giorgi gedeniZe eTer lazaraSvili

giorgi gedeniZeeTer lazaraSvili

inteleqti X

klasissaxelmZRvanelo

giorgi gedeniZe

eTer lazaraSvili

fizika

gamomcemloba inteleqti

Tbilisi 2012

X klasis saxelmZRvanelo

grifi mieniWa 2012 wels ssip ganaTlebis xarisxis ganviTarebis

erovnuli centris (brZaneba ##375, 18.05.2012) mier

© gamomcemloba ìnteleqti~, 2012ISBN 978-9941-439-66-7

giorgi gedeniZe, eTer lazaraSvili

fizika X

Giorgi Gedenidze, Eter Lazarashvili

PHYSICS X

INTELEKTI PUBLISHERSTbilisi 2012

redaqtorebi gvanca gedeniZe naTia mamulaSvili

Editor Gvantsa Gedenidze Natia Mamulashvili

gamomcemloba inteleqti

Tbilisi, ilia WavWavaZis gamziri 5

225-05-22, 599 55-66-54

faqsi: 225-05-22

[email protected] www.intelekti.ge

iNtELEKti Publishers

5 ilia Chavchavadze ave., tbilisi, Georgia. tel.: 225-05-22, 599 55-66-54

3

Sinaarsi

I Tavi. eleqtrostatika .....................................................................................................6

1.1. ra da rogor iswavleT, SeamowmeT Tqveni codna ..........................................8

1.2. eleqtruli muxti da elementaruli nawilakebi ............................................10

1.3. damuxtuli sxeulebis urTierTqmedeba. kulonis kanoni ............................13

1.4. eleqtruli velis daZabuloba ...............................................................................16

1.5. eleqtruli velis daZabulobis wirebi ..............................................................19

1.6 gamtari eleqtrostatikur velSi ..........................................................................21

1.7. dieleqtriki eleqtrostatikur velSi. ori saxis dieleqtriki..............24

1.8. dieleqtrikis polarizacia. dieleqtrikuli SeRwevadoba .........................26

1.9. damuxtuli sxeulis potenciuri energia erTgvarovan

eleqtrostatikur velSi ..................................................................................................28

1.10. eleqtrostatikuri velis potenciali da potencialTa sxvaoba ..........31

1.11. ekvipotenciuri zedapirebi. potencialTa sxvaobis gazomva ..................34

1.12. amocanis amoxsnis nimuSi ........................................................................................36

1.13. eleqtrotevadoba. brtyeli kondensatori .....................................................38

1.14. brtyeli kondensatoris eleqtrotevadoba ..................................................40

1.15. damuxtuli kondensatoris energia. kondensatoris gamoyeneba .............42


1.17. SeamowmeT Tqveni codna ..........................................................................................47

II Tavi. mudmivi eleqtruli deni ................................................................................48

2.1. eleqtruli wredi da misi Semadgeneli nawilebi...........................................49

2.2. eleqtruli deni. denis Zala ..................................................................................52

2.3. gamtaris winaRoba. kuTri winaRoba .....................................................................55

2.4. winaRobis damokidebuleba temperaturaze .......................................................58

2.5. zegamtaroba ...................................................................................................................61

2.6. ra da rogor iswavleT, SeamowmeT Tqveni codna ..........................................63

2.7. saSualo winaRobis gansazRvra ampermetrisa da voltmetris

meSveobiT .................................................................................................................................66

2.8. amocanis amoxsnis nimuSi ..........................................................................................68


2.10. jibis farnisa da binis gasanaTebeli naTurebis

SeerTebis gamokvleva .......................................................................................................72

4

2.11. erTnair Zabvasa da sxvadasxva simZlavreze gaangariSebuli

naTurebis SeerTeba .....................................................................................................74

2.12. sami erTnairi naTuras Sereuli SeerTebis gamokvleva ............................77

2.13. denis wyaros eleqtromamoZravebeli Zala ...................................................79

2.14. omis kanoni sruli wredisaTvis ..........................................................................81



2.17. eleqtruli deni siTxeSi ........................................................................................87

2.18. eleqtruli deni airSi ............................................................................................90

2.19. TavisTavadi ganmuxtvis sxvadasxva tipi ..........................................................92

2.20. eleqtruli deni naxevargamtarSi .......................................................................95

2.21. eleqtruli deni p da n tipis naxevargamtarTa kontaqtSi ....................98



III Tavi. magnituri veli ....................................................................................................105

3.1. denis magnituri veli. denebis magnituri urTierTqmedeba ......................106

3.2. magnituri velis induqciis moduli. amperis Zala .......................................109

3.3. magnituri velis moqmedeba moZrav muxtze. lorencis Zala .....................112

3.4. nivTierebis magnituri Tvisebebi ..........................................................................114


3.6. SeamowmeT Tqveni codna ............................................................................................118

IV Tavi. eleqtromagnituri induqcia ......................................................................119

4.1. magnituri nakadi. eleqtromagnituri induqciis movlena .........................120

4.2. induqciuri denis mimarTuleba. lencis wesi. grigaluri

eleqtruli veli ..........................................................................................................123

4.3. eleqtromagnituri induqciis kanoni ..................................................................125

4.4. TviTinduqcia.................................................................................................................128

4.5. induqciuroba. magnituri velis energia ...........................................................131


4.7. SeamowmeT Tqveni codna ............................................................................................135

5

rogor vixelmZRvaneloT saxelmZRvaneloTi

paragrafis nomeri

paragrafis

saxelwodeba

individualuri

samuSao

jgufebad

muSaoba

amocanebi logikuri

msjelobis gamoyenebiT

informacia suraTis

mixedviT

wyvilebad

muSaoba

48-e gverdis

me-2 suraTi

saSinao cda

axali terminebi

daskvnebi

eleqtruli velis daZabuloba1.3

eleqtruli velis ZiriTadi Tvisebaa, imoqmedos eleqtrul muxtebze ZaliT.

SeiZleba vTqvaT, rom Tu gvecodineba Zala, romliTac veli ama Tu im wertilSi

moTavsebul muxtze moqmedebs, maSin velis Sesaxeb

viciT yvelaferi. amitom saWiroa, SemoviRoT velis

iseTi maxasiaTebeli, romlis codniTac SeiZleba

ganvsazRvroT es Zala.

vTqvaT, eleqtruli veli Seqmnilia q

wertilovani muxtiT (sur. 9). velis erTsa

1. eleqtrobis gamtarobis mixedviT, rogor arian dayofili

nivTierebebi?

saSinao cda cdis mizani: naTurebis naTebaze dakvirveba da daskvnis

gamotana.

1. a suraTze gamosaxuli sqemiT Seadgine

wredi.

cdebisTvis saWiroa

denis wyaro _ mSrali elementi

sami erTnairi naTura

3. rogori warmodgena SegeqmnaT, 1 k muxti Zalian didia?

SesaZleblad migaCniaT Tu ara gamtar sferos, romlis diametri

ramdenime metria, 1 k muxti mivaniWoT? axseniT, ratom fiqrobT ase?

2. Tqveni azriT, rogor SeiZleba davadginoT eleqtruli velis arseboba?

I. ori erTnairi liTonis damuxtuli burTulis Sexebisas maTze

muxtebi Tanabrad nawildeba.

kulonis kanonidan da am winadadebidan gamomdinareobs, rom raRac manZiliT

daSorebuli q da 5q muxtebis ori erTnairi gamtari burTulis Sexebisas da

Semdeg imave manZiliT daSorebisas maTi urTierTqmedebis Zalis moduli

a. 1,25-jer gaizarda; b. 1,25-jer Semcirda; g. 1,8-jer gaizarda;

d. 1,8-jer Semcirda; e. ar Seicvala.

wertilovani muxti, kulonis kanoni, centruli Zala

nebismieri formis iseT damuxtul sxeulebs, romelTa zomebi mcirea im

manZilTan SedarebiT, romelzec ganixileba maTi moqmedeba, wertilovani

muxtebi ewodeba.

4. daakvirdiT suraTs da isau b reT, ra informacias iRebT suraTidan.

sur. 48.2

6

gamoTqviT mosazreba 6.1 suraTze gamosaxuli buStebis urTierTqmedebis Sesaxeb.

Tqveni varaudiT, aqvs Tu ara damuxtul sxeulTa sistemas energia? axseniT,

ratom fiqrobT ase?

sur. 6.1a b g

I Tavi

eleqtrostatika

am TavSi gaixsenebT da gaecnobiT

damuxtul nawilakebs da sxeulebs;

damuxtuli sxeulebis urTierT-

qmedebas, kulonis kanons;

eleqtruli velis daZabulobas;

superpoziciis princips;

eleqtrostatikuri velis muSao-

bas;

eleqtruli velis potencials;

potencialTa sxvaobas _ Zabvas;

eleqtrotevadobas;

kondensators;

eleqtruli velis energias.

l2

l1

A

mg

F

+++

7

dRes civilizebuli adamianis cxovreba eleqtruli energiis gareSe warmoudgenelia. eleqtrul energiasTanaa dakavSirebuli radiomimRebis, telefonis, televizoris, kompiuteris, sxvadasxva saxis eleqtruli Zrav-asa da sxvaTa muSaoba.

sxva saxis energiasTan SedarebiT eleqtrul energias mravalgvari upiratesoba aqvs: igi martivad gardaiqmneba meqanikur, siTbur, qimiur, sinaTlisa da sxva saxis energiebad. erTi da imave denis wyarodan energiis miReba SeiZleba gansxvavebuli momxmareblebis mier. magaliTad, SeiZleba erTdroulad vamuSaoT televizori, uTo, naTura, macivari, mtversasruti da a. S. eleqtruli energia SeiZleba gadavceT Zalian Sor manZilze, Zalian mcire droSi, mcire danakargebiT. eleqtruli energiis gadacemisa da mox-marebisas garemo ar binZurdeba.

fotoebze gamosaxulia zogierTi mecnieri, romlebsac eleqtrobis Teoriisa da praqtikis ganviTarebaSi didi wvlili miuZRviT.

daiyaviT jgufebad da moipoveT informacia am mecnierebisa da maTi naSromebis Sesaxeb. moam zadeT sakiTxi gakveTilze warsadgenad.

davaleba

andre mari amperi(1775-1836)

benjamin franklini (1706-1790)

georg omi (1787-1854)

jeims maqsveli (1831-1879)

Tomas edisoni (1847-1931)

nikola tesla (1856-1943)

hainrix herci (1857-1894)

maikl faradei (1791-1867)

jozef henri (1797-1878)

gustav kirhofi (1824-1887)

alesandro volta (1745-1827)

kristian erstedi(1777-1851)

8

ra da rogor iswavleT, SeamowmeT Tqveni codna

1.1

testi1. Zala aris a. sxeulis inertulobis zoma; b. sidide, romliTac xasiaTdeba erTi sxeulis moqmedeba meoreze; g. skalaruli sidide; d. sidide, romlis moqmedebiTac sxeuli moZraobs

Tanabrad.

2. Zalis erTeulad SI-Si miRebulia a. 1 niutoni (1 n); b. 1 kilogrami (1 kg); g. 1 kiloniutoni (1 kn); d. 1 jouli (1 j).

3. masa aris a. sxeulis inertulobis zoma; b. sidide, romliTac xasiaTdeba erTi

sxeulis moqmedeba meoreze; g. veqtoruli sidide; d. sxeulze moqmedi Zalisa da aCqarebis namravli.

4. Tu 2 kg masis sxeulis siCqare 1 wm-Si 4 m/wm-iT icvleba, maSin masze moqmedi Zalebis tolqmedis moduli aris

a. 0,5 n; b. 1 n; g. 4 n; d. 8 n.

5. Tu ori Zalis moqmedebiT sxeuli Tanabrad moZraobs, maSin a. es Zalebi moduliT tolia da aqvT Tanxvdenili mimarTuleba; b. es Zalebi moduliT tolia da aqvT urTierTsapirispiro mimarTuleba; g. es Zalebi moduliT tolia da erTmaneTis marTobia; d. Zala, romlis moduli metia, mimarTulia moZraobis mimarTulebiT.

6. Tu uZrav sxeulze erTdroulad iwyebs moqmedebas erTmaneTisadmi kuTxiT mimarTuli ori Zala (F1>F2), maSin sxeuli moZraobas daiwyebs

a. F1-is mimarTulebiT; b. F2

-is mimarTulebiT;

g. F1-isa da F2

-is tolqmedis mimarTulebiT;

d. arc erTi pasuxi swori ar aris.

