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ELEKTRO-MGNESESTEREK
Dr. Zombory Lszl
ELEKTROMGNESEST E R E KDR. ZOMBORYLSZL
Lektor: Dr. Veszely Gyula
A kiadvny A Korszer Mrnkrt Alaptvny tmogatsval kszlt,a Tanknyv, Szakknyv, Jegyzet projekt keretn bell. Dr. Zombory Lszl
Hungarian edition Mszaki Knyvkiad Kft., 2006
A kiadvny tmogatja:
i
TARTALOM
E L S Z
AZ ELEKTROMGNESES TEREK ALAPVET SSZEFGGSEI ............................................ 1
Az elektromos ram........................................................................................................................ 1
s a tlts? .................................................................................................................................... 3
A tlts klnbz megjelensi formi ............................................................................................ 5
Intenzitsvektorok ........................................................................................................................... 6
Az intenzitsvektorok integrljai ....................................................................................................... 7
Az elektromos trerssg vonalintegrlja, a skalrpotencil ............................................................. 7
Az elektromos s mgneses trerssg
felleti integrlja. A fluxus ............................................................................................................... 9
Gerjesztett vektorok ...................................................................................................................... 10
Faraday indukcitrvnye ............................................................................................................. 10
Az elektromgneses tr egyenletei vkuumban .............................................................................. 11
AZ ELEKTROMGNESES TR S KZEG KLCSNHATSA ................................ 12
Mi hinyzik az egyenletekbl? ....................................................................................................... 12
Egy kis kitr: a diplus ................................................................................................................ 12
A kzegek befolysa a trre ltalnos esetben ............................................................................... 18
Trjellemz vektorok viselkedse kzegek hatrn ......................................................................... 20
A trvektorokra vonatkoz trstrvnyek ...................................................................................... 24
A MAXWELL-EGYENLETEK ................................................................................................ 25
Az elektromgneses tr egyenletei vkuumban .............................................................................. 25
Mit is mondanak a Maxwell-egyenletek? ....................................................................................... 28
Energiasrsg s energiaramls ................................................................................................ 29
A Maxwell-egyenletek egyrtelm megoldhatsga ....................................................................... 31
Az elektrodinamika felosztsa a Maxwell-egyenletek alapjn ......................................................... 33
A Maxwell-egyenletek tiszta szinuszos idbeli vltozs esetn ......................................................... 34
A Poynting-vektor szinuszos idfggs esetn ................................................................................. 35
ELEKTROSZTAT IKA S STACIONRIUS RAMLSI TR ........................................... 36
Adott tltselrendezs tere ............................................................................................................ 36
A gyakorlati elektrosztatika krdsei .............................................................................................. 39
Az elektrosztatika egyenleteinek egyrtelm megoldsa .................................................................. 39
Kondenztor ................................................................................................................................ 44
1. fejezet
2. fejezet
3. fejezet
4. fejezet
ii
Rszkapacitsok ........................................................................................................................... 45
Stacionrius ramlsi tr .............................................................................................................. 47
STACIONRIUS RAM MGNESES TERE ..................................................................... 49
Vonalszer vezetkben foly ram tere .......................................................................................... 51
Mgneses skalrpotencil ............................................................................................................ 53
A mgneses tr energija; az n- s klcsns induktivits ............................................................ 55
Klcsns indukci; nindukci .................................................................................................... 56
Maxwell-egyenletek Kirchhoff-egyenletek .................................................................................... 58
Egyenram hlzatok ................................................................................................................. 58
Tetszleges idfggs hlzatok .................................................................................................. 61
SZTAT IKUS, STACIONRIUS FELADATOK MEGOLDSI MDSZERE I ................. 63
Az elektrosztatika megoldsi mdszerei ......................................................................................... 63
Analitikus megoldsi mdszerek ................................................................................................... 63
A helyettest tltsek mdszere .................................................................................................... 63
Az integrlegyenletek mdszere .................................................................................................... 64
Parcilis differencilegyenletek ...................................................................................................... 69
Megolds a vltozk sztvlasztsval .......................................................................................... 69
Varicis formalizmus ................................................................................................................... 72
Numerikus mdszerek .................................................................................................................. 74
A vges differencik mdszere ...................................................................................................... 75
A vges elemek mdszere ............................................................................................................. 76
Momentummdszer.
Integrlegyenletek numerikus megoldsa ...................................................................................... 79
sszefoglals .............................................................................................................................. 82
TVVEZETKEK ..................................................................................................................... 83
Bevezet ...................................................................................................................................... 83
A tvregyenletek megoldsa szinuszos gerjeszts esetn .............................................................. 88
Specilis tvvezetkek ................................................................................................................... 93
Fzis- s csoportsebessg ............................................................................................................. 95
Lezrt tvvezetk ........................................................................................................................... 97
Klnleges lezrsok .................................................................................................................. 101
Idelis vezetkszakasz .................................................................................................................102
sszetett vezetkhlzatok ..........................................................................................................104
Idelis vezetk specilis lezrssal ..............................................................................................105
Tvvezetk illesztse ................................................................................................................... 108
Illeszt ktkapuk ......................................................................................................................... 109
Tvvezetk-rezgkr ................................................................................................................... 112
Tvvezetkek idtartomnybeli vizsglata .................................................................................... 114
A menetdiagramok mdszere .....................................................................................................120
ltalnos tranziensek .................................................................................................................. 121
ELEKTROMGNESES HULLMOK KELTSE ................................................................123
A diplusantenna sugrzsa.
Hertz-diplus .........