Komputasi Elektromagnetik

8/9/2019 Komputasi Elektromagnetik

1/23

Electromagnetic Computationin Power System Engineering

Khairina Noor Astuti (2321430 !

"iel#

Constituti$e %elations

&eneral 'ector "iel#s

Electric Source "iel#

Electric an# agnetic 'orte) "iel#s

*+,-.NE

"un#amental ,ermso/ Electric

an#agnetic

"iel#

,ypes o/

'ector"iel#s

"lu) an# ensity o/ 'ector "iel#


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an#agnetic"iel#

Function that has diferent value at every point inspace.

A nite or in nite set whose elements are assignedunique value o a certain quantity. Eg: pointcontinuum o the Euclidian Space

"iel#

Represented as S A!AR

F"E!#

$ass% water volume%

temperature


3/23

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an#agnetic"iel#

"iel#

&emperature o earth's sur ace

( )[ ] ( ) Rr eT T T r T +++= sin1sin),,( 2210


4/23

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an#agnetic"iel#

"iel#

Represented as (E &)R F"E!# (elocity% momentum% orce% etc

^^^

),,(),,(),,(),,( k z y x F j z y x F i z y x F z y x F z y x ++=

*+"& (E &)RS


5/23

*+,-.NE


an#agnetic"iel#


Electric eld e,ists -etweemparallel plate capacitor with

area A S

eV C .=

d V

E AB=


6/23

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an#agnetic"iel#


"nside capacitor e,ists electric

eld strength E

d V

E e=

*ni ormontour

*nuni ormontour

SE d

V S V

d

S e

e ===


7/23

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an#agnetic"iel#


$agnetic eld e,ists when the platesrepresents the pole o permanent magneto the magnetic gap -etween stator and

rotor

mV P .= 2 N

L P =

$agnetic eldstrength :

d V H M =


8/23

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an#agnetic"iel#


d V H M =

*ni ormontour

*nuni orm ontour


9/23

/*+,-.

NE


an#agnetic"iel#


" the volume -etween -oth plates is lled withconductance and connected to constanvoltage% electrical current is o-served:

eV G I .=

Flu, line is a scalar eld -ut 0u, density is a vector eld.#irection # is diretion o the 0u, line at that point. $agnitudeis the num-er o 0u, lines crossing a sur ace divided -y S.

Flu, density is measured in coulom-s per square meter1#2

S D

=Electric density or

*ni orm eldElectric density or

nonuni orm eld dS d

D

=

*


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an#agnetic"iel#


S D

=

Electric density or*ni orm eld

*


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an#agnetic"iel#


Electric density or nonuni orm eld dS

d D

=

*


12/23

and

and

*+,-.NE


an#agnetic

"iel#


cos DS =

At any point 3 % # ma4e an angle %so the the value o 0u, 5

cosS D

=

cosdS

d D

=

= nDS

D cos

^

cosnD

dS d

D

=$ultiply those scalar # -y the unit

vector n #

*+


13/23

Faraday's e,periment :

*+,-.NE


an#agnetic

"iel#


)(cou om!"#=

Flu, density in a radial direction has value

^

2

^

2

^

2

4

4

4

$r r

# D

$r !

# D

$r $#

D

=

=

= "nner space

)utter space

!r $

*+


14/23


an#agnetic

"iel#


From the given 0u, density and area%0u, can -e calculatedany time -y means o sur ace integral

dS DS

. =

=S

dS B .

=S

dS % I .

and

= BnS

B cos

^

cos Bn

dS

d B

=

and

= % nS

I %

cos

^

cos % n

dS

d %

=

*+,-.NE

*+


15/23

Farad m

henry m


an#agnetic

"iel#


&he electric magnetic 0u, density% #% 6 are related to theeld intensities E% 7% so 8called )+S&"&*&"(E RE!A&")+S

H B

E D

o

o

==

7

12

104

10854,8

==

o

o

"n vacuum condition% they ta4e their simplest

orm :

E %

H B

E D

=

==

For simple homogeneous isotropic dielectric andor magnetic materials:

)1(

)1(

mo

o

+=

+=

*+,-.NE

*+


16/23


an#agnetic

"iel#


"n many inter acepro-lems% there are noe,ternally appliedsur ace on the-oundary% so the-oundary conditionsmay -e stated as

nn

nn

nn

% %

B B

D D

21

21

21

=

=

=

1source9 ree-oundarycondition2

&he eld strength depends on its conductivity.$aterial with the least permittivity sufer the highest electric stress

"n general% or electric% magnetic % and conductioneld %

nn

nn

nn

E E

H H

E E

21

21

21

21

21

2

1

=

=

=

*+,-.NE

*+


17/23


an#agnetic

"iel#


*+,-.NE

*+


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,ypes o/'ector

"iel#s

(E &)R F"E!# is a region o space under the in0uenceo some vector quantity% such as magnetic eld or

electric eld strength% in which the quantity ta4es aunique vector value at every point o the region.

lassi edas

S)*R E F"E!# &he eld lines possessstarting and

terminating point

()R&E F"E!#

a mass o energy thatmoves in a rotary orwhirling motion% causing adepression or vacuum at

the center

*+


19/23

*+,-.NE

,ypes o/'ector

"iel#sElectric Source "iel#

Electric source elds e,ist in the environment o electriccharges at rest 1electrostatic charges% ,ed or locali;ed charges2

3ure space

charge

6oundaryvalue

pro-lem

*+


20/23

*+,-.NE

,ypes o/'ector

"iel#s

Electric vorte, e,ist in the environment o a time9varying magnetic 0u,

Electric 'orte) "iel#s

*+


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*+,-.NE

,ypes o/'ector

"iel#sagnetic 'orte) "iel#

$agnetic vorte, elds e,ist in the environment o a time9varying orconstant current 0u,

#irection o magnetic eld lines always ollow the right hand rule

*+ -


22/23

+,-.NE

,ypes o/'ector

"iel#s

&eneral 'ector "iel#s

"n general% a vector eld% e.g. E1,%y%;2% can -ecomposed o -oth a source eld and a vorte, eld

E(x,y,z) = E S (x,y,z) + E V (x,y,z)

s = sourcev = vortex

An ar-itrary vector eld is uniquely speci ed only i itssources and vortices can -e identi ed% in other words%i its source density and vortex density are given


23/23

REFERE+ ES

Schwa-% Adol ??. @ermany: Springer 8 (erlag 6erlin7eidel-erg +ew or4.

)r anidis% Sophocles

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