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