir
ical
r
elatio
n
;
th
e
co
m
p
o
n
en
ts
r
ea
l
an
d
im
ag
in
ar
y
o
f
in
jectin
g
cu
r
r
e
n
t a
r
e
ca
lcu
late
d
ac
co
r
d
i
n
g
to
t
h
e
(
1
9
)
an
d
(
2
0
)
d
ef
i
n
ed
wr
itten
as
[
5
6
]
:
[
[
]
−
[
]
−
[
]
2
+
2
]
[
[
]
−
[
]
−
[
]
2
+
2
]
(
1
9
)
w
h
er
e
[
0
]
an
d
[
0
]
ar
e
th
e
b
o
th
c
o
m
p
o
n
e
n
ts
o
f
th
e
s
tar
tin
g
m
a
g
n
etic
in
d
u
ctio
n
d
u
e
to
th
e
o
v
er
h
ea
d
p
o
wer
lin
e
at
th
e
d
esti
n
ed
p
o
i
n
t
;
an
d
ar
e
th
e
b
o
th
co
m
p
o
n
en
ts
o
f
th
e
m
ag
n
etic
in
d
u
ctio
n
em
itted
at
a
s
im
ilar
p
o
s
itio
n
ac
r
o
s
s
th
e
ac
ti
v
e
co
m
p
e
n
s
atio
n
lo
o
p
,
ass
u
m
i
n
g
th
e
i
n
p
u
t
c
u
r
r
en
t
in
th
is
lo
o
p
h
as
a
m
a
g
n
itu
d
e
I
=
1
A
an
d
a
p
h
ase
θ
=
0
.
Sim
ilar
ly
,
to
(
1
8
)
n
o
ted
ab
o
v
e,
t
h
e
r
esu
ltin
g
m
ag
n
etic
in
d
u
ctio
n
is
eq
u
al
to
th
e
s
u
m
o
f
th
e
m
ag
n
etic
in
d
u
ctio
n
v
ec
to
r
s
o
f
th
e
o
v
er
h
ea
d
p
o
wer
lin
e
an
d
th
at
estab
lis
h
ed
b
y
th
e
ac
tiv
e
co
m
p
en
s
atio
n
(
)
11
,
xy
1
5
m
(
)
22
,
xy
1
5
m
(
)
,
ii
xy
(x
L2
G
ro
u
n
d
w
ire
y
l
s
x
P
a
ss
iv
e
lo
o
p
P
h
a
se
c
o
n
d
u
c
to
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
timiz
ed
p
a
s
s
ive
a
n
d
a
ctive
s
h
ield
in
g
o
f m
a
g
n
etic
in
d
u
ctio
n
g
en
era
ted
b
y
…
(
S
a
la
h
-
E
d
d
in
e
Ho
u
ich
er
)
5151
lo
o
p
.
T
o
q
u
a
n
tify
th
e
p
er
f
o
r
m
an
ce
o
f
m
ag
n
etic
in
d
u
ctio
n
atten
u
atio
n
ca
r
r
ie
d
o
u
t
i
n
a
s
p
ec
if
ied
r
eg
i
o
n
;
it
is
im
p
o
r
tan
t
t
o
tak
e
in
to
ac
co
u
n
t
th
e
r
ed
u
ctio
n
f
ac
t
o
r
(
o
r
s
h
ield
in
g
f
ac
to
r
)
,
wh
ich
is
th
e
r
atio
o
f
m
a
g
n
etic
in
d
u
ctio
n
with
o
u
t
th
e
co
m
p
en
s
atio
n
ef
f
ec
t
to
th
e
m
ag
n
etic
in
d
u
ctio
n
with
co
m
p
en
s
atio
n
e
f
f
ec
t;
it
is
o
b
tain
ed
f
r
o
m
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
[
4
6
]
,
[
5
5
]
,
[
5
7
]
:
=
0
(
2
0
)
w
h
er
e,
0
is
th
e
m
ag
n
etic
in
d
u
cti
o
n
with
o
u
t sh
ield
in
g
;
is
th
e
m
ag
n
etic
in
d
u
ctio
n
with
s
h
ield
i
n
g
.
3.