7. ori burTulidan erT-erTis masis samjer gadidebiT, maT centrebs Soris manZilis Seucvlelad, maTi urTierTmizidvis Zalis moduli

a. samjer mcirdeba; b. samjer izrdeba; g. cxrajer izrdeba; d. ar icvleba.

8. erTsa da imave simaRleze sxeulis haersa da wyalSi awevisas simZimis Zalis mier Sesrulebuli muSaoba

a. haerSi metia; b. haerSi naklebia; g. erTmaneTis tolia; d. zogjer haerSia meti, zogjer wyalSi.

9. rodesac 90 n/m sixistis aradeformirebuli zambara 0,1 m-iT SekumSes, maSin misi potenciuri energia Seicvala

a. 0,45 j-iT; b. 1 j-iT; g. 1,4 j-iT; d. 9 j-iT.

Tu testebze pasuxis gacema gagiWirdaT, maSin gaiRrmaveT codna qvemoT moyvanili winadadebebiT. miRebuli informaciiT da azrovnebiT aucileblad SeZlebT testebze swori pasuxebis gacemas.

www.physics.ge | saZiebo fraza k10t1p1

9

sidides, romliTac xasiaTdeba erTi sxeulis moqmedeba meoreze, Zala ewodeba. Zalis moqmedebiT icvleba sxeulis siCqare.

masa sxeulis inertulobis zomaa. inertuloba Tvisebaa, romelic yvela sxe uls axasiaTebs, igi SemdegSi mdgomareobs: raime sididiT sxeulis siCqaris Sesac vlelad saWiroa, masze sxva sxeulis moqmedeba grZeldebodes garkveuli drois ganmavlobaSi. rac metia es dro, miT ufro inertulia sxeuli. masis erTeulad SI-Si miRebulia 1 kilogrami (1 kg).

niutonis meore kanoni _ aCqareba, romliTac moZraobs sxeuli,

tolia masze moqmedi Zalisa da sxeulis masis Sefardebis:

,a mF F ma&= = gegmilebiT Fx=max.

Zalis erTeulad SI-Si miRebulia 1 niutoni (1 n). es aris Zala, romelic 1 kg masis sxeuls 1 m/wm2 aCqarebas aniWebs. 1 n = 1 kg.m/wm2.

ori sxeuli urTierTmiizideba ZaliT, romlis moduli pirdapirproporciulia maTi masebis namravlisa da ukuproporciulia

maT Soris manZilis kvadratisa: ,F GRmM

2= (1) sadac m da M

urTierTmimzidavi nivTieri wertilebis an sferos formis sxeulebis

masebia, R _ maT centrebs Soris manZili, G=6,67.10–11 n.m2/kg2 _ gravitaciuli mudmiva, F mizidulobis Zalis moduli.

ori Zalis moqmedebiT berketi gawonasworebulia, Tu isini cdiloben misi sxvadasxva mimarTulebiT mobrunebas da Zalebis modulebis Sefardeba maTi mxrebis Sebrunebuli Sefardebis tolia.

wrfivi moZraobisas mudmivi F Zalis muSaoba tolia Zalisa da S

gadaadgilebis modulebisa da maT mimarTulebebs Soris arsebuli α

kuTxis kosinusis namravlis: A=FScosα. muSaobis erTeulad SI-Si miRebulia 1 jouli (1 j).

fizikur sidides, romelic axasiaTebs sxeulis an sxeulTa sistemis mier muSaobis Sesrulebis unars, meqanikuri energia ewodeba.

energias, romelic sxeuls moZraobis Sedegad aqvs, kinetikuri

energia ewodeba: ,vE m2

2

kin= sadac Ekin

aris v siCqariT moZravi m masis

sxeulis kinetikuri energia.Tu sxeulze moqmedi Zala asrulebs dadebiT muSaobas, maSin sxeulis

kinetikuri energia izrdeba. energiis erTeulad SI-Si miRebulia 1 jouli (1 j).

energias, romelic ganisazRvreba urTierTmoqmedi sxeulebis an erTi da imave sxeulis nawilebis urTierTmdebareobiT, potenciuri energia ewodeba.

potenciuri energia aqvs dedamiwis zedapiridan raime simaRleze aweul sxeuls da yvela drekadad deformirebul sxeuls.

potenciuri energiis aTvlis nulovani donidan h simaRleze aweuli m masis sxeulis Epot

potenciuri energia ganisazRvreba Epot

=mgh formuliT.

im zambaris potenciuri energia, romlis sixistea k, xolo defor-

maciis sidide (wagrZeleba an SekumSva) _ x, ganisazRvreba E kx2

2

pot= formuliT.

10

gavixsenoT zogierTi sakiTxi da miRebuli codnisa da logikuri msjelobis gamoyenebiT gamovitanoT daskvnebi.

XX saukunis mecnierebam uamravi dakvir-vebiTa da cdiT sabolood daasabuTa azri, rom nivTiereba Sedgeba Zalian mcire nawilakebisagan. isini ganuwyvetliv, qaosurad moZraoben da urTierTqmedeben. es nawilakebia molekulebi da atomebi.

gamoCenilma ingliselma fizikosma ernst rezerfordma mravalgzis Catarebuli cdebis safuZvelze daadgina, rom

I. atomi Sedgeba atombirTvisa da mis garSemo moZravi eleqtronebisagan.

Semdeg daadgines atombirTvis rTuli agebuleba. igi Sedgeba Zalian mcire masis nawilakebisagan _ protonebisa da neitronebisagan.

atomebi erTmaneTisagan gansxvavdeba protonebis, neit ronebisa da eleqtronebis raodenobiT.

II. atombirTvSi protonebis raodenoba atomSi eleqtronebis raode-nobis tolia.

2. cxrilis da I-II winadadebebis gamoyenebiT gamoitaneT daskvna: atomi

a. damuxtulia dadebiTad; b. damuxtulia uaryofiTad;

g. daumuxtavia; d. zogjer damuxtulia dadebiTad, zogjer uaryofiTad.

atomi (berZnuli) _ niSnavs ganuyofels.molekula (laTinuri) _ niSnavs `mcire masas~.

1 kuloni

(1k) _ muxtis

erTeulia SI-Si

ernst rezerfordi

(1871-1937)

daaxloebiT 2500 wlis win, berZen swavluls demokritoss miaCnda, rom sxeulebi Sedgeba umciresi, TvaliT uxilavi nawilakebisagan

_ atomebisagan

1. gaecaniT cxrils.

isaubreT, ra informacias iRebT cxrilidan.

masa muxti

neitroni 1,675.10-27 kg elqtrulad neitraluria

protoni 1,672.10-27 kg +1,6.10-19 k

eleqtroni 9,1.10-31 kg -1,6.10-19 k

eleqtruli muxti da elementaruli nawilakebi

1.2www.physics.ge | saZiebo fraza k10t1p2

11

III. rodesac atomi kargavs an miierTebs eleqtrons, miiReba ioni.

3. cxrilis da I, II, III winadadebebis gamoyenebiT gamoitaneT daskvna: rodesac atomi kargavs eleqtrons,a. miiReba dadebiTi ioni; b. miiReba uaryofiTi ioni; g. miiReba zogjer dadebiTi, zogjer ki _ uaryofiTi ioni; d. miiReba sxva atomi.

IV. damuxtuli nawilakebi urTierTqmedebs eleqtruli ZaliT, romelic gacilebiT aRemateba msoflio mizidulobis (gravitaciul) Zalas. magaliTad, ori eleqtroni erTmaneTs ganizidavs ZaliT, romelic ≈4,2.1042-jer aRemateba maTi gravitaciuli mizidulobis Zalas.

V. Tanasaxeliani muxtis nawilakebi ganizideba, sxvada sxva-saxeliani muxtis nawilakebi miizideba.

4. cxrilis da IV-V winadadebebis gamoyenebiT SeiZleba davaskvnaT, rom

a. protoni protons izidavs; b. protoni eleqtrons izidavs;g. protoni eleqtrons ganizidavs; d. protoni da eleqtroni ar

urTierTqmedeben.

VI. Caketil sistemaSi sxeulebis nebismieri urTierTqmedebisas am sistemis yvela nawilakis muxtis algebruli jami mudmivi rCeba.

5. VI winadadebis gamoyenebiT gamoitaneT daskvna:ori damuxtuli sxeulis Sexebisas, Tu orive sxeuli gani-

muxta, maSin am sxeulebis saerTo muxtia. Semcirda; b. gaizarda; g. ar Seicvala;

d. jer Semcirda, Semdeg gaizarda.

6. VI winadadebis gamoyenebiT gamoitaneT daskvna:Tu eleqtrulad neitraluri ori sxvadasxva zomis sxeulis

Sexebisa da dacilebis Semdeg orive sxeuli damuxtuli aRmoCnda, maSin

a. am sxeulebs aqvT erTnairi niSnis toli muxtebi;

b. am sxeulebs aqvT sapirispiro niSnis moduliT toli muxtebi;

g. didi sxeulis muxtis moduli metia patara sxeulis muxtis modulze; d. didi sxeulis muxtis moduli naklebia patara sxeulis muxtis modulze.

7. daakvirdiT 11.1 suraTs. ra cvlilebebs ganicdis

gamtarebi da mu-

x tuli sxeu le bis

eleq trul ve lSi?

axse niT, ra tom?

sur. 11.1a b

12

molekula, atomi, protoni, eleqtroni, neitro-

ni, ioni

davaleba

gaecaniT 12.1 suraTze gamosaxul mgrZnobi-are, ara tol mxrian berketian saswors. saswori Sedgeba danayo febiani CarCosagan (1), skalis nulovan danayofTan damagrebuli kavisagan (2), romlis RerZze brunva SeuZlia patara WoWonaqs (3). WoWonaqze mimagrebulia msubuqi isari _ aratolmxriani berketi (4), romlis horizontalur mdebareobaSi gaCereba Sesa-Zlebelia moZravi sapirwoneTi (5). WoWonaqs qvemodan, berketisa da misi RerZis marTobu-lad, gakeTebuli aqvs xvreli momWeri xraxniT (6). xvrelSi aTavseben mavTuls, romelzedac jer izolatori, Semdeg ki liTonis msubuqi burTulaa damagrebuli (7).

Tu liTonis burTulaze marjvnidan imoqmedebs Zala, maSin sasworis wonasworoba dairRveva. berketi zeviT aiwevs. berketi horizontalur

mdgomareobaSi mohyavT cnobili masis moRunuli patara fir-fitis (8) meSveobiT (sur. 12.2).

burTulaze moqmedi F Zalis modulis gasagebad davweroT

berketis wonasworobis piroba

F.l1=mgl2 ⇒ .F mllg1

2= (*)

suraTze gamosaxuli A, B da C liTonis burTulebi erTnair-ia da izolatorzea moTavsebu-li.

SeecadeT, egeb analogiuri an ukeTesi konstruq ciis mgrZno-biare saswori daam zadoT. mi-

iReT monawileoba konkursSi, romelic yovel wliurad tardeba. SeiZ leba Tqveni xelsawyo saukeTeso aR moCndes.

8 4

1 2 5

63

7

sur. 12.1.

sur. 12.2

l2

l1

A

mg

F

B C

13

daakvirdiT 13.1 suraTs.

or damuxtul sxeuls Soris urTierTqmedebis Zalis moduli damokidebulia sxeulebis damuxtvis xarisxze, maT formasa da sxeulebs Soris manZilze. dadginda, rom SeuZlebelia martivi formulis miReba, romliTac SesaZlebeli iqneboda eleqtruli urTierTqmedebis aRwera nebismieri SemTxvevisaTvis. magram iseTi damuxtuli sxeulebis urTierTqmedebis aRwera, romelTa zomebi gacilebiT naklebia maT Soris manZilze, martivi aRmoCnda.

nebismieri formis iseT damuxtul sxeulebs, romelTa zoma mcirea im manZilTan SedarebiT, romelzec ganixileba maTi moqmedeba, wertilovani muxtebi ewodeba.

ori uZravi wertilovani muxtis urTierTqmedebis kanoni 1785 wels eqsperi mentulad daadgina frangma fizikosma Sarl kulonma (1736-1806).

kanoni, romelsac Semdeg kulonis kanoni uwodes, eleqtrostatikis ZiriTadi kanonia.

vakuumSi ori wertilovani uZravi damuxtuli sxeulis urTierTqmedebis Zalis moduli pirdapirproporciulia mux tebis modulTa namravlisa da ukupro-porciulia maT Soris manZilis kvad ratisa. es Zala mimarTulia muxtebis Semaer Tebeli wrfis gaswv-

+

+

+

–

F F12 21=-

F F12 21=-F F12 21=-

F F12 21=-1

1

2

2

sur. 13.2

1. aRwereT 13.1 su raTze gamosaxuli si tuacia.

