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rusudan qanTaria
Teimuraz CiCua
leila CiCua
fizika
10m o s w a v l i s w i g n i
2012
grifi mieniWa 2012 wels ganaTlebis xarisxis ganviTarebis erovnuli centris mier
rusudan qanTaria
Teimuraz CiCua
leila CiCua
fizika
10m o s w a v l i s w i g n i
© gamomcemloba `klio~ 2012© gamomcemloba `meridiani~ 2012© r. qanTaria, T. CiCua, l. CiCua 2012yvela ufleba daculia
Rusudan Qantaria, Teimuraz Chichua, Leila Chichua PHYSICS10th Grade Textbook
gamomcemloba `klio~ aRmaSeneblis gamziri 181, Tbilisi, 0112, saqarTvelo tel.: (+995 32) 234 04 30 E-mail: book@klio.ge www. klio. ge
gamomcemloba `meridiani~ al. yazbegis gamz. 47, Tbilisi, 0112, saqarTvelo tel.: (+995 32) 239 15 22
redaqtori Temur gaCeCilaZe
kompiuteruli uzrunvelyofaelene varamaSvili
ISBN 978-9941-415-81-4
4
1 eleqtrostatika 7
1.1 eleqtruli muxtis Senaxvis kanoni 8
1.2 kulonis kanoni 10
1.3 amocanebis amoxsna 12
1.4 eleqtruli velis daZabuloba 14
1.5 eleqtruli velis Zalwirebi 16
1.6 eleqtruli veli gamtarebSi 18
E1.7 eleqtruli veli dieleqtrikebSi 21
1.8 eleqtrostatikuri velis muSaoba da energia 24
1.9 eleqtrostatikuri velis potenciali 27
1.10 potencialTa sxvaoba 29
1.11 amocanebis amoxsna 30
1.12 eleqtrotevadoba. kondensatorebi 32
1.13 brtyeli kondensatoris eleqtrotevadoba 34
1.14 kondensatorebis tipebi. kondensatorebis SeerTeba 36
1.15 eleqtruli velis energia.kondensatoris energia 38
1.16 amocanebis amoxsna 40
I Tavis Sejameba 42
testebi TviTSefasebisaTvis 43
2 eleqtruli deni 45
2.1 eleqtruli deni 46
2.2 kuTri winaRoba 48
2.3 amocanebis amoxsna 51
2.4 gamtaris winaRobis damokidebuleba temperaturaze 52
2.5 denis wyaros eleqtromamoZravebeli Zala 55
2.6 omis kanoni sruli wredisaTvis 57
2.7 amocanebis amoxsna 59
2.8 eleqtruli deni metalebSi 61
2.9 eleqtruli deni siTxeebSi. 62
2.10 faradeis kanoni 64
S i n a a r s i
5
2.11 mudmivi denis qimiuri wyaroebi 66
2.12 eleqtruli deni airSi 68
2.13 eleqtruli deni vakuumSi. vakuumiani diodi 71
2.14 naxevargamtarebi. naxevargamtarebis sakuTari gamtaroba 73
2.15 naxevargamtarebis minarevuli gamtarebloba 76
2.16 n da p tipis naxevargamtarebis kontaqti 78
II Tavis Sejameba 81
testebi TviTSefasebisaTvis 82
3 magnituri veli 83
3.1 magnituri veli. deniani gamtarebis urTierTqmedeba 84
3.2 magnituri velis induqcia 86
3.3 magnituri velis induqciis veqtoris mimarTuleba 88
3.4 magnituri induqciis nakadi 90
3.5 amperis Zala 91
3.6 lorencis Zala 93
3.7 eleqtromagnituri induqcia 95
3.8 lencis wesi 97
3.9 eleqtromagnituri induqciis kanoni 99
3.10 TviTinduqcia. induqtivoba 101
3.11 nivTierebis magnituri Tvisebebi 103
3.12 eleqtrogamzomi xelsawyoebi 105
3.13 usafrTxoebis wesebi 107
III Tavis Sejameba 108
testebi TviTSefasebisaTvis 110
7
1eleqtrostatika
Seiswavli: eleqtruli muxtebis urTierTqmedebas; kulonis kanons; eleqtruli velis daZabulobas; superpoziciis princips; eleqtruli velis muSaobas; eleqtruli velis potencials; potencialTa sxvaobas, dieleqtrikis polarizacias; dieleqtrikul SeRwevadobas; eleqtrotevadobas; kondensatorebs; kondensatorebis mimdevrobiT da paralelur SeerTebas; kondensatoris energias.