G
RE
Y
WO
L
F
O
P
T
I
M
I
Z
E
R
GW
O
i
s
an
alg
o
r
ith
m
in
itially
d
ev
elo
p
ed
b
y
Mir
jalili
in
2
0
1
4
,
b
ased
o
n
h
o
w
a
p
ac
k
o
f
g
r
ay
wo
lv
es
h
u
n
ts
in
th
e
wild
.
T
h
is
p
ac
k
in
clu
d
es
alp
h
a
wo
lv
es
(
α
)
,
b
et
a
wo
lv
es
(
β),
d
elta
w
o
lv
es
(
δ)
,
an
d
o
m
e
g
a
w
o
lv
es
(
ω
)
,
ea
ch
with
a
s
p
ec
if
ic
s
o
cial
r
o
le
an
d
h
ier
ar
c
h
y
[
3
0
]
.
T
h
e
h
u
n
tin
g
p
r
o
ce
s
s
in
v
o
lv
es
tr
ac
k
in
g
,
tr
ap
p
in
g
,
a
n
d
th
en
attac
k
in
g
p
r
e
y
.
I
n
th
e
G
W
O
m
ath
em
atica
l
m
o
d
el,
th
e
p
r
im
ar
y
s
o
lu
tio
n
is
alp
h
a,
f
o
llo
wed
b
y
b
eta
an
d
d
elta,
wh
ile
th
e
r
em
ain
d
e
r
i
s
o
m
eg
a.
T
h
e
p
r
ey
e
n
cir
clem
en
t
b
eh
av
i
o
r
is
m
o
d
eled
u
s
in
g
m
ath
em
atica
l
r
elatio
n
s
h
ip
s
th
at
m
ain
l
y
in
v
o
lv
e
co
e
f
f
icien
t
v
ec
to
r
s
an
d
p
o
s
itio
n
v
ec
to
r
s
.
T
h
e
co
r
e
p
u
r
s
u
it
o
f
t
h
e
h
u
n
t
is
ca
r
r
ied
o
u
t
b
y
alp
h
a
wo
lv
es,
with
s
ec
o
n
d
ar
y
p
a
r
ticip
atio
n
f
r
o
m
b
eta
an
d
d
elta
wo
lv
es.
T
h
e
p
o
ten
tial
lo
ca
tio
n
o
f
th
e
p
r
ey
is
ev
alu
ated
u
s
in
g
th
e
b
est
s
o
lu
tio
n
s
,
an
d
th
e
o
th
er
wo
lv
es
ad
ju
s
t
th
eir
p
o
s
itio
n
s
ac
co
r
d
in
g
ly
.
T
h
e
f
in
al
s
tag
e
is
th
e
ac
tu
al
attac
k
an
d
ca
p
t
u
r
e
o
f
th
e
p
r
e
y
,
wh
ich
o
cc
u
r
s
wh
en
t
h
e
wo
lv
es
co
m
p
letely
s
to
p
m
o
v
in
g
.
E
x
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
ar
e
b
alan
ce
d
b
y
ad
a
p
t
iv
e
v
alu
es
[
5
8
]
–
[
6
2
]
.
T
h
e
en
v
i
r
o
n
m
en
tal
b
e
h
av
io
r
o
f
all
s
tag
es o
f
th
e
p
r
ed
atio
n
a
ct
ca
n
b
e
ef
f
ec
tiv
ely
m
o
d
eled
u
s
in
g
th
e
f
o
ll
o
win
g
s
et
o
f
e
q
u
atio
n
s
:
⃗
⃗
⃗
=
|
⃗
⃗
(
)
−
⃗
⃗
(
)
|
(
2
1
)
⃗
(
+
1
)
=
⃗
(
+
1
)
−
⃗
⃗
⃗
⃗
(
2
2
)
w
h
er
e;
⃗
an
d
⃗
ar
e
th
e
p
o
s
s
ib
le
lo
ca
tio
n
v
ec
to
r
s
o
f
t
h
e
p
r
e
y
an
d
a
g
r
e
y
wo
lf
r
esp
ec
tiv
el
y
;
⃗
an
d
⃗
ar
e
co
ef
f
icien
t v
ec
to
r
s
,
is
th
e
iter
atio
n
n
u
m
b
er
.