2. rogor icvleba damuxtuli A sxeulisa da msubuqi burTulebis urTier Tqmedebis Za la maT Soris man Zilis

gadidebiT? pasu xis marTebuloba ganamtkiceT msjelobiT.

3. rogor SevamciroT liTonis A sxeulis muxti orjer?

4. ra moxdeba, Tu A sxeulis muxts sapirispiro niSnis muxtiT SevcvliT?

5. moifiqreT da aRwereT cda, romliTac daadgenT damuxtul sxeulebs Soris urTierTqmedebis Zalis damokidebulebas maT muxtze. daasabuTeT Tqveni mosazrebis marTebuloba da SeamowmeT cdiT.

sur. 13.1

A

Sarl kuloni

1.3damuxtuli sxeulebis urTierTqmedeba. kulonis kanoni


14

riv muxtebidan gareT Tanasaxeliani muxtebisaTvis da muxtebisaken sapirispiro niSnis muxtebisaTvis (sur. 13.2). msgavs Zalebs centruli Zalebi ewodeba.

niutonis III kanonis Tanaxmad, F F12 21=- .Tu muxtebis modulebs aRvniSnavT |q1| da |q2|-iT, maT Soris manZils ki

_ r-iT, kulonis kanoni Semdegnairad daiwereba:

F kr

q q2

1 2$= , (1)

sadac k proporciulobis koeficientia. k ricxobrivad im Zalis modulis tolia, romliTac urTierTqmedebs erTeulis toli muxtebi, roca maT Soris manZili erTeulis tolia. misi ricxviTi mniSvneloba damokidebulia formulaSi Semavali fizikuri sidideebis erTeulebis arCevaze da eqsperimentulad ganisazRvreba. dadgenilia, rom SI-Si k=9.109 n.m2/k2.

miRebulia, k koeficienti SI-Si Caiweros Semdegi saxiT:

.k41

0rf= (2) (2) ⇒ , .k4

1 8 85 10n mk

0

12

2

2

$$

f = =r-

e0-s eleqtruli mudmiva ewodeba.(2)-is gaTvaliswinebiT (1) Semdeg saxes miiRebs:

.Fr

q q

4 0

21 2$

=rf

(3)

SemdegSi formulebis Caweris simartivisaTvis gamoviyenoT (1) Canaweri.

sworad Catarebuli gamoTvlebiT miviRebT, sxeulis masa 900 000 tonaa.

8. rogori warmodgena SegeqmnaT, 1 k muxti Zalian didia? SesaZleblad migaCniaT Tu ara gamtar sferos, romlis diametri ramdenime metria, 1 k muxti mivaniWoT?

axseniT, ratom fiqrobT ase?

6. imsjeleT, mgrZnobiare sasworis meSveobiT rogor SeamowmebT kulonis kanonis marTebulobas.

7. gansazRvreT, ra masis sxeuls izidavs dedamiwa im ZaliT, romliTac ganizideba 1 m-iT daSorebuli ori burTula im SemTxvevaSi, Tu SesaZlebeli iqneboda TiToeulisaTvis 1 k muxtis miniWeba.

e0 berZnuli _ ikiTxeba èpsilon~

wertilovani muxti, kulonis kanoni, centruli

Zala

nebismieri formis iseT damuxtul sxeulebs, romelTa zomebi mcirea im manZilTan SedarebiT, romelzec ganixileba maTi moqmedeba, wertilovani muxtebi ewodeba.

vakuumSi ori wertilovani uZravi damuxtuli sxeulis urTierTqmedebis Zalis moduli pirdapirproporciulia muxtebis modulTa namravlisa da ukuproporciulia maT Soris manZilis kvad-ratisa.

15

davaleba

kulonma ori damuxtuli sxeulis ur-Tier Tqme debis kanoni daadgina grexiTi sasworis meSveobiT (sur. 15.1). moipoveT informacia, rogor aRmoaCina kulonma ele-qtrostatikis ZiriTadi kanoni.

SeiswavleT grexiTi sasworis moqmedebis principi. daadgineT, ra problemis winaSe idga kuloni cdebis Catarebisas da rogor gadawyvita es problema.

moamzadeT masala gakveTilze warsad-genad.

sakiTxis Sesaswavlad gamoiyeneT TqvenT-vis xelmisawvdomi sainformacio wyaro (be-WdviTi, audiovizualuri, interneti).

sarekomendacio CamonaTvali ixileT 138-e gv-ze.

I. liTonis ori erTnairi damuxtuli burTulis Sexebisas maTze muxtebi Tanabrad nawildeba.

II. Caketil sistemaSi sxeulebis nebismieri urTierTqmedebisas am sistemis yvela nawilakis muxtis algebruli jami mudmivi sididea.

kulonis kanonidan da am winadadebebidan gamomdinareobs:

raRac manZiliT daSorebuli liTonis ori erTnairi burTula, romelTa muxtebia q da 5q, erTmaneTs Seaxes da Semdeg imave manZiliT daaSores. maTi urTierTqmedebis Zalis moduli

a. 1,25-jer gaizarda; b. 1,25-jer Semcirda; g. 1,8-jer gaizarda;d. 1,8-jer Semcirda; e. ar Seicvala.

kulonis kanonidan da I-II winadadebebidan gamomdinareobs:

raRac man ZiliT daSorebuli liTonis ori erTnairi burTula, romelTa muxtebia q da –5q, erTmaneTs Seaxes da Semdeg imave manZiliT daaSores. maTi urTierTqmedebis Zalis moduli

a. 1,25-jer gaizarda; b. 1,25-jer Semcirda;. g. 1,8-jer gaizarda;d. 1,8-jer Semcirda; e. ar Seicvala.

sur. 15.1. es suraTi kulonis

statiidanaa aRebuli.

16

ris meSveobiT xorcieldeba damuxtuli sxeulebis urTierTqmedeba?didma ingliselma mecnierma maikl faradeim (1791-1867) Camoayaliba

hipoTeza, romlis Tanaxmad, damuxtuli sxeulebis an nawilakebis urTierTqmedeba xorcieldeba im eleqtruli velis meSveobiT, romelsac damuxtuli nawilakebi qmnian.

SemdgomSi eleqtruli velis arseboba eqsperimentiT iqna dasabuTebuli.eleqtruli velis ZiriTadi Tvisebaa, imoqmedos eleqtrul muxtebze

ZaliT.Zalas, romliTac erTi damuxtuli nawilakis an sxeulis eleqtruli

veli moqmedebs meore damuxtul nawilakze an sxeulze, eleqtruli Zala ewodeba.

SemoviRoT velis iseTi maxasiaTebeli, romlis meSveobiTac SesaZlebeli iqneba ganvsazRvroT masSi Setanil muxtze moqmedi Zala.

vTqvaT, eleqtruli veli Seqmnilia q werti lovani muxtiT (sur. 16.1). velis erTsa da imave

wer tilSi q muxtidan R manZilze rigrigobiT movaTavsoT q0, 2q0, 3q0 da a. S. sacdeli muxtebi.

radgan velSi Setanil sacdel muxtze moqmedi Zala am muxtis pirdapir proporciulia, amitom Zalis fardoba sacdel muxtTan ar aris damokidebuli sacdeli muxtis sidideze, velis mocemuli wertilisaTvis mudmivi sididea da vels axasiaTebs im wertilSi, sadac sacdeli muxtia moTavsebuli.

am fardobas eleqtruli velis daZabuloba ewodeba. aRvniSnoT igi

E-Ti. ganmartebis Tanaxmad,

.E qF0

= (1) (1) ⇒ .F q E0= (2)

eleqtruli velis daZabuloba fizikuri sididea, romelic tolia

velis mocemul wertilSi moTavsebul sacdel muxtze moqmedi

Zalisa da am muxtis Sefardebisa.

eleqtruli velis daZabuloba

1. Tqveni azriT, rogor SeiZleba davadginoT eleqtruli velis arseboba?

2. daadgineT, rogori damokidebulebaa q muxtsa da mis mier Seqmnili velis romelime wertilSi Setanil sacdel muxtze moqmed Zalas Soris?

3. damokidebulia Tu ara sacdel muxtze moqmedi Zalis Sefardeba sacdeli muxtis sidideze? axseniT, ratom fiqrobT ase?

sur. 16.1

R

q

q0+

+

sacdeli muxti _ wertilovani, iseTi mcire eleqtruli muxti,

romelic praqtikulad ar cvlis Sesaswavl eleqtrul vels.


17

daZabulobis mimarTuleba emTxveva dadebiT muxtze moqmedi Zalis

mimarTu lebas.

E qF0

&= formulidan ⇒ daZabulobis erTeulia 1 n/k.

Semdeg davamtkicebT, rom 1 n/k = 1 v/m.

kulonis kanonis Tanaxmad, sacdel muxtze moqmedi Zalis moduli

.F kR

q q2

0$= (3) (3) (1) ⇒ .E k

R

q2= (4)

am formuliT ganisazRvreba wertilovani

muxtis mier Seqmnili velis daZabu lobis

moduli misgan R manZilze.

Tu sivrcis mocemul wertilSi eleqtrul vels qmnis q1, q2 ... qn

nawilakebi, maSin am wertilSi moTavsebul uZrav q0 muxtze moqmedi Zala

... ,F F F Fn1 2= + + + (5) sadac , , ...q q qF E F E F En n1 0 1 2 0 2 0= = = TiToeuli

muxtidan q0-ze moqmedi Zalaa, xolo F qE= rezultaturi Zala. CavsvaT

TiToeuli (5)-Si ⇒ ... ... .q q q qE E E E E E E En n0 0 1 0 2 0 1 2&= + + + = + + + (6)

amgvarad, Tu veli Seqmnilia ramdenime muxtiT, maSin velis mocemul wertilSi rezultaturi velis daZabuloba tolia calkeuli muxtebis velebis daZabulobaTa jamisa. aseT jams xSirad geometriuls uwodeben.

amaSi mdgomareobs velebis superpoziciis principi.velebis zeddebisas isini gavlenas ar axdenen er T maneTze. TiToeuli

muxti mocemul wertilSi damoukideblad qmnis eleqtrul vels, miuxedavad imisa, mis maxloblobaSi aris Tu ara sxva damuxtuli sxeulebi.

ganvixiloT kerZo SemTxveva, ro desac eleq tru li veli A wertilSi Seqmnilia ori wertilovani dadebiTi q1 da q2 muxtebis mier (sur. 17.2). suraTze E1

da E2 Sesabamisad q1 da q2 muxtebis

mier Seqmnili eleqtruli velis daZa-bulebebia.

5. ras warmoadgens E 17.2 suraTze?

6. 17.3 suraTis mixedviT gan-sazRvreT TiToeuli muxtisa da re-zul taturi velis daZabulobis mo-dulebi Tu erTi danayofi aris 1 v/m.

superpozicia _

zeddebas niSnavs.

E kr

qB

B

2$=

E kr

qA

A

2$=

q

rA rA=2.rB

EB=4.EA

A

B

sur. 17.1

sur. 17.2

+q1

+q2

sur. 17.3

4. daakvirdiT 17.1 suraTs da isau b reT, ra informacias iRebT suraTidan.

18

paralelogramis diagonalis sigrZe SeiZleba ganvsazRvroT

formuliTac:

,cosE E E E E21

2

2

2

1 2= + + a (7)

sadac α aris kuTxe E1 da E2

daZabulobebs Soris.

gaecaniT zogierTi eleqtruli velis daZabulobis mniSvnelobas (sur. 18.2).

daZabuloba, superpoziciis principi,

daZabulobis erTeuli

damuxtuli sxeulebis an nawilakebis urTierTqmedeba xorcieldeba im eleqtruli velis meSveobiT, romelsac damuxtuli nawilakebi qmnis.

eleqtruli velis ZiriTadi Tvisebaa, imoqmedos eleqtrul muxtebze ZaliT.

Zalas, romliTac erTi damuxtuli nawilakis an sxeulis eleqtruli veli moqmedebs meore damuxtul nawilakze an sxeulze, eleqtruli Zala ewodeba.

eleqtruli velis daZabuloba fizikuri sididea, romelic tolia velis mocemul wertilSi moTavsebul sacdel muxtze moqmedi Zalisa da am muxtis Sefardebisa.