SeZleb: eleqtrul muxtebs Soris urTierTqmedebis eqsperimentul Seswavlas; velis daZabulobis gamoTvlas; superpoziciis principis gamoyenebas; eleqtruli velis muSaobisa da energiis gamoTvlas; velis potencialis da potencialTa sxvaobis gamoangariSebas; damuxtuli sxeulebis eleqtrotevadobis Sefasebas; kondensatoris tevadobis gamoangariSebas; kondensatoris Semcveli wredebis saerTo tevadobis gamoTvlas; kondensatoris energiis gamoangariSebas.
8
eqsperimenti
1.1 eleqtruli muxtis Senaxvis kanoni
ZvelTagan cnobili iyo, rom zogierTi sxeuli xaxunis Sedegad amJRavnebda mcire zomis nawilakebis mizidvis unars. es unari yvelaze mkafiod qarvis xaxunis dros SeimCneoda. qarvas berZnulad – eleqtroni qvia, amotom am movlenas eleqtruli movlena ewoda. eleqtruli movlenebi ganpirobebulia eleqtruli muxtebis arsebobiT. eleqtruli muxti fizikuri sididea da aRiniSneba q asoTi. movlenas, romlis drosac sxeulebis damuxtva xdeba, eleqtrizacia ewodeba. SI sistemaSi muxtis erTeuli aris 1 kuloni (1 k). erTi kuloni aris muxti, romelic erT wamSi gaivlis gamtaris ganiv kveTSi, rodesac am gamtarSi gadis erTi amperi Zalis deni.
bunebaSi arsebuli elementaruli muxti SI sistemaSi (sididiT) tolia e = 1,6•10–19 k.
amerikelma sazogado moRvawem da mecnierma benjamin franklinma (17061790 ww.) eleqtrobis Teoria SeimuSava, romelic emyareboda im mosazrebas, rom yvela nivTiereba Sedgeba e. w. `eleqtruli siTxisgan~, Tumca eleqtruli siTxis buneba im droisTvis jer kidev ar iyo garkveuli.
Tanamedrove, eleqtronuli Teoriis mixedviT, nivTierebis atomi Sedgeba dadebiTad damuxtuli birTvisa da uaryofiTi muxtis mqone garsisasgan, romelic Seicavs erT an ramdenime eleqtrons. eleqtrons gaaCnia elementaruli eleqtruli uaryofiTi niSnis muxti. muxtis elementaruloba niSnavs, rom bunebaSi Tavisufali saxiT ufro mcire muxtis mqone nawilakebi ar arsebobs. elementaruli muxtis sididea e = 1,6•10-19 kuloni.
birTvi Seicavs dadebiTi niSnis elementaruli muxtebis mqone nawilakebs – protonebs da umuxto nawilakebs – neitronebs. nebismieri muxti q jeradia elementaruli muxtisa, q = ne! .
normalur mdgomare obaSi dadebiTi da uaryofiTi muxtebis raodenoba atomSi erTMmaneTis tolia, amitom atomi eleqtrulad neitraluria. Tu atomi dakargavs erT an ramdenime eleqtrons, dadebiTad daimuxte
sur. 1
9
ba, eleqtronebis mierTe bisas ki – uaryofiTad. damuxtul atoms ioni ewodeba.
minaze abreSumis qsovilis xaxunis dros mina dadebiTad imuxteba, qsovili – uaryofiTad. plastmasis Salis qsovilze xaxunisas plastmasi uaryofiTad imuxteba, qsovili – dadebiTad. orive procesis dros jamuri muxti ar icvleba – mxolod gadanawildeba ise, rom dadebiTi da uaryofiTi muxtebis algebruli jami nulis toli rCeba. erTnair niSniani muxtebi erTmaneTs ganizidaven, sxvadasxva niSniani – miizidaven. eleqtrizacia SesaZlebelia daumuxtav sxeulze damuxtuli sxeulis SexebiTac. aris movlenebi, romlis drosac muxtebi Sexebis gareSec warmoiqmneba. magaliTad, radioaqtiuri gamosxivebis an sinaTlis zemoqmedebiT. muxtebis warmoqmnas da maT gadanawilebas gansazRvravs muxtis mudmivobis kanoni:
izolirebul sistemaSi anu sistemebSi, romelsac garedan arc gadaecema da ar waerTmeva eleqtruli muxtebi, jamuri eleqtruli muxti mudmivia. Tu sxeulebis an nawilakebis muxtis sidideebs aRvniSnavT q1, q2... qn, maSin q1+ q2+...+qn= const.