T
h
e
co
ef
f
icien
t
v
ec
to
r
s
⃗
an
d
⃗
ar
e
ev
alu
ated
as
[
5
8
]
–
[
6
2
]
:
→
=
2
→
×
1
→
−
→
(
2
3
)
→
=
2
×
2
→
(
2
4
)
w
h
er
e;
⃗
is
a
co
ef
f
icien
t
v
ec
to
r
wh
ich
g
r
a
d
u
ally
d
ec
r
ea
s
es
f
r
o
m
2
to
0
o
v
er
th
e
co
u
r
s
e
o
f
i
ter
atio
n
s
in
GW
O
alg
o
r
ith
m
;
⃗
1
an
d
⃗
2
ar
e
r
an
d
o
m
v
ec
to
r
s
with
v
alu
es r
an
g
i
n
g
in
t
h
e
in
ter
v
al
[
0
-
1
]
.
R
eg
ar
d
in
g
th
e
(
2
5
)
-
(
2
7
)
g
o
v
e
r
n
in
g
t
h
e
m
ath
em
atica
l
m
o
d
e
l
o
f
th
e
g
r
ey
wo
lf
h
u
n
tin
g
p
r
o
ce
s
s
,
it
is
ass
u
m
ed
th
at
Alp
h
a
α
,
B
êta
β
an
d
Delta
δ
wo
lv
es
b
r
in
g
g
r
e
ater
k
n
o
wled
g
e
ab
o
u
t
th
e
lik
e
ly
s
ea
t
o
f
th
e
p
r
ey
;
th
ey
d
ir
ec
t
th
e
s
ea
r
ch
p
r
o
ce
s
s
an
d
th
e
Om
ég
a
ω
wo
lv
es
ad
j
u
s
t
th
eir
em
p
lace
m
en
ts
,
b
ased
o
n
th
e
s
ites
o
f
th
e
th
r
ee
m
o
s
t sk
illfu
l w
o
lv
es,
th
i
s
ca
n
b
e
ex
p
lain
e
d
in
th
e
f
o
llo
win
g
f
o
r
m
[
5
8
]
–
[
6
2
]
:
→
=
|
1
→
(
)
→
−
(
)
→
|
,
→
=
|
2
→
→
(
)
−
(
)
→
|
,
→
=
|
3
→
→
(
)
−
(
)
→
|
(
2
5
)
→
1
=
|
→
(
)
−
1
→
→
|
,
→
2
=
|
→
(
)
−
2
→
→
|
,
→
3
=
|
→
(
)
−
3
→
→
|
(
2
6
)
→
(
+
1
)
=
1
→
+
2
→
+
3
→
3
(
2
7
)
w
h
er
e,
⃗
(
)
,
⃗
(
)
an
d
⃗
(
)
ar
e
th
e
p
o
s
itio
n
s
v
ec
to
r
s
o
f
t
h
e
g
r
ey
wo
lv
e
s
,
an
d
at
ℎ
iter
atio
n
r
esp
ec
tiv
ely
,
⃗
1
,
⃗
2
an
d
⃗
3
ar
e
ad
ap
tiv
e
v
ec
to
r
s
.
I
n
GW
O
alg
o
r
ith
m
,
ex
p
lo
r
atio
n
(
s
ea
r
ch
f
o
r
p
r
ey
)
a
n
d
ex
p
lo
itatio
n
(
attac
k
in
g
p
r
e
y
)
ar
e
two
o
p
p
o
s
ite
p
h
ases
.
T
h
e
r
an
d
o
m
v
ec
to
r
a
⃗
⃗
m
en
tio
n
ed
i
n
(
2
3
)
is
co
n
s
id
er
e
d
as
a
b
asic
f
ac
to
r
c
o
n
tr
o
llin
g
e
x
p
lo
r
atio
n
an
d
ex
p
l
o
itatio
n
;
it
d
ec
lin
es
in
a
lin
ea
r
m
a
n
n
er
f
r
o
m
th
e
v
alu
e
2
to
0
o
v
er
th
e
g
en
er
atio
n
s
an
d
is
ca
l
cu
lated
as sh
o
wn
in
th
e
[
5
8
]
–
[
6
2
]
:
=
2
−
×
2
(
2
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
1
4
4
-
5
1
6
1
5152
w
h
er
e;
is
th
e
cu
r
r
e
n
t iter
atio
n
an
d
is
th
e
m
ax
im
u
m
n
u
m
b
e
r
o
f
l
iter
atio
n
.
As
a
r
esu
lt,
th
e
eq
u
iv
alen
t
q
u
an
tity
o
f
v
ec
to
r
⃗
also
ch
an
g
es
in
th
e
r
an
g
e
[
−
,
]
.
Po
s
s
ib
le
s
o
lu
tio
n
s
r
ep
r
esen
t
wo
lv
es
ap
p
r
o
ac
h
in
g
th
e
p
r
ey
at
|
⃗
|
>
1
an
d
m
o
v
in
g
awa
y
f
r
o
m
it
at
|
⃗
|
<
1
;
wh
en
|
⃗
|
=
1
,
th
er
e
is
n
o
c
o
n
v
er
g
en
ce
to
war
d
s
t
h
e
d
esire
d
r
esu
lt.
All
th
e
b
asi
c
s
tag
es
o
f
th
e
GW
O
alg
o
r
i
th
m
ar
e
co
n
cisely
r
ep
r
esen
ted
in
t
h
e
p
s
eu
d
o
-
co
d
e
in
d
icate
d
in
T
a
b
le
1
[
6
3
]
,
[
6
4
]
:
T
ab
le
1
.
Ps
eu
d
o
-
co
d
e
o
f
th
e
GW
O
o
p
tim
izatio
n
alg
o
r
ith
m
P
seu
d
o
-
c
o
d
e
o
f
t
h
e
G
W
O
a
l
g
o
r
i
t
h
m
1:
Generate randomly an initial population of grey wolves
2:
Initialize the values of a=2, A, C and Max_iter
3:
Evaluate the fitness function of each member of the
population, Xα, Xβ and Xδ
4:
While
(t< Max_iter)
do
5:
For
each search agent
do
6:
Update the location of all wolves (using (25), (26)
and (27)
7: Update A, C (using (23) and (24)
8: Update a (using (28))
9:
end for
10:
Calculate Fitness value of all search agents
11
: Update Xα, Xβ, Xδ
12: t = t+1
13:
end
while
14:
Return the best solution Xα
An
o
p
tim
izatio
n
o
f
m
ax
im
izat
io
n
o
f
an
o
b
jectiv
e
f
u
n
ctio
n
is
d
esig
n
ed
,
in
o
r
d
er
to
d
ec
id
e
th
e
lo
ca
tio
n
o
f
th
e
co
m
p
e
n
s
atio
n
lo
o
p
c
o
n
d
u
cto
r
s
co
o
r
d
in
ates,
as
well
as
th
e
v
alu
es
o
f
d
if
f
er
en
t
elem
en
ts
ass
o
ciate
d
with
th
e
co
m
p
en
s
atio
n
s
tr
ateg
y
,
to
ef
f
icien
tly
r
ed
u
ce
th
e
m
ag
n
etic
in
d
u
ctio
n
in
th
e
ar
ea
to
b
e
p
r
o
tecte
d
.
T
h
e
u
s
ed
o
b
jectiv
e
f
u
n
ctio
n
in
th
is
m
ax
im
izatio
n
p
r
o
ce
s
s
is
b
ased
o
n
th
e
s
q
u
ar
e
r
o
o
t
o
f
th
e
d
is
tin
ctio
n
b
etwe
en
th
e
in
itial
m
ag
n
etic
in
d
u
ctio
n
s
tr
en
g
th
at
a
g
iv
en
p
o
in
t
an
d
it
s
in
ten
s
ity
af
ter
co
m
p
en
s
atio
n
at
th
e
s
am
e
p
o
in
t.
T
h
is
f
u
n
ctio
n
ca
n
b
e
e
x
p
r
ess
e
d
m
ath
em
atica
lly
u
s
in
g
th
e
f
o
r
m
u
la
s
h
o
wn
[
6
5
]
:
=
−
√
(
−
)
2
(
2
9
)
wh
er
e,
is
th
e
m
ag
n
etic
in
d
u
ctio
n
q
u
an
tity
b
ef
o
r
e
th
e
c
o
m
p
e
n
s
atio
n
d
esig
n
at
a
d
esig
n
ated
p
o
in
t;
is
th
e
m
ag
n
etic
in
d
u
ctio
n
q
u
a
n
tity
af
ter
th
e
co
m
p
en
s
atio
n
,
b
ased
o
n
all
o
p
tim
ized
q
u
a
n
titi
es
at
th
e
s
am
e
p
o
in
t.
T
h
e
n
eg
ativ
e
s
ig
n
lin
k
e
d
with
th
e
b
eg
in
n
in
g
o
f
th
e
o
b
jectiv
e
f
u
n
ctio
n
in
d
icate
s
th
at
th
e
d
esig
n
ed
o
p
tim
izatio
n
p
r
o
ce
d
u
r
e
is
f
o
r
th
e
f
u
n
ctio
n
m
ax
im
izatio
n
.
4.
E
L
L
I
P
T
I
CA
L
P
O
L
A
RI
Z
A
T
I
O
N
I
n
a
p
er
m
a
n
en
t
s
in
u
s
o
id
al
r
eg
im
e,
ea
ch
s
in
u
s
o
id
al
q
u
an
tity
at
co
n
s
tan
t
f
r
eq
u
en
cy
is
a
p
h
a
s
o
r
wh
ich
ca
n
b
e
ex
p
r
ess
ed
b
y
a
m
ag
n
it
u
d
e
an
d
a
p
h
ase
an
g
le.
T
h
e
e
x
tr
em
ity
o
f
th
e
v
ec
to
r
o
f
th
e
r
esu
ltan
t
m
ag
n
etic
in
d
u
ctio
n
⃗
⃗
d
u
e
to
th
r
ee
-
p
h
ase
p
o
wer
lin
e
tr
ac
es
at
a
f
ix
ed
o
b
s
er
v
atio
n
p
o
in
t
a
n
ellip
s
e
as
a
f
u
n
ctio
n
o
f
tim
e
as
th
e
v
ec
to
r
r
o
tates.
T
h
is
p
r
o
p
er
ty
r
ep
r
esen
ts
an
ellip
tical
p
o
lar
izatio
n
s
tate
th
at
d
escr
i
b
es
th
e
ch
a
n
g
e
with
tim
e
in
th
e
am
p
litu
d
e
an
d
p
h
a
s
e
an
g
le
o
f
th
e
v
ec
to
r
as r
e
f
lec
ted
in
Fig
u
r
e
6
.
Gen
er
ally
,
th
e
ellip
s
e
eq
u
atio
n
is
d
eter
m
in
e
d
b
y
o
r
t
h
o
g
o
n
al
co
m
p
o
n
en
ts
,
b
y
p
r
o
jectio
n
o
n
to
th
e
o
r
th
o
g
o
n
al
a
x
es
o
f
th
e
(
x
,
y
)
p
lan
e,
ea
ch
v
ec
to
r
ca
n
b
e
d
ec
o
m
p
o
s
ed
in
t
o
two
c
o
m
p
o
n
en
ts
,
r
ea
l
an
d
im
ag
i
n
ar
y
,
as n
o
ted
[
6
6
]
–
[
7
1
]
:
⃗
⃗
=
(
+
)
⃗
⃗
⃗
⃗
=
(
+
)
⃗
⃗
(
3
0
)
T
h
e
p
ea
k
v
alu
e
o
f
m
ag
n
etic
in
d
u
ctio
n
is
r
ea
c
h
ed
b
y
th
e
p
r
o
jectio
n
o
f
th
e
i
n
s
tan
tan
eo
u
s
r
o
tatio
n
v
ec
to
r
s
alo
n
g
th
e
two
ax
es.
T
h
e
m
ag
n
itu
d
e
o
f
th
e
m
ag
n
etic
in
d
u
ctio
n
,
in
a
d
ir
ec
tio
n
d
eter
m
in
ed
b
y
an
o
r
ien
tatio
n
an
g
le
ca
n
b
e
ex
p
r
ess
ed
as
[
6
6
]
–
[
7
1
]
:
=
(
+
)
=
(
+
)
(
3
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
timiz
ed
p
a
s
s
ive
a
n
d
a
ctive
s
h
ield
in
g
o
f m
a
g
n
etic
in
d
u
ctio
n
g
en
era
ted
b
y
…
(
S
a
la
h
-
E
d
d
in
e
Ho
u
ich
er
)
5153
T
h
e
s
q
u
ar
e
o
f
th
e
m
a
g
n
etic
in
d
u
ctio
n
is
eq
u
al
to
th
e
s
u
m
o
f
th
e
s
q
u
ar
es o
f
th
e
co
m
p
lex
v
e
cto
r
s
alo
n
g
two
ax
es x
an
d
z;
I
t is g
iv
en
b
y
th
e
f
o
llo
win
g
r
elatio
n
[
6
6
]
–
[
7
1
]
:
2
=
2
+
2
(
3
2
)
T
h
e
ellip
s
e
f
u
n
ctio
n
wh
ich
p
r
esen
ts
th
e
m
a
g
n
etic
i
n
d
u
ct
io
n
p
ass
es
th
r
o
u
g
h
a
m
ax
im
u
m
an
d
a
m
in
im
u
m
wh
e
n
its
f
ir
s
t d
er
iv
a
tiv
e
is
n
u
ll.
T
h
is
ca
n
b
e
e
x
p
r
es
s
ed
m
ath
em
atica
lly
as
[
6
6
]
–
[
7
1
]
.
2
=
0
(
3
3
)
I
n
d
ee
d
,
th
e
r
esu
ltin
g
m
ag
n
etic
in
d
u
ctio
n
at
a
k
n
o
w
n
p
o
in
t
is
eq
u
al
to
th
e
s
u
m
o
f
th
e
s
q
u
ar
es
o
f
two
s
o
lu
tio
n
s
co
n
ce
r
n
i
n
g
th
e
e
x
tr
e
m
e
m
o
d
u
les o
f
two
s
em
i
-
ax
es,
it is
d
ef
in
ed
as
[
6
6
]
–
[
7
1
]
:
22
m
ax
m
i
n
=+
res
B
B
B
(
3
4
)
w
h
er
e,
an
d
ar
e
th
e
s
em
i
-
m
aj
o
r
an
d
s
em
i
-
m
in
o
r
R
m
s
v
alu
es
o
f
m
ag
n
etic
in
d
u
ctio
n
ax
ia
l
ellip
s
e,
r
esp
ec
tiv
ely
,
as sh
o
wn
in
Fig
u
r
e
6
.
C
o
n
s
id
er
a
s
eg
m
en
t
o
f
a
7
5
0
k
V
th
r
ee
-
p
h
ase
tr
an
s
m
is
s
io
n
p
o
wer
lin
e
with
a
s
y
m
m
etr
ical
h
o
r
izo
n
tal
p
h
ase
s
eq
u
en
ce
ar
r
a
n
g
em
en
t
with
two
ea
r
th
wir
es.
T
h
e
a
r
r
an
g
em
en
t
an
d
g
eo
m
etr
ic
co
o
r
d
in
ates
with
th
e
av
er
ag
e
h
eig
h
t
o
f
th
e
co
n
d
u
ct
o
r
s
o
f
th
e
tr
an
s
m
is
s
io
n
lin
e
r
elativ
e
to
th
e
s
u
s
p
en
s
io
n
p
y
lo
n
ar
e
illu
s
tr
ated
in
Fig
u
r
e
7
[
7
1
]
.
E
ac
h
p
h
ase
c
o
n
d
u
ct
o
r
is
b
u
n
d
led
with
f
o
u
r
s
u
b
-
co
n
d
u
cto
r
s
,
th
e
p
o
wer
tr
an
s
f
er
r
ed
f
o
r
th
is
tr
an
s
m
is
s
io
n
lin
e
is
co
n
s
id
er
e
d
eq
u
al
to
S=4
0
0
0
MV
A.
T
h
e
ea
r
th
is
s
u
p
p
o
s
ed
to
b
e
u
n
i
f
o
r
m
o
f
elec
tr
ical
r
esis
tiv
ity
1
0
0
Ω
/
m
;
th
e
n
o
r
m
al
f
r
eq
u
e
n
cy
o
f
5
0
Hz,
th
e
d
i
r
ec
t
cu
r
r
en
t
(
DC
)
r
esis
tan
ce
f
o
r
p
h
ase
co
n
d
u
cto
r
is
0
.
0
6
8
4
Ω
/k
m
,
wh
ile
f
o
r
th
e
ea
r
th
wir
e
is
0
.
6
4
3
Ω
/
k
m
.
C
o
n
ce
r
n
in
g
th
e
g
e
o
m
etr
ic
p
ar
am
eter
s
o
f
th
e
co
m
p
en
s
atio
n
lo
o
p
,
a
r
ec
tan
g
u
lar
co
n
d
u
ctiv
e
lo
o
p
with
a
r
ad
iu
s
eq
u
al
to
1
.
1
2
m
m
a
n
d
a
r
esis
tan
ce
p
er
u
n
it
len
g
th
with
a
v
al
u
e
o
f
0
.
2
2
5
Ω
/k
m
;
th
e
le
n
g
th
o
f
th
e
cl
o
s
ed
lo
o
p
f
o
r
m
ed
b
y
th
e
two
co
n
d
u
cto
r
s
lo
ca
ted
in
t
h
e
ar
ea
to
b
e
p
r
o
tecte
d
is
eq
u
al
to
1
0
0
0
m
.
Fig
u
r
e
6
.
C
o
m
p
o
n
en
ts
o
f
ellip
tically
p
o
lar
ized
m
ag
n
etic
in
d
u
ctio
n
Fig
u
r
e
7
.
Geo
m
etr
ic
co
n
f
ig
u
r
a
tio
n
o
f
a
7
5
0
k
V
s
in
g
le
-
cir
cu
it h
o
r
iz
o
n
tal
o
v
e
r
h
ea
d
p
o
wer
lin
e
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
f
ir
s
t
s
tep
o
f
th
is
s
tu
d
y
in
v
o
lv
es
th
e
m
ag
n
etic
in
d
u
ctio
n
co
m
p
u
tatio
n
g
en
er
ated
in
th
e
v
icin
ity
o
f
an
ex
tr
em
e
h
ig
h
v
o
ltag
e
lin
e
o
f
7
5
0
k
V.
I
n
itially
,
as
th
is
p
o
wer
lin
e
is
d
esig
n
ed
to
d
eliv
e
r
an
ap
p
ar
en
t
p
o
wer
o
f
4
0
0
0
MV
A,
th
e
v
alu
e
o
f
th
e
m
o
d
u
lu
s
o
f
th
e
c
u
r
r
e
n
t
p
ass
in
g
th
r
o
u
g
h
th
e
p
h
ase
co
n
d
u
ct
o
r
is
3
0
7
9
.
2
0
A,
th
e
cu
r
r
en
ts
in
d
u
ce
d
in
th
e
ea
r
th
wir
es
ac
co
r
d
in
g
to
(
9
)
m
e
n
tio
n
ed
ab
o
v
e
,
in
o
r
d
e
r
to
tak
e
th
em
in
to
ac
co
u
n
t
in
th
e
co
n
tr
ib
u
tio
n
to
t
h
e
ca
lcu
lat
io
n
o
f
m
ag
n
etic
in
d
u
ctio
n
ar
e
r
esp
ec
tiv
ely
:
1
=
495.07
(
15
8.4
6
)
∘
,
2
=
496.2
(
-
23
.92
)
∘
T
h
e
later
al
p
r
o
f
ile
o
f
th
e
m
a
g
n
etic
in
d
u
ctio
n
in
te
n
s
ity
o
f
th
is
p
o
wer
lin
e
g
eo
m
etr
y
s
tu
d
ied
at
1
m
ab
o
v
e
t
h
e
g
r
o
u
n
d
is
in
d
icate
d
in
Fig
u
r
e
8
,
it
r
ea
ch
es
its
m
a
x
im
u
m
u
n
d
er
th
e
ce
n
tr
al
p
h
ase
co
n
d
u
cto
r
with
a
(
,
,
)
r
B
x
y
t
y
x
x
u
r
m
a
x
B
m
i
n
B
y
u
r
R
ad
iu
s
0.4
5
m
21
m
2
9
m
1
9
.
1
m
34.2
m
R
ad
iu
s
x
y
14.3
1
m
m
1
1
.
2
mm
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