Tu veli Seqmnilia ramdenime muxtiT, maSin velis mocemul wertilSi sruli daZabuloba tolia calkeuli muxtebis velebis daZabulobaTa jamisa.

+

–

wyalbadis atomis bi-r Tvis mier Seqmni-l i eleqtruli ve-li s daZabuloba mi-s gan orbitis ra di -usis tol 0,5.10-10 m manZilze daax lo ebiT 6.1011 v/m.

daZabuloba eleqtrul

naTuraSi 10000 v/mvelis daZabuloba,

romlis drosac normaluri

atmosferuli wnevisas haerSi naperwkali

Cndeba 3 000 000 v/m.

dedamiwis mier Seqmnili eleqtruli

velis daZabuloba mis zedapirTan 130 v/m.

sur. 18.2

7. dawereT, rogor saxes miiRebs (7) formula, rodesac E1

da E2 veqtorebs Soris kuTxe a. α=0;

b. α=900; g. α=1800. Sedegi gamosaxeT samuSao rveulSi suraTiT.

8. samuSao rveulSi daxazeT, rogori mimarTuleba eqneba E veqtors (sur. 17.3), rodesac q2 muxti uaryofiTia.

9. isaubreT, ra informa cias iRebT 18.1 suraTidan.

sur. 18.1

19

xilulia Tu ara eleqtruli veli? rogoria sxvadasxva muxtis, aseve gansxvavebuli formisa da zomis sxeulebis mier Seqmnili veli?

am SekiTxvebze pasuxis gasacemad saWiroa, SevimuSaoT iseTi meTodi, rom saTanado pirobiTi niSnebiT da SeTanxmebiT davxatoT konkretuli velis suraTi. miRebuli suraTis meSveobiT unda SeiZlebodes Tqma, sad aris veli Zlieri da sad _ susti. agreTve, velis mocemul wertilSi saiT aris mimarTuli muxtze moqmedi Zala.

sivrceSi eleqtruli velis TvalsaCinod warmosadgenad maikl faradeim SemoiRo eleqtruli velis Zalwirebis cneba.

I. velis wertilebze gamaval uwyvet wirebs, romelTa mxebi mis yovel wertilSi daZabulobis veqtors emTxveva, eleqtruli velis daZabulobis wirebi anu Zalwirebi ewodeba (sur. 19.1).

II. daZabulobas velis mocemul wertilSi dadebiT muxtze moqmedi Zalis mimarTuleba aqvs.

III. Zalwirebs atareben iseTi sixSiriT, rom farTobis erTeulze gamavali Zalwirebis raodenoba ricxobrivad daZabulobis modulis tolia.

sur. 19.1

A

B

2. III winadadebis gamoyenebiT da 19.2, b suraTze gamosaxuli wertilovani muxtis velis Zalwirebis ganawilebis mixedviT Sei-Zleba vTqvaT, rom

muxtidan daSorebis mixedviT velis daZabulobis moduli a. izrdeba; b. mcirdeba; g. ar icvleba.d. jer izrdeba, Semdeg mcirdeba; eE. jer mcirdeba, Semdeg izrdeba.

1.5eleqtruli velis daZabulobis wirebi

–Q


1. 19.2 suraTze gamosaxulia sxvadasxva damuxtuli sxeulis velis daZabulobis wirebi. samuSao rveulSi cxrilSi mocemulia am sxeulTa CamonaTvali.

I da II winadadebebis gamoyenebiT daadgineT da CawereT cxrilSi, romeli suraTi romel sxeuls Seesabameba

sur. 19.2

z

+Q1 +Q2

ba

-Q3

g

T

-Q+Q

d

+Q -Q

C

+Q +Q

D

M

E

ev

+Q

i

+Q +Q

20

3. III winadadebis da 20.1 suraTze gamosaxuli daZabulobis wirebis mixedviT SeiZleba vTqvaT, rom

daZabulobis wirebis mimarTulebiT velis daZ-abulobis moduli

a. izrdeba; b. mcirdeba; g. ar icvleba. d. jer izrdeba, Semdeg mcirdeba; e. jer mcirdeba, Semdeg izrdeba;

IV. eleqtrul vels, romelSic daZabuloba sivrcis yvela wertilSi erTnairia, erTgva-rovani ewodeba.4. III-IV winadadebebis da 20.2 suraTis mixedviT Sei-

Zleba vTqvaT, rom Tu Zalwirebi paraleluria da erTmaneTisagan

to li manZilebiTaa daSorebuli, maSin aseTi eleqtruli veli a. erTgvarovania. daZabuloba yvelgan erTnairia;b. araerTgvarovania. Zalwirebis mimarTulebiT daZabuloba iz-

rdeba; g. araerTgvarovania. Zalwirebis mimarTulebiT daZabuloba mcirdeba. d. araerTgvarovania. Zalwirebis mimarTulebis mixedviT daZabuloba jer izrdeba, Semdeg mcirdeba; e. araerTgvarovania. Zalwirebis mimarTulebiT daZabuloba jer mcirdeba, Semdeg iz-rdeba.

5. Tqveni varaudiT, Caketilia Tu ara eleqtruli velis Zalwirebi?

6. SesaZleblad migaCniaT Tu ara, rom Zalwirebma erTmaneTi gadakveTon? axseniT, ratom fiqrobT ase?

7. gansazRvreT, 10-8 k muxtidan ra manZilze iqneba eleqtruli velis daZabuloba 10-9 n/k-ze naklebi.

8. 20.3 suraTze gamosaxulia moduliT toli da sapiri spiro niSnis muxtebis liTonis ori burTula da sacdeli q muxti. samuSao rveulSi sqematurad gamosaxeT sacdel muxtze gamavali daZabulobis wiri da axseniT, ratom aqvs mas aseTi konfiguracia.

daZabulobis wirebi

q

sur. 20.3

sur. 20.2

sur. 20.1

ganvmarteT eleqtruli velis daZabulobis wirebi _ Zalwirebi da erTgvarovani veli. SeviswavleT eleqtruli velis gamosaxva Zalwirebis meSveobiT

21

ra moxdeba liTonis gamtaris eleqtrostatikur velSi moTavse-bisas? eleqtrostatikuria veli Tu igi ùZravi~ muxtebis mieraa Seqmnili.

am SekiTxvaze swori pasuxis gasa-cemad gavixsenoT, rom

I. liTonis gamtari Sedgeba kris-ta luri mesris kvanZebSi ganla gebuli ùZravi~ _ bmuli dadebiTi ionebisa da qaosurad moZravi Tavisufali eleqtronebisagan (sur. 21.1).

II. eleqtruli veli dadebiT muxtze moqmedebs ZaliT, romelsac eleqtruli velis daZabulobis mimarTuleba aqvs, uaryofiT muxtze _ daZabulobis sapirispiro.

21.2 suraTze liTonis firfitaSi eleqtronebia sqematurad gamosaxuli. 21.3 suraTze ki _ eleqtruli veli.

miiReba situacia, romelic sqematurad 21.5 suraTzea gamosaxuli. punqtiriT gamosaxulia gadanawilebuli muxtebis mier `Seqmnili~ velis Zalwirebi.

III. Tu veli Seqmnilia ramdenime muxtiT, maSin velis mocemul wertilSi sruli daZabuloba tolia calkeuli muxtebis velebis daZabulobaTa jamisa.

sur. 21.1

1. ra `dae ma -r Te baT~ eleq -

tro nebs, Tu firfitas eleq-trul velSi movaTavsebT (sur. 21.4).

sur. 21.2 sur. 21.3 sur. 21.4

sur. 21.5

2. I da II winadadebidan gamomdinareobs, rom Tu liTonis firfitas eleqtrul velSi movaTavsebT (sur.

21.4), maSin eleqtronebi qaosur moZraobasTan erTad daiwyeben mimarTul moZraobas da firfitis marcxena mxare

a. daimuxteba dadebiTad; b. daimuxteba uaryofiTad; g. eleqtrulad neitraluri darCeba; d. jer daimuxteba dadebiTad, Semdeg uaryofiTad; e. jer daimuxteba uaryofiTad, Semdeg dadebiTad.

3. III winadadebis gamoyenebiT SeiZleba vTqvT, rom eleqtrul velSi moTavsebuli gamtaris SigniT (sur. 21.5)

eleqtruli velia. ar arsebobs; b. arsebobs da mimarTulia marjvniv; g. arsebobs da mimarTulia marcxniv; d. arsebobs. gamtaris Suamde

mimarTulia marjvniv, Semdeg marcxniv; e. arsebobs. gamtaris Suamde mimarTulia marcxniv, Semdeg marjvniv.

1.6gamtari eleqtrostatikur velSiwww.physics.ge | saZiebo fraza k10t1p6

22

SeiZleba davaskvnaT: eleqtrostatikur velSi moTav se bu li gamtaris SigniT eleqtruli veli ar arsebobs (sur. 22.1).

es daskvna marTebulia eleqtrul velSi moTavsebuli rogorc damuxtuli, ise daumuxtavi gamtarisaTvis. damux tuli gamtaris SigniT Warbi muxti ar arsebobs. davadginoT, rogor nawildeba Warbi muxti gamtarze.

CavataroT cda: davmuxtoT liTonis bade. amisaTvis bade SevaerToT eleqtroforuli manqanis erT-erT polusTan da eleqtroforuli manqana moviyvanoT moqmedebaSi.

gavWimoT bade da davakvirdeT qaRaldis Txel zolebs, romlebic badezea miwebebuli (sur. 22.2).

movxaroT bade rkalad da davak -virdeT qaRaldis zolebs, Seva m CnevT, zolebi badis gare zedapirze kidev ufro gaiSleba, xolo Siga zedapirze CamoeSveba (sur. 22.3).

cdis Sedegebis analiziT SeiZ leba gamovitanoT daskvna: Warbi muxti

nawil deba damuxtuli gamtaris mxolod gare zedapirze. gamtaris SigniT ar aris arc Warbi muxti da arc eleqtruli veli.

didi zomis gamtari sibrtyis, aseve damuxtuli gamtari sferos zedapirze muxti Tanabradaa ganawilebuli, Tu isini sakmaod aris daSorebuli sxva sxeulebisgan.

rogoraa muxti ganawilebuli araswori formis sxeulebze? am SekiTxvaze pasuxis gasacemad CavataroT cda: movxaroT damuxtuli bade sxvadasxva radiusis rkalebad. SevamCnevT, qaRaldis zolebis gadaxra badidan iqaa meti, sadac metia badis gare zedapiris simrude, e. i. naklebia badis simrudis radiusi. aseT adgilebSi muxtebi erTmaneTTan ufro mWidrodaa ganlagebuli da maT maxloblad, sxeulis gareT, didia eleqtruli velis daZabuloba (sur. 22.4).

damuxtuli sxeulis zedapirze eleqtruli muxtis ganawileba xasiaTdeba fizikuri sididiT _ muxtis zedapiruli simkvriviT.

muxtis zedapiruli simkvrive aris gamtaris muxtis Sefardeba im zedapiris farTobTan, romelzedac muxtia ganawilebuli.

sur. 22.1

4. ras amCnevT? ratom ganizida furclebi badisagan?

5. yvela zoli erTnairad gadaixara badisagan?raze miuTiTebs SemCneuli movlena, rogor aris

ganawilebuli muxti gaWimul badeze?

6. ratom moxda ase? cda CaatareT ramden-jerme, SeecadeT axs naT

SemCneuli movlena.

sur. 22.3sur. 22.2

izolatoriliTonis

bade

sur. 22.4

23

Tu q muxti Tanabradaa ganawilebuli S zedapirze, maSin ,Sq

=v (1)

sadac s aris muxtis zedapiruli simkvrive, romlis erTeulis dasaxeleba SI-Si aris 1 k/m2.

daakvirdiT 23.1 da 23.2 suraTebs.

radgan damuxtuli gamtari sferos eleqtruli velis Zalwirebi sferos gareT isevea ganawilebuli, rogorc wertilovani muxtis Zalwirebi (sur. 23.1, 23.2), damuxtuli gamtari sferos eleqtruli velis daZabuloba misi

centridan r>R manZilze SeiZleba ganvsazRvroT E ,kr

q2= (2) formuliT,

sadac q aris sferos eleqtruli muxti. sferos SigniT r<R velis daZabuloba nulis tolia. R _ sferos radiusia.

damuxtuli gamtaris (aseve eleqtrul velSi mo Tav sebuli gamtaris) zedapirze muxtebi wo nas worobaSia. muxtebi gamtaris gaswvriv ar gada ad-gildeba. amitom Zalwirebi yovelTvis damuxtuli gamtaris zeda pi ris mar-Tobia (sur. 23.4,a). es rom ase ar iyos (sur. 23.4,b), maSin daZabulobis E veq-toris gamtaris zedapiris mxebi (Emx

) mdgenelis moqmedebiT ze dapiruli mux tebi mxebis gas wvriv ganuwyvetliv imoZravebda. energiis mudmivobis kanonis Tanaxmad, es SeuZ lebelia, amitom Emx

=0, e.i. Zalwirebi zedapiris marTobia.