eleqtruli muxtis Senaxvis kanoni sruldeba yovelTvis, roca muxtebis mocemuli sistema Caketil sistemas warmoadgens. elementaruli nawilakebis gaCenisas an mospobisas, isini wyvilwyvilad ibadebian urTierT sapirispiro niSnis muxtiT, an qrebian ise (anihilireben), rom saerTo muxti sistemaSi ucvleli rCeba. xaxuniT sxeulebis daeleqtroebis procesSi monawileobs nivTierebis Semadgeneli atomebis Zalian mcire raodenoba, romlebic sxeulis zedapirze arian ganTavsebuli. mTeli sxeulis Tundac memilionedi eleqtronebis sxva sxeulze gadatana, warmoudgenlad didi (damangreveli!) sididis eleqtruli Zalebis aRZvras gamoiwvevda.
eleqtrobis nawils, romelSic Seiswavleba uZravi eleqtruli muxtebis urTierTqmedebis kanonzomierebebi, eleqtrostatika ewodeba.
gaazreba
me2 suraTze gamosaxul SemTxvevebSi miuTiTe muxtis niSnebi.
a b
sur. 2
sur. 3
saSinao davaleba
10
1.2 kulonis kanoni
eleqtruli muxtebis urTi erTqmedeba 1785 wels Seiswavla frangma mecnierma Sarl ogiusten kulonma. kuloni gazomvebisTvis iyenebda grexiT saswors, romlis ZiriTadi nawili aris drekad Zalian wvril Zafze Camokidebuli msubuqi horizontaluri Rero (sur. 4). Reros erT boloze damagrebuli msubuqi mooqvrili burTuUla gawonasworebulia meore boloze moTavsebuli tvirTiT (sapirwone). Rero sapirwoniTurT moTavsebulia minis WurWelSi, romelsac aqvs xvreli meore aseTive Reroze damagrebuli burTulas CasaSvebad. burTulas Seaxeben imave zomis uZravad damagrebul winaswar damuxtul iseTive burTulas. muxti burTulebs Soris Tanabrad ganawildeba. erTniSna muxtiT burTuUlebis urTierTganzidva iwvevs Reros Semobrunebas da Zafis grexas. Reros Semobrunebis kuTxe proporciulia burTulebs Soris urTierTqmedebis Zalis. eqsperimentis dros SesaZlebeli iyo rogorc burTulebis muxtis, aseve maT Soris manZilis Secvla. cdebis Sedegebis safuZvelze kulonma Camoayaliba kanoni:
wertilovan muxtebs Soris urTierTqmedebis Zalis moduli pirdapirproporciulia muxtebis sidideebis, ukuproporciulia maT Soris manZilis kvadratis da mimarTulia muxtebis SemaerTebeli wrfis gaswvriv.
F k rq q
21 2=
proporciulobis koeficienti k = 14 πε0
, sadac ε0 eleqtruli mudmivaa
8,85 10 nmk
012
2
2
$=f - , amitom k = 9•109 n•m2/k2.
k ricxobrivad tolia Zalis, romliTac vakuumSi urTierTqmedebs ori TiToO kuloni sididis wertilovani muxti, Tu maT Soris manZili erTi
sur. 4
kvarcis drekadi Zafi
sapirwone
damuxtuli burTulebi
11
gaazreba
1. me6 suraTis mixedviT imsjele muxtebs Soris urTierTqmedebis Zalebis Sesaxeb. Seadare am Zalebis sidideebi da mimarTulebebi.
2. Seadare erTmaneTs or eleqtrons Soris moqmedi eleqtrostatikuri da gravitaciuli Zalebi. eleqtronis masa m = 9,1•1031kgia.
3. kulonis kanonis formulis gamoyenebiT daamtkice, rom k-s ganzomilebaa n•m2/k2.
q1
q1
F21
F21
r12
r12
F12
F12
q2
q2
sur. 6
metria. es Zalian didi Zalaa, romelic daaxloebiT egviptis piramidebis wonas utoldeba. am Sefasebidan Cans, rom kuloni muxtis didi erTeulia. praqtikaSi iyeneben muxtis wilad erTeulebs:
1 mk = 103 k, 1 mkk = 106 k, 1 nk = 109 k.
wertilovani muxti anu wertilovani damuxtuli sxeuli bunebaSi ar arsebobs. aseTad SeiZleba miviCnioT sferuli formis Tanabrad da muxtuli sxeuli an sxeuli, romlis zoma gacilebiT naklebia sxva damuxtul sxeulamde manZilTan SedarebiT.
kulonis kanoni Zalian gavs msoflio mizidulobis kanons. marTlac, orive kanoni asaxavs manZilis kvadratze Zalis ukuproporciul damokidebulebas. gansxvaveba isaa, rom muxtis sididis nacvlad msoflio mizidulobis kanonSi gvaqvs masa, xolo k koeficientis nacvlad – gravitaciuli mudmiva (sur. 5). magram unda gvaxsovdes, rom msoflio mizidulobis Zalebi mxolod mizidvis Zalebia, xolo kulonuri Zalebi SeiZleba iyos rogorc mizidvis, aseve ganzidvis.
unda aRiniSnos, rom uZravi wertilovani muxtebis urTierTqmedebis Zalebi mimarTulia am wertilebis SemaerTebeli wrfis gaswvriv da maTi Tavmoyra SeiZleba sivrcis erT wertilSi – aseTi Tvisebis Zalebs centraluri Zalebi ewodeba. amrigad, kulonuri Zalebi centraluri Zalebia. centraluria agreTve gravitaciuli Zalebic.
sur. 5
m2m1
q1 q2
F G rm m
21 2
g$=
F k rq q
21 2
el
$=
saSinao davaleba
42
I Tavis Sejameba
movlena mecnieruli faqtebi
hipoteza sidideebi kanonebi dakanonzomierebebi
eleq
tr
ul
i mu
xteb
is u
rT
ier
Tqm
edeb
a
damuxtuli sxeulebis mizidva,ganzidva
damuxtuli sxeulis garSemo eleqtruli velisarseboba
muxtebis dagroveba metalisfirfitebze
`el
eqt
ro
nul
i si
Txi
s~ a
rse
boba
+q – muxti;–q – muxti;
eleqtruli velis daZabuloba
E qF=
eleqtruli velis potenciali
qW={
eleqtrotevadoba
Cq={
eleqtruli muxtis Senaxvis kanoni
q1 + q2 + q3 +.... + qn = q
kulonis kanoni
F rq q
k 21 2=
eleqtruli velis Zalwirebi mimarTulia
dadebiTi muxtidan uaryofiTi muxtisaken
kondensatori.paraleluri SeerTeba
C = C1 + C2 + .... + Cn.
mimdevrobiTi SeerTeba
1C =
1C1
+ 1C2
.
mocemuli sqemis mixedviT imsjele eleqtruli muxtebis urTierTqmedebis Sesaxeb.
45
2 eleqtruli deni
Seiswavli: eleqtrul dens; kuTr winaRobas; reostatis moqmedebis princips; gamtaris winaRobis damokidebulebas temperaturaze. zegamtarobas; omis kanons sruli wredisaTvis; eleqtrul dens sxvadasxva garemoSi; faradeis kanonebs. galvanur elements, akumulators; dens naxevargamtarebSi da maT gamoyenebas;
SeZleb: imsjelo eleqtruli denis Taviseburebaze sxvadasxva garemoSi; daaxasiaTo eleqtrolizis movlena; gaaanalizo faradeis kanonebi; imsjelo eleqtruli denis Taviseburebaze naxevargamtarebSi; mopovebuli informaciis xarjze moamzado proeqti sxvadasxva tipis
eleqtruli xelsawyoebis Seqmnasa da ganviTarebaze.
81
II Tavis Sejameba
mocemuli sqemis mixedviT Seadare erTmaneTs metalebis, siTxeebis, airebisa da naxevargamtarebis maxasiaTeblebi.
diagramis gamoyenebiT gaixsene eleqtruli denis maxasiaTebeli formulebi.
sqemis mixedviT imsjele eleqtruli denis Sesaxeb airSi.
gamtarebi
metalebi siTxeebi airebinaxevargam-
ta rebi
eleqtruli muxtebis Tavisufa-li matareb-lebi
eleqtronebidadebiTi da uaryofiTi
ionebi
eleqtronebi, dadebiTi da uaryofiTi
ionebi
eleqtronebi, xvrelebi
voltam pe-ruli maxa-siaTebeli
wrfivia arawrfivia arawrfivia arawrfivia
o
Ia
eleqtru-li denis gamtarSi gavli sas
ar xdebanivTierebis
gadatana
Tan axlavsnivTierebis
gadatana
Tan axlavsnivTierebis
gadatana
ar xdebanivTierebis
gadatana
winaRoba tempera-turis gazrdi sas
izrdeba mcirdeba mcirdeba mcirdeba
vatiIP
U Romi
amperi
volti
P R$
I R$
IP
IP2
IU
PU2
RU
I R2 $
UP
U I$
RU2
RP
eleqtruli ganmuxtva airebSi
araTavisTavadi TavisTavadi
dabali wnevispirobebSi
mRvivari
gvirgvinisebrinaperwkluri rkaluri
normaluri atmosferuli wnevis pirobebSi
IaIaIa
83
Seiswavli: Mmagnitur vels. deniani gamtarebis magnitur urTierTqmedebas;
nivTierebis magnitur Tvisebebs;
amperisa da lorencis Zalas;
e induqciis movlenas. lencis wess;
induqciur dens. TviTinduqcias. induqtivobas;
ampermetris, voltmetris moqmedebis princips;
usafrTxoebis wesebs eleqtroxelsawyoebis moxmarebisas.
SeZleb: Caataro cdebi magnituri velis Tvisebebis Sesaswavlad;
gaaanalizo raodenobrivad denis magnituri moqmedeba;
dagegmo da Caataro cdebi eleqtromagnituri induqciis gamosakvlevad;
aRwero inuqciuri deni Tvisebrivad da raodenobrivad.
gamoiyeno cnebebi, kanonebi da formulebi amocanebis amosaxsnelad.
3 magnituri veli
mzis magnituri qariSxalis moqmedeba dedamiwis magnitur velze
108
III Tavis Sejameba
Sesadarebelielementebi
eleqtruli veli magnituri veli
1. ris garSemo warmoiqmneba veli
2. ris mixedviT ikvleven vels
3. velis Zaluri maxasiaTebeli
mimarTuleba
moduli
erTeuli
4. Zalwirebi
1. eleqtruli muxtis garSemo
2. wertilovani muxti
3. daZabuloba E
Q q F E
E qF
; ;=
[ ] 1E kn=
4.E
E
1. mudmivi magnitebisa da deniani gamtarebis garSemo
2. deniani gamtari
magnituri isari
3. magnituri induqcia B
B
B IlF
; ; = F
B
Il
[ ] 1 1B a mn tl$
= =
4.
B
I
mocemuli sqemis mixedviT Seadare erTmaneTs eleqtruli da magnituri velis maxasiaTeblebi
109
Sesadarebelielementebi
eleqtruli veli magnituri veli
5. velebis moqmedeba
6. nivTiereba velSi
7. energiis damgrovebeli mowyobiloba
8. velebis urTierTkavSiri
5. muxtze:
F
E
qF E$=
6. gamtarebi:
veli ar arisdieleqtriki: E
E0=fveli Sesustebulia εjer
7. kondensatori:
2W CU2
el =
8. eleqtruli veli warmoqmnis dens. deni qmnis magnitur vels
I
eleqtruliveli↓
deni↓
magnituriveli
5. swori denis gamtarze
I lF B $ $; ; ; ;= F
B
Il
denian konturze
I
B
Bb
damuxtul moZrav nawilakebze
B
F
υ
6. BB0
=n paramagnitebi:
μ > 1 veli Zlierdebadiamagnitebi:μ < 1 veli sustdebaferomagnitebi: μ >> 1,veli mniSvnelovnadZlierdeba
7. induqciurobis koWa:
2W LI2=
8. xviaSi magnituri velis cvlileba warmoqmnis dens
magnituri veliscvlileba
↓deni xviaSi
I
116
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