E EE

EEmar

Emx

sur. 23.4

a

+ +b

sur. 23.5

muxtis zedapiruli simkvrive

eleqtrostatikur velSi moTavse buli gamtaris SigniT eleqtruli veli ar arsebobs.

Warbi muxti nawildeba damuxtuli gamtaris mxolod gare zedapirze. gamtaris SigniT ar aris arc Warbi muxti da arc eleqtruli veli.

7. isaubreT, ra informacias iRebT 23.5 suraTidan.

sur. 23.1. liTonis dadeb-iTad damuxtuli sferos

daZabulobis wirebi.

sur. 23.2. wertilovani muxtis Zalwirebi.

sur. 23.3. dadebiTad damuxtuli usasrulo sibrtyis eleqtruli

velis daZabulobis wirebi si-brtyis marTobuli wrfeebia.

EE

E E

RR

+q

24

liTonis 1 sm3 moculobaSi 1022÷1023 Tavisufali eleqtronia. diele-qtrikSi _ 108÷1010. dieleqtrikSi gamtarebTan SedarebiT Tavisufali ele-qtronebis raode noba Zalian mcirea, amitom eleqtrul velSi dieleqtri-kis moTavsebisas Tavisu fali eleq tronebis gadaadgilebiT ga mo w ve uli efeqti imdenad sustadaa ga mo xatuli, rom SeiZleba ar gaviTvaliswinoT.

CavataroT cda: eleqtrometris Re roze dava magroT liTonis dis ko. davmuxtoT eleq trometri (sur. 24,1). eleqtrometris dis kos mivuax looT daumuxtavi dieleq tri ki, maga li Tad, polieTilenis boT li da davakvirdeT. SevamCnevT, eleq tro metris isari odnav daeSveba (sur. 24.2).

es faqti SeiZleba aixsnas im daSvebiT, rom eleqtrul velSi moTavsebuli dieleqtriki TviT qmnis iseT eleqtrul vels, romelic amcirebs isrisa da Reros muxts da, Sesabamisad, adidebs diskos muxts.

rogor qmnis eleqtrul vels daumuxtavi dieleq-triki?

am SekiTxvaze pasuxis gasacemad gavixsenoT atomebisa da mole kulebis eleqtruli Tvisebebi.

eleqtroni ≈10-9 wm-Si birTvis garSemo ≈milioni brunis Sesru lebas aswrebs. es imdenad didi siCqarea, rom eleqtroni wamis memiliarded nawilSi milionjer imyofeba or, nebismier, A da B wertilebSi, romlebic simetriulad aris ganlagebuli birTvis mimarT (sur. 24.3). SegviZlia CavTvaloT, rom saSualod (drois mixedviT) uaryofiTi muxtis ganawi-

1. eleqtrobis gamtarobis mixedviT, rogor arian dayofili nivTierebebi?

2. rogor nivTierebebs uwodeben gamtarebs? riT aris ganpirobebuli am nivTierebebis kargi eleqtrogamtaroba?

3. rogor nivTierebebs uwodeben dieleqtrikebs? riT aris ganpirobebuli am nivTierebebis cudi eleqtrogamtaroba?

4. rogor Seicvala isrisa da Reros eleqtruli muxti? axseniT, ratom fiqrobT ase?

5. rogor icvleba diskos eleqtruli muxti? axseniT, ratom fiqrobT ase?

6. risgan Sedgeba atomi? molekula?

7. ra aris gamosaxuli 24.3 suraTze?

B

A

e

e

sur. 24.3

1.7

sur. 24.1

++++ +++

+ +

–

+ +

–

+ +

–

+ +

–+ + + ++

sur. 24.2

dieleqtriki eleqtrostatikur velSi. ori saxis dieleqtriki


25

lebis centri atomis SuaSia, e. i. emTxveva dadebiTad damuxtul birTvs.iseTi atomebisa da molekulebisagan Sedgenil dieleqtriks, romelSic

dadebiTi da uaryofiTi muxtebis ganawilebis centrebi erTmaneTs emTxveva, arapolaruli dieleqtriki ewodeba.

arapolaruli dieleqtrikebia: inertuli airebi, wyalbadi, Jangbadi, polieTileni da sxva.

zogierT dieleqtrikSi (magaliTad: wyali, spirti da sxva) ase ar aris. ganvixiloT sufris marilis NaCl-is molekula.

NaCl-is molekulis warmoqmnisas natriumis erTaderT savalento eleqtrons miierTebs qlori. orive atomi gadaiqceva urTierTsapirispiro niSnis ionebis sistemad (sur. 25.1).

iseTi molekulebisagan Sedgenil dieleqtriks, ro-melSic dadebiTi da uaryofiTi muxtebis ganawilebaTa centrebi erTmaneTs ar emTxveva polaruli dieleqtriki ewodeba.

ori toli da sapirispiro niSnis muxtebis erTobliobas, romelTa Soris manZili gacilebiT naklebia im manZilTan SedarebiT, sadac mis moqmedebas ganvixilavT, eleqtruli dipoli ewodeba (sur. 25.2).

8. ramdeni savalento eleqtroni aqvs natriumis atoms gare SreSi? qloris atoms?

11. NaCl-is molekula SeiZleba Tu ara ganvixiloT eleqtrul dipolad? axseniT, ratom fiqrobT ase?

12. Tqveni azriT, NaCl-is molekula qmnis Tu ara eleqtrul vels? axseniT, ratom fiqrobT ase?

9. romel ionSia ganawilebuli dadebiTi muxti? uaryofiTi?

10. emTxveva Tu ara dadebiTi da uaryofiTi muxtebis ganawilebis centrebi erTmaneTs?

arapolaruli dieleqtriki, polaruli diele-

qtriki, eleqtruli dipoli

iseTi atomebisa da molekulebisagan Sedgenil dieleqtriks, romelSic dadebiTi da uaryofiTi muxtebis ganawilebis centrebi erTmaneTs emTxveva, arapolaruli dieleqtriki ewodeba.

iseTi molekulebisagan Sedgenil dieleqtriks, romelSic dadebiTi da uaryofiTi muxtebis ganawilebaTa centrebi erTmaneTs ar emTxveva polaruli dieleqtriki ewodeba.

+|q| –|q|

L

sur. 25.1

sur. 25.2

26

26.3 suraTze polaruli di-eleq triki erTgvarovan eleq trul velSi _ liTonis or pa ralelur fir fitas Sori saa moTav sebuli, fir fitebi sa pi ris piro niSnis mux-tiTaa damuxtuli. ele q truli veli Ti Toeul molekulaze _ eleq-trul dipo lze moqmedebs ise Ti ZaliT, rome lic qmnis Zalis mab-runebel moments, cdilobs dipoli Semoabrunos da misi RerZi daayenos velis Zalwirebis gaswvriv (sur. 26.2,a). amis gamo dadebiTi muxtebi wainacvlebs eleqtruli velis daZabulobis mimarTulebiT, uaryofiTebi ki _ sapirispiro mxares (sur. 26.2, b).

dieleqtrikis bmuli dadebiTi da uaryofiTi muxtebis sapirispiro mimarTulebiT wanacvlebas polarizacia ewodeba.

radgan molekulebis qaosuri siTburi moZraoba ewinaaRmdegeba dipolebis mowesrigebuli orientaciis Seqmnas, Zalwirebis gaswvriv ganlagdeba di polebis mxolod nawili. es imas niSnavs, rom saSualod velis gaswvriv ori entirebuli dipolebis raodenoba metia, vidre velis sapirispirod orientirebuli dipolebisa.

amgvarad, eleqtrul velSi dieleqtrikis zedapirze dadebiTad damuxtul firfitasTan upiratesad dipolTa uaryofiTi muxtebi ganlagdeba, uaryofiTad damuxtul firfitasTan ki _ dadebiTi. dieleq-trikis zedapirze Cndeba e. w. bmuli muxtebi (sur. 26.3). dieleqtrikis SigniT ki dipolTa dadebiTi da uaryofiTi muxtebis jami isev nuli rCeba.

dieleqtrikis zedapirze warmoqmnili bmuli muxtebi dieleqtrikis SigniT qmnis gare velis sapirispirod mimarTul eleqtrul vels, ris gamoc dieleqtrikSi veli sustdeba. bmuli muxtebis mier Seqmnili velis Zalwirebi 26.4 suraTze punqtiriTaa gamosaxuli. superpoziciis principis Tanaxmad, jamuri veli dieleqtrikis SigniT ufro sustia, vidre gare eleqtruli veli (sur. 26.5). Tu ramdenad Sesustdeba veli, damokidebulia dieleqtrikis Tvisebebze.

dieleqtrikis eleqtrul Tvisebebs axasiaTeben fizikuri sididiT _ dieleqtri-kuli SeRwevadobiT.

dieleqtrikis polarizacia. dieleqtrikuli SeRwevadoba

1.8

1. qmnis Tu ara eleqtrul vels dieleq-

trikis SigniT eleq truli dipolebi (sur. 26.1)? axseniT, ratom fiqrobT ase?

2. ra moxdeba, Tu eleqtrul dipols eleqtrul velSi movaTavsebT (sur. 26.2)?

sur. 26.1. siTburi moZraobis gamo dieleqtrikSi molekulebi – eleqtruli dipolebi – uwes-rigodaa ganlage-buli.

sur. 26.4 sur. 26.5

sur. 26.2a b

sur. 26.3

E


27

garemos dieleqtrikuli SeRwevadoba fizikuri sididea, romelic gviCvenebs, ramdenjer naklebia eleqtruli velis E daZabulobis moduli erTgvarovan dieleqtrikSi imave Tavisufali muxtebis mier Seqmnili velis E0

daZabulobis modulze vakuumSi.dieleqtrikuli SeRwevadoba aRvniSnoT e-iT: .

EE0=f formula

marTebulia mxolod erTgvarovani velisaTvis, sadac E0 aris eleqtruli velis daZabuloba vakuumSi, E _ dieleqtrikSi. vakuumic dieleqtrikia. vakuumis dieleqtrikuli SeRwevadoba miRebulia 1-is tolad. zogierTi nivTierebis dieleqtrikuli SeRwevadoba mocemulia cxrilSi 137-e gv-ze.

e dieleqtrikuli SeRwevadobis erTgvarovan garemoSi wertilovani muxtis da gamtari damuxtuli sferos mier Seqmnili velis daZabuloba

centridan r manZilze ganisazRvreba E kr

q2f

= formuliT. roca sferos centridan r manZili naklebia sferos R radiusze, maSin E=0. damuxtuli gamtaris sferos SigniT eleqtruli veli ar arsebobs. damuxtuli gamtari

sibrtyis mier Seqmnili velis daZabuloba ganisazRvreba E k 2$= fr v

formuliT.

damuxtul sxeulTa urTierTqmedebis Zala damokidebulia am sxeulTa Soris arsebuli garemos Tvisebebze. damuxtul sxeulTa urTierTqmedebis Zala dieleqtrikSi naklebia, vidre vakuumSi.

erTgvarovan dieleqtrikSi moTavsebuli muxtebisaTvis kulonis kanoni

ase Caiwereba: .F kr

q q2

1 2$

f=

5. Tqveni varaudiT, mniSvnelovania Tu ara haeris gavlena muxtebis urTierTqmedebis Zalaze? axseniT,

ratom fiqrobT ase?6. aris Tu ara msoflio mizidulobis Zala damokidebuli im garemos

Tvisebebze, romelSic urTierTmimzidavi sxeulebia moTavsebuli? 7. ra msgavseba da gansxvavebaa msoflio mizidulobis

kanonsa da kulonis kanons Soris?

3. Tqveni varaudiT, rogor Seicvleba dieleqtrikSi moTavsebuli wertilovani muxtis da gamtari damux tuli

sferos mier Seqmnili velis daZabuloba? axseniT, ratom fiqrobT ase?

4. rogor Seicvleba ori wertilovani damuxtuli sxeulis urTierTqmedebis Zala dieleqtrikSi? pasuxi

daasabuTeT.

dieleqtrikis polarizacia, dieleqtrikuli

SeRwevadoba

dieleqtrikis bmuli dadebiTi da uaryofiTi muxtebis sapirispiro mimarTulebiT wanacvlebas polarizacia ewodeba.

garemos dieleqtrikuli SeRwevadoba aris fizikuri sidide, romelic gviCvenebs, ramdenjer naklebia eleqtruli velis E daZabulobis moduli erTgvarovan dieleqtrikSi imave Tavisufali muxtebis mier Seqmnili velis E0

daZabulobis modulze vakuumSi.

28

aqvs energia eleqtrul velSi moTavsebul damuxtul sxeuls? sakiTxi gadavwyvitoT wina wlebSi miRebuli codnisa da logikuri

msjelobis gamoyenebiT.

I. nulovani donidan aTvlili h1 simaRlidan h2 simaR-lemde gadasvlisas (sur. 28.1) m masis sxeulze moqmedi simZimis Zalis muSaoba udris potenciuri energiis cvlilebas mopirdapire niSniT, e. i.

A=–(mgh2–mgh1)=–(Epot2–E

pot1), (1)

sadac Epot2

=mgh2, Epot1

=mgh1, Sesabamisad, saboloo da sawyis mdeba reobaSi sxeulis potenciuri energiebia.

II. wirs, romelsac sxeulis romelime wertili Semowers, am wertilis moZraobis traeqtoria ewodeba.

3. I da II winadadebebis gamoyenebiT upasuxeT:M wertilidan N wertilSi sxeulis nebismieri

traeqtoriiT Camotanisas simZimis Zalis muSaobaa. dadebiTia da traeqtoriis sigrZis pirdapirproporciulia;b. dadebiTia da traeqtoriis formaze ar aris damokidebuli;g. uaryofiTia da traeqtoriis sigrZis pirdapirproporciulia;d. uaryofiTia da traeqtoriis formaze ar aris damokidebuli.

4. I da II winadadebebis gamoyenebiT upasuxeT:

N wertilidan M wertilSi sxeulis nebismieri traeqtoriiT atanisas simZimis Zalis muSaoba

a. dadebiTia da traeqtoriis sigrZis pirdapirproporciulia;b. dadebiTia da traeqtoriis formaze ar aris damokidebuli;g. uaryofiTia da traeqtoriis sigrZis pirdapirproporciulia;d. uaryofiTia da traeqtoriis formaze ar aris damokidebuli.

5. I da II winadadebebis gamoyenebiT upasuxeT:

Tu sxeuli raime wertilidan moZraobisas h simaRleze nebismieri traeqtoriiT adis da Semdeg imave doneze brundeba,

maSin simZimis Zalis muSaobaa

a. nuli; b. 2mgh; g. –2mgh; d. mgh; e. –mgh.

1. ra SemTxvevaSi aqvs sxeulTa sistemas energia?

2. aqvs Tu ara energia dedamiwis zedapiridan aweul sxeuls? rogori energia? pasuxis marTebuloba ganamtkiceT msjelobiT.

1.9 damuxtuli sxeulis potenciuri energia erTgvarovan eleqtrostatikur velSi

sur. 28.1

h2

h1

∆h

N

M


29

vTqvaT, q wertilovani muxti moTavse-bulia erTgvarovani eleqtruli velis M wertilSi. ganvsazRvroT muSaoba, romelsac asrulebs eleqtruli veli M wertilidan imave Zalwirze mdebare N wertilSi q muxtis gadaadgilebisas. M wertili uaryofiTad damuxtuli firfi-tidan d1 manZilzea, N wertili ki _ d2-ze (sur. 29.1).

A=F(d1–d2), (2)sadac F _ eleqtrul velSi q muxtze moqmedi Zalis modulia.

F=qE, (3)sadac E aris firfitebs Soris eleqtruli velis daZabulobis moduli.

(3) (2) ⇒ A=qE(d1–d2)=–(qEd2–qEd1)=qE∆d, (4) sadac ∆d=d1–d2.vnaxoT, eleqtruli velis mier muxtis gadaadgilebisas Sesrulebuli

muSaoba damokidebulia Tu ara traeqtoriis formaze. ganvsazRvroT M wertilidan N-Si muxtis gadaadgilebisas Sesrulebuli muSaoba nebismieri mrudis gaswvriv. muSaobis gansazRvrisas traeqtoria SeiZleba SevcvaloT

mcire safexurebis mqone texili wirebiT (sur. 29.2). im safexurebis

gaswvriv moZraobisas, romlebic marTobia E daZabulobisa, eleqtruli

veli muSaobas ar asrulebs. E-s paralelur safe xurebze horizontaluri

monakveTebis sigrZeTa jami aris ∆d=d1–d2, amitom Sesrulebuli muSaoba ganisazRvreba (4) formuliT.

miviReT: eleqtruli velis erTi wertilidan meoreSi muxtis gadaad-gilebisas Sesrulebuli muSaoba damokidebuli ar aris traeqtoriis formaze da ganisazRvreba A=qE∆d formuliT.

(1)-is analogiurad SegviZlia davaskvnaT: Tu muSaoba damokidebuli ar aris sxeulis traeqtoriis formaze, maSin is tolia sxeulis potenciuri energiis cvlilebisa sapirispiro niSniT:

(4) ⇒ A=–(Epot2–E

pot1), (5)

sadac Epot1

=qEd1 da Epot2

=qEd2 muxtis velTan urTierTqmedebis potenciuri energiebia sawyis da saboloo mdebareobaSi, d1 da d2 _ manZilebi aTvlili potenciuri energiis nulovani donidan. potenciuri energiis nulovani done, rogorc mizidulobis ZalTa SemTxvevaSia, nebismierad SeirCeva. (5) formula marTebulia nebismieri eleqtrostatikuri velisaTvis. kerZo SemTxvevaSi, roca veli erTgvarovania, potenciuri energia gamoisaxeba Epot

=qEd (6) formuliT, sadac d aris potenciuri energiis nulovani donidan aTvlili manZili.

SeiZleba gamovitanoT daskvna: eleqtrostatikur velSi muxtis velTan urTierTqmedebis potenciuri energia damokidebulia rogorc

eleqtrul velze, aseve muxtze da nulovani donidan aTvlil manZilze.

6. Tqveni varaudiT, rogor icvleba damuxtuli sxeulis potenciuri energia, rodesac veli dadebiT

muSaobas asrulebs? kinetikuri energia? pasuxi daasabuTeT.

–

B

MN

d1

d2d2

+ +–

D B D

MN

sur. 29.1 sur. 29.2

30

9. rogori velia gravitaciuli? eleqtro-

statikuri? axseniT, ratom fiqrobT ase?

7. Tqveni varaudiT, rogor icvleba damuxtuli sxeulis potenciuri energia, rodesac veli uaryofiT

muSaobas asrulebs? kinetikuri energia? pasuxi daasabuTeT.

8. gansazRvreT velis muSaoba Caketil traeqtoriaze, roca muxti sawyis wertilSi brundeba.

vels, romelSic nebismier Caketil traeqtoriaze Sesrulebuli muSaoba nulis tolia, potenciuri (konservatiuli) veli ewodeba.

saSinao cda

cdis mizaniL: damuxtuli sxeulisa da wylis Wavlis urTierT-qmedebaze dakvirveba.

onkanidan sust nakadad gamouSviT wyali. polieTilenis mSrali boTli sxvadasxva mxridan miuaxloeT wylis nakads da daakvirdiT. Semdeg boTls ramdenjerme swrafad gausviT mSrali xeli an qaRaldi da cdebi gaimeoreT. ras amCnevT? SemCneuli movlena CawereT samuSao rveulSi da SeecadeT axsnaT.

eleqtruli velis muSaoba, muxtis velTan

urTierTqmedebis potenciuri energia, potenciuri

veli

eleqtruli velis erTi wertilidan meoreSi muxtis gadaad-gilebisas Sesrulebuli muSaoba damokidebuli ar aris traeqtoriis formaze da ganisazRvreba A=qE∆d formuliT.

eleqtrostatikur velSi muxtis velTan urTierTqmedebis potenciuri energia damokidebulia rogorc eleqtrul velze, aseve muxtze da nulovani donidan aTvlil manZilze.

vels, romelSic nebismier Caketil traeqtoriaze Sesrulebuli muSaoba nulis tolia, potenciuri (konservatiuli) veli ewodeba.

31

erT gvarovan eleqtrul velSi moTavsebuli wertilovani muxtis vel-

Tan urTierTqmedebis potenciuri energiis Epot

=qEd (1) formulidan

gamomdi nareobs

.E qEd qE

Edpotpot

&= = (2)

(2) ⇒ muxtis velTan urTierTqmedebis potenciuri energiis Sefardeba am muxtTan damokidebuli ar aris velSi moTavsebul muxtze. igi velis mocemul wertilSi moTavsebuli nebismieri muxtisaTvis erTi da igivea, amitom es fardoba SeiZleba eleqtrostatikuri velis raodenobriv maxasiaTeblad miviCnioT _ es samarTliania araerTgvarovani velisTvisac.

vuwodoT mas eleqtrostatikuri velis potenciali da aRvniSnoT ϕ-Ti.

.qEpot

={ (3) (3) ⇒ Epot

=qϕ. (4)

eleqtrostatikuri velis potenciali ewodeba velSi moTavsebuli werti lovani muxtis velTan urTierTqmedebis potenciuri energiis Sefardebas am mux tTan. sxva sityvebiT, potenciali ricxobrivad tolia erTeuli muxtis ener giisa velSi.

praqtikuli mniSvneloba aqvs ara TviT potencials wertilSi, aramed or wertils Soris potencialTa sxvaobas, romelic damokidebuli ar aris nulovani donis arCevaze.

eleqtruli velis erTi wertilidan meoreSi muxtis gadaadgilebisas eleqtruli velis mier Sesrulebuli muSaoba

A=–(Epot2

–Epot1

)=–(qEd2–qEd1). (5)Tu gaviTvaliswinebT, rom Ed2=ϕ2 da Ed1=ϕ1, miviRebT:

A=–q(ϕ2–ϕ1)=–q∆ϕ=q(ϕ1–ϕ2), (6)

sadac ∆ϕ=(ϕ2–ϕ1) aris traeqtoriis bolo da sawyisi wertilebis poten-cialis mniSvnelobebis sxvaoba _ potencialis cvlileba. mis nacvlad gamoviyenoT traeqtoriis sawyisi da bolo wertilebis potencialis mniSvnelobaTa sxvaoba _ potencialTa sxvaoba. mas Zabva ewodeba. aRvniSnoT igi U-Ti.

U=ϕ1–ϕ2= qA (7) (7)⇒ A=qU. (8)

eleqtrostatikuri velis potenciali da potencialTa sxvaoba

1.10

2. romel fizikur sidideebzea damokidebuli eleqtros tatikur velSi muxtis velTan urTierT-

qmedebis potenciuri energiis Sefardeba muxtTan? axseniT, ratom fiqrobT ase?

3. rogor fiqrobT, velis mocemul wertilSi moTavsebuli nebismieri muxtisTvis erTi da igivea Tu ara muxtis velTan urTierTqmedebis potenciuri energiis Sefardeba am muxtTan?

1. daasaxeleT fizikuri sidideebi, romelzec damokidebulia eleqtrostatikur velSi moTavsebuli

muxtis velTan urTier Tqme debis potenciuri energia.


32

or wertils Soris Zabva tolia erTi wertilidan meoreSi muxtis gadaadgilebisas velis mier Sesrulebuli muSaobis fardobisa am muxtTan. Zabvis codna saSualebas gvaZlevs nebismieri eleqtruli wredisaTvis ganvsazRvroT muSaoba, romelsac Seasrulebs eleqtruli veli rozetis erTi kontaqtidan meoreSi erTeuli muxtis gadatanisas.

davadginoT SI-Si Zabvis erTeuli.davuSvaT, q=1 k, A=1 j, maSin (7) ⇒ or wertils Soris potencialTa

sxvaoba (Zabva) tolia erTeulisa, Tu 1 k muxtis gadatanisas erTi wertilidan meoreSi eleqtruli veli asrulebs 1 j muSaobas. am erTe-

uls volti (1 v) ewodeba.

1v1k1j

.=

vTqvaT, E daZabulobis erTgvarovan eleqtrul velSi Zalwirebis gaswvriv A-dan B wertilSi gadaadgilda q muxti ∆d manZilze (sur. 32.1) am dros eleqtruli velis muSaoba SeiZleba ganvsazRvroT formulebiT: A=qE∆d, (9) A=q(ϕ1–ϕ2), (10)

sadac ϕ1 da ϕ2, Sesabamisad, A da B wertilebis

potencialebia.

(9)∧(10) ⇒ qE∆d=q(ϕ1-ϕ2) ⇒ .E

d dU1 2

D{ {

D=

-= (11)

(11) ⇒ rac ufro naklebad icvleba velis potenciali ∆d manZilze,

miT naklebia eleqtrostatikuri velis daZabuloba.

SeiZleba davaskvnaT: eleqtruli velis daZabuloba mimarTulia

potencialis Semcirebis mimarTulebiT.

Tu eleqtrul velSi moTavsebuli

Tavi sufali eleqtronis sawyisi siCqare nulia, maSin velis moqmedebiT igi iwyebs aCqarebul moZraobas, amitom misi siCqare, e.i. kinetikuri energia, izrdeba.

energia, romelsac eleqtroni SeiZens eleqtrul velSi moZraobisas, rodesac gadava erTi wertilidan meoreSi, romlis potenciali 1v-iT ufro maRalia, cnobilia 1 eleqtronvoltis (1ev) saxelwodebiT.

ganvsazRvroT, ramdeni joulia 1 ev. eleqtronis mier SeZenili kinetikuri energia eleqtruli velis mier

Sesrulebuli muSaobis tolia A=eU. (12)

4. dadebiTia Tu uaryofiTi eleqtruli velis muSaoba E daZabulobis mimarTulebiT dadebiTi muxtis gadaadgilebisas? axseniT, ratom fiqrobT ase?

5. A=q(ϕ1–ϕ2) formulidan gamoitaneT daskvna, romelia meti ϕ1 Tu ϕ2?

6. 32.2 suraTze A wertilis potencialia meti Tu B wertilis; axseniT, ratom fiqrobT ase?

EBA ∆d

sur. 32.1

+QR

A B+q

rsur. 32.2

r2

r1

33

potenciali, potencialTa sxvaoba, volti,

eleqtronvolti

eleqtrostatikuri velis potenciali ewodeba velSi moTavsebuli muxtis potenciuri energiis Sefardebas am muxtTan. sxva sityvebiT, potenciali ricxobrivad tolia erTeuli muxtis energiisa velSi.

or wertils Soris Zabva tolia erTi wertilidan meoreSi muxtis gadaadgilebisas velis mier Sesrulebuli muSaobis fardobisa am muxtTan. or wertils Soris potencialTa sxvaoba (Zabva) tolia erTeulisa, Tu 1 k muxtis gadatanisas erTi wertilidan meoreSi eleqtruli veli asrulebs 1 j muSaobas. am erTeuls volti (v) ewodeba. eleqtruli velis daZabuloba mimarTulia potencialis Semcirebis mimarTulebiT. 1 eleqtronvolti aris energia, romelsac SeiZens eleqtroni eleqtrul velSi moZraobisas, rodesac gadava erTi wertilidan meoreSi, romlis potenciali 1v-iT ufro maRalia.

sadac e=-1,6.10-19 k eleqtronis muxtia, U = –1v.

(12): 1 ev = 1,6.10-19 j.

muxtebis urTierTqmedebis potenci uri energia im muSaobis tolia, ro mel sac Seasrulebs maTi ur Ti erT qme debis eleqtruli Zala muxtebis us as ru lod daSorebisas, e. i. iseT man Zilze daSorebisas, rodesac maTi urTi erTqmedebis Za lis moduli, praqtikulad, nuls utoldeba.

Tu CavTvliT, rom aseT manZilze muxtebis urTierTqmedebis potenciuri energia nulis tolia, maSin R manZiliT daSorebuli Q da q wertilovani

muxtebis urTierTqmedebis potenciuri energia ganisazRvreba E kRQq

pot.=

(13) formuliT.

e dieleqtrikuli SeRwevadobis erTgvarovani garemosaTvis

.E kR

Qqpot= f

(14)

vTqvaT, veli Seqmnilia Q wertilovani muxtiT. am muxtis velSi

misgan R manZiliT daSorebul wertilSi movaTavsoT q muxti, maSin am

wertilSi potenciali .qE

kRQpot

&{ {= = (15) (13) (14) .qE

kRQpot

&{ {= = (16)

erTgvarovan dieleqtrikSi .kRQ

={f

(17)

Tu velis Semqmneli muxti uaryofiTia, am velis nebismier wertilSi

potenciali uaryofiTi iqneba.

vTqvaT, veli Seqmnilia ramdenime q1, q2, ..., qn muxtiT. superpoziciis principis Tanaxmad, nebismier wertilSi velis potenciali ganisazRvreba TiToeuli muxtis velis ϕ1, ϕ2, ..., ϕn potencialTa algebruli jamiT:

ϕ=ϕ1+ϕ2+ ... +ϕn. (18)

7. rogor urTierTqmedebs 32.2 suraTze gamosaxuli R manZiliT daSorebuli ori Q da q dadebiTi wertilovani muxtebi erTmaneTze?

8. aqvT Tu ara Q da q muxtebs urTierTqmedebis potenciuri energia? axseniT, ratom fiqrobT ase.

34

ekvipotenciuri zedapirebi. potencialTa sxvaobis gazomva

1.11

1. eleqtruli velis rogori maxasiaTebelia daZabuloba? axseniT, ratom fiqrobT ase?

2. eleqtruli velis rogori maxasiaTebelia potenciali? axseniT, ratom fiqrobT ase?

zedapirs, romlis yovel wertils toli potenciali aqvs, ekvipotenciuri zedapiri ewodeba.

I. eleqtrul velSi muxtze moqmedi Za la yovelTvis daZabulobis veqtoris parale-luria.

II. sxeulis gadaadgilebis marTobulad moqmedi Zala muSaobas ar asrulebs.

am ori winadadebidan gamomdinareobs:daZabulobis wirebis marTobulad muxtis

gadaad gilebisas eleqtruli veli muSaobas ar asrulebs.

ekvipotenciur zedapirze muxtis gadaadgilebisas eleqtruli veli muSaobas ar asrulebs.

aqedan ki SeiZleba davaskvnaT, romdaZabulobis wirebi ekvipotenciuri zedapirebis marTobia.34.1 suraTze uwyveti xazebiT gamosaxulia eleqt ruli velis Zalwirebi

da punqtiriT ekvipotenciuri zedapirebi.

Zalwirebis msgavsad ekvipotenciuri zedapirebi Tvisebrivad axasiaTebs velis ganawilebas sivrceSi.

3. gansazRvreT ekvipotenciuri zedapiris or wertils Soris potencialTa sxvaoba.

4. gansazRvreT ekvipotenciur zedapirze muxtis gadaadgilebisas eleqtruli velis mier Sesrulebuli muSaoba.

E

ϕ3

ϕ2

ϕ1sur. 34.1

5. ra aris gamo saxuli 34.2 suraTze?

6. daxazeT werti lovani mux-tis mier Seqmnili eleqtruli ve-lis ekvipotenciuri zedapirebis ganawilebis savaraudo suraTi.

7. ra aris gamosaxuli 34.3 suraT ze? pasuxis marTebuloba daasabuTeT.

sur. 34.2

q

sur. 34.3


35

damuxtuli gamtaris yvela wertils erTi da igive potenciali aqvs.

or gamtars Soris potencialTa sxvaoba SeiZleba gavzomoT eleq tro-metriT. amisaTvis erTi sxeuli gam-tariT SevaerToT eleqtrometris Re-rosTan, meore ki _ korpusTan (sur. 35.2).

eleqtrometris Reros erTi sxeulis potenciali eqneba, korpuss _ meore sxeu lis. Rerosa da korpuss Soris Seiqmneba ele q truli veli. eleqtrometris isari gada ixreba. roca xelsawyo dagraduirebulia, isris gadaxris kuTxis mixedviT gavzomavT sxeulebs Soris potencialTa sxvaobas.

dedamiwis mimarT sxeulis potencialis gasazomad Rero sxeulTan SevaerToT, korpusi ki _ davamiwoT.

8. SeadareT eleqtrosta-tikur velSi mo Tav sebu-

li gamtarebis A, B da C wertilebis potencialebi erTmaneTs (sur. 35.1). axseniT, ratom fiqrobT ase?

9. romeli sxeulis potenciali eqneba Reros? korpuss? axseniT, ratom fiqrobT ase?

10. 35.3 suraTis mixedviT imsje leT, rogor xdeba damuxtuli gamtari sxeulis zedapiris potencialis gamok vleva.

sur. 35.1

AA

B BC C

ab

E

daZabulobis wirebi, ekvipotenciuri zedapiri

zedapirs, romlis yovel wertils toli potenciali aqvs ekvipotenciuri zedapiri ewodeba.

sur. 35.3. damuxtuli gamtaris zeda-

piris potencialis gamokvleva.

izolatori

liTonis burTula

sur. 35.2

36

amocanis amoxsnis nimuSi1.12

1. liTonis ori erTnairi patara burTula damuxtulia, Sesabamisad,

–3,2 mkk da q2=9,6 mkk muxtebiT. burTulebi erTmaneTs Seaxes da daaSores

1 m-iT. gansazRvreT burTulebis urTierTqmedebis Zala.

amoxsna

burTulebis urTierTqmedebis Za-

lis moduli F kR

q q2

3 4= , (1) sadac

k 9 10knm9

2

2

$= , q3 da q4 burTulebis

muxtebia Sexebis Semdeg.

orive burTulis saerTo Q muxti Q=q1+q2. (2)muxtis Senaxvis kanonis Tanaxmad, orive burTulis saerTo muxti ar

icvleba. amitom, radgan burTulebi erTnairia, saerTo muxti maTze

Tanabrad ganawildeba da TiToeulze iqneba q3=q4=Q2

. (3)

(2) (3) ⇒ .q qq q23 4

1 2= =+ (4) (4) (1) ⇒ .F k

R

q q

4 21 2

2

=+ (*)

(*): F ≈ 92,2.10-3 n.radgan burTulebs erTnairi niSnis muxti eqnebaT, amitom isini

erTmaneTs ganizidavs.

2. 30 sm-iT daSorebul A da B wertilebSi damag rebulia q1=10 nk da q2=20 nk werti-lovani muxtebi. gansazRvreT eleqtruli velis daZabu loba A da B wertilebis SemaerTebeli wrfis C da D wertilebSi, romlebic 10 sm-iT arian da-Sorebuli A wertilidan (sur. 36.1).

amoxsna

eleqtruli velis daZabuloba C wertilSi ,E E Ec 1 2= + (1)sadac E1

da E2 aris q1 da

q2 muxtebis mier C wertilSi Seqmnili ve lis daZabulobebi (sur. 36.2). radgan E1

da E2 erTi wrfis

gaswvriv urTier Tsapirispirodaa

mimarTuli, ami tom maTi tolqmedis moduli Ec=|E2–E1|. (2) tolqmedi

mimarTulia E1 da E2-dan udidesisaken.

E kAC

q1 2

1=^ h

, (3) .E kAB AC

q2 2

2=-^ h

, (4)

D

A

Cq1

sur. 36.1

B

q2

D A

Cq1

sur. 36.2q2

B


Fv

37

(3)∧(4) (2) ⇒ .E kAB AC

q

AC

qc 2

22

1=-

-^ ^h h

(*) (*): Ec=4500 v/m.

D wertilSi eleqtruli velis daZabuloba ,E E ED 1 2= +l l (5) sadac E 1l da

E 2l aris q1 da q2 muxtebis mier D wertilSi Seqmnili velis daZabulobebi,

romlebsac erTnairi mimarTuleba aqvs (sur. 36.2). ED veqtorsac iseTive

mimarTuleba aqvs da misi moduli E E ED 1 2= +l l . (6)

,E kAD

q1 2

1=l] g

(7) .E kAB AD

q2 2

2=+

l^ h

(8)

(7)∧(8) (6) ⇒ .E kAD

q

AB AD

qD 2

12

2= ++] ^

eg h

o (**)

(**): ED=10125 v/m.

3. 0,4g masis ori erTnairi burTula Camokidebulia erT wertilSi damagrebul 1m sigrZis Zafebze. damuxtvis Semdeg burTulebi erTmaneTs daSorda 9 sm-iT. gansazRvreT TiToeuli burTulis muxti da Zafis daWimulobis Zala.

amoxsna

erT-erT burTulaze moqmedi mg simZimis, Q Zafis daWimulobis da F eleqtruli Zalebi gamosaxulia 37.1 suraTze.

radgan burTulebi wonasworobaSia, masze

moq medi Zalebis jami nulis tolia, e.i.

.g gm Q F m F Q0 &+ + = + =- (1)

es imas niSnavs, rom simZimisa da eleqtruli

Zalebis jami moduliT tolia Tokis daWimulobis

Zalisa da mis sapirispirodaa mimarTuli

.Q Q/- l (2)

suraTze gamosaxuli `ZalTa~ samkuTxedidan

F=Q′sinα. (3) mg=Q′cosα. (4) (3)∧(4) ⇒ mF tg g= a. (5)

kuTxe α mcirea, amitom g sintl

R

lR22

a a. = = . (6)

(6) (5) ⇒ .mF

lR2g = (7)

kulonis kanonis Tanaxmad, .F kR

q2

2

= (8)

(8) (7) ⇒ .g

qkl

m R2

3

= (*)

radgan Q=Q′, amitom (4) ⇒ .g

cos sinQ

mQ

m

1

g2

&a

= =-a

(9)

(6) (9) ⇒ .g gl

Q

lR

mQ

l R

m

14

4

2

2

2 2 2&=

-

=-

(**)

(*): q=10–8 k. (**): Q=4.10–3 n.

F

Q

mg .Q Q/- l

l

B

A

C

R

α

αsur. 37.1

38

eleqtrotevadoba. brtyeli kondensatori

1.13

davmuxtoT ganmxoloebuli gamtari (sur. 38.1).

Tu gamtaris muxts orjer gavzrdiT, maSin àxali~ muxti mis zedapirze iseve ganawildeba, rogorc pirvelad miniWebuli muxti da gamtaris

TiToeul wertilSi muxtis zedapiruli simkvrive orjer gaizrdeba. Tu

ganmxoloebul gamtars sferos forma aqvs, maSin kRq

={ (3) formulidan

gamomdinareobs, rom misi potencialic orjer gaizrdeba.

ganmxoloebuli gamtaris q muxtis Sefardeba mis ϕ potencialTan

mudmivi sididea da mas gamtaris eleqtrotevadoba ewodeba .Cq

= { (4)

igi damokidebulia gamtaris formasa da zomaze.

(4) ⇒ SI-Si eleqtrotevadobis erTeulad miRebulia iseTi ganmxo-loebuli gamtaris eleqtrotevadoba, romlis potenciali icvleba erTi voltiT misi muxtis erTi kuloniT Secvlis Sedegad. am erTeuls 1 faradi (1 f) hqvia.

1f 1 vk.=

(3) (4) ⇒ ,CkR= , (5) sadac R sferos radiusia.

(5) ⇒ eleqtrotevadoba damokidebulia sxeulis zomebze.(5) ⇒ R=kC. (6)

Tu Tqven sworad SeasruleT moqmedeba, miiRebT R=9.109 m.gavarkvioT, Seicvleba Tu ara gamtaris A eleqtro tevadoba, Tu mas

meore, daumuxtav B gamtars mivuaxloebT (sur. 39.1)?

1. Tqveni azriT, ramdenad srulyofilad iqneba eleqtruli velis energia gamoyenebuli, Tu ar

gvecodineba misi dagrovebis da Senaxvis wesi? axseniT, ratom fiqrobT ase?

3. rogor fiqrobT, Seicvleba Tu ara am dros gamtaris muxtis Sefardeba mis potencialTan? axseniT, ratom

fiqrobT ase.

4. gansazRvreT im ganmxoloebuli gamtari sferos radiusi, romlis eleqtrotevadoba 1 faradia.

2. rogor nawildeba muxti gamtaris zedapirze?

sad aris muxtis zedapiruli simkvrive udidesi? umciresi?

ganmxoloe-buli _ sxva

sxe ulebisagan daSorebuli.sur. 38.1


39

dadebiTad damuxtul A gamtars mivuaxlooT daumux tavi B gamtari (sur. 39.1). B gamtari daimuxteba gavleniT. B gamtarze A-s maxloblad dag rovdeba uaryofiTi muxti, daSorebul mxareze _ dadebiTi (sur. 39.2). induqcirebuli muxtebi qmnis damatebiT eleqtrul vels, romelic moqmedebs A gamtarze.

superpoziciis principis gamoyenebiT davadgenT, dama tebiTi velis moqmedebiT Semcirdeba A gamtaris potenciali, magram ar Seicvleba misi muxti.

.Cq

= { formulis gamoyenebiT SeiZleba

davaskvnaT: A gamtaris eleqtrotevadoba gaizarda masTan B gamtaris miaxloebisas. am movleniT SeiZleba visargebloT iseTi xelsawyoebis dasamzadeblad, romlebsac didi eleqtrotevadoba aqvT. aseT xelsawyoebze SedarebiT dabali Zabvis dros didi muxtis dagrovebaa SesaZlebeli.

mowyobiloba, romelsac iyeneben eleqtruli muxtisa da eleqtruli energiis dasagroveblad, cnobilia konden-satoris saxelwodebiT.

umartivesi kondensa tori aris ori gamtaris erTob lioba, rom lebic erTma-neTisagan gamoyo filia dieleq trikis Tx-eli fe niT. fenis sisqe gaci lebiT nak lebia gamtarebis zo mebze.

gamtarebs kondensatoris Semona fe nebi ewodeba. Tu Semonafenebi erTma neTis para-leluri brtyeli fir fitebia, maSin kon-densatori brtyelia.

kondensators muxtaven _ mis Semo nafenebs aniWeben moduliT tol da sapirispiro niSnis muxtebs. ami saT vis kondensatoris erT Semo nafens aerTeben denis wyaros da debiT po lusTan, meores _ uaryo fiTTan (sur. 39.3).

39.4 suraTze kondensatori sqe ma turadaa gamosa xuli.kondensatoris erT-erTi Semonafenis muxtis moduls konden-

satoris muxti ewodeba. kondensatoris firfitebs Soris eleqtruli velis daZabulobis wirebi erTmaneTis paraleluria da erTmaneTisagan toli manZilebiTaa daSorebuli (sur. 39.3).

++

+ + +++

++++

+

sur. 39.1

B A

+++

++

+ + ––––––

++ + +

++

++++

+

sur. 39.2

B A

sur. 39.4

sur. 39.3

+ –

5. rogor fiqrobT, SegviZlia Tu ara davamzadoT iseTi sfero, romlis eleqtrotevadoba 1 faradi iqneba?

axseniT, ratom fiqrobT ase?6. rogori warmodgena SegeqmnaT 1 f tevadobaze? didia Tu mcire

tevadobis es erTeuli?

40

Tu kondensatoris erT Semonafens Se-vuer TebT eleqtrometris Reros, meore Semonafens _ korpuss (sur. 40.1) da kondensators davmuxtavT, maSin eleqtro-metri gviCvenebs firfitebs Soris Zabvas.

Tu kondensatoris Semonafenebze muxts gavadi debT orjer, samjer da a. S. maSin Semonafenebs Soris Zabva izrdeba orjer, samjer da a. S.

kondensatoris muxtis Sefardeba Semonafenebs Soris ZabvasTan axasiaTebs kondensatoris mier muxtis dagrovebis unars da mas eleqtrotevadobas uwodeben. im kondensatoris eleqtrotevadobaa meti, romlis Semonafenebze ufro naklebi U Zabva miiReba +|q| da –|q| muxtebis gadacemisas.

kondensatoris eleqtrotevadoba ewodeba kondensatoris muxtis Sefar debas Semonafenebs Soris ZabvasTan:

.CUq

= (1)

davadginoT, raze aris damokidebuli brtye li kondensatoris eleqtro teva-doba. Cava taroT cda. gamoviyenoT 40.2 suraTze gamosaxuli danadgari. damux tuli kondensatoris Semonafenebs So ris manZili gavadidoT orjer, samjer da davakvirdeT eleqtrometrs. SevniSnavT, misi Cveneba gaizrdeba orjer, samjer.

kondensatoris muxtisa da Semonafenebs Soris man Zilis Seucvlelad SevamciroT Semonafenebis urTierT gadamfaravi farTobi (sur. 40.3). eleqtrometris Cveneba gaizrdeba.

3. rogor icvleba kon-densatoris eleq tro te-va doba Semona fe nebs So-

ris manZilis gadidebiT? axseniT, ratom fiqrobT ase?

sur. 40.3

2. Tqveni varaudiT, Semonafenis muxtis Sefardeba Semonafenebs Soris ZabvasTan aris Tu ara damokidebuli

Semonafenis muxtze? axseniT, ratom fiqrobT ase?

sur. 40.2

1. rogori velia kondensa-toris Semo nafe nebs Soris

(sur. 40.1)? axseniT, ratom fiqrobT ase?

sur. 40.1

brtyeli kondensatoris eleqtrotevadoba


41

4. rogor icvleba kondensatoris eleqtrotevadoba Semonafenebis urTierTgadamfaravi farTobis Semci-

rebiT? axseniT, ratom fiqrobT ase?

kondensatoris Semonafenebs Soris CavdgaT dieleq trikis firfita, magaliTad, organuli mina. davinaxavT, rom Zabva mcirdeba (sur. 41.1).

cdebis monacemebis gaanalizebiT SeiZleba davadginoT, rom brtyeli kondensatoris eleqtrotevadoba pirdapirpro porciulia misi firfitebis farTobis, dieleqtrikuli SeRwevadobis da ukuproporciulia firfitebs Soris manZilisa.

.CdS0ff

= . (2)

kondensatoris eleqtrotevadoba ar aris damokidebuli gamtarTa masalaze.

es imas niSnavs, rom erTnair pirobebSi spilenZisa da aluminis kondensa-torebs erTnairi eleqtrotevadoba aqvT.

5. rogor icvleba kon-densatoris eleqtrote vadoba

Semonafenebs Soris minis dieleqtrikis SetaniT? axseniT, ratom fiqrobT ase?

sur. 41.1

kondensatori, eleqtrotevadoba, faradi

umartivesi kondensa tori aris ori gamtaris erTob lioba, rom lebic erTma neTisagan gamoyo filia dieleq trikis Txeli fe niT.

kondensatoris eleqtrotevadoba ewodeba kondensatoris muxtis Sefar debas Semonafenebs Soris ZabvasTan.

SI-Si ori gamtaris eleqtrotevadoba erTi faradis tolia, Tu +1k da -1k muxtebis gadacemisas am gamtarTa Soris 1 v potencialTa sxvaoba aRiZvreba.

brtyeli kondensatoris eleqtrotevadoba pirdapirpro porciulia misi firfitebis farTobisa, dieleqtrikuli SeRwevadobisa da ukuproporciulia firfitebs Soris manZilisa.

davaleba

CaatareT viqtorina Temaze _ ra viciT eleqtruli velis Sesaxeb.

viqtorina (laT.) _ erTgvari Ta-

maSoba, pasuxebis gacema kiTxveb ze

codnis sxvadasxva dargidan.

42

1.15 damuxtuli kondensatoris energia. kondensatoris gamoyeneba

aqvs energia damuxtul kondensators?CavataroT cda: davmuxtoT kondensatori da

misi gamomyvanebi CamrTvel-amomrTvelis meSveobiT SevaerToT jibis farnis naTurasTan (sur. 42.1). CavrToT CamrTveli. naTura akaSkaSdeba da Caqreba. kondensatori ganimuxteba.

romeli energiis xarjze gaxurda naTuras spirali da gamosxivda sinaTle? ra Seicvala kondensatoris ganmux tvisas?

am sakiTxebis gadasawyvetad upasuxeT SekiTxvebs.

erTaderTi, ramac cvlileba ganicada kondensatoris ganmuxtvisas, eleqtruli velia, romelic arsebobda damuxtuli kondensatoris Semonafenebs Soris da ar arsebobs ganmuxtvis Semdeg.

amgvarad, eleqtrul vels gaaCnia energia, romlis xarjzedac gaanaTa na Turam.

eleqtruli velis energiis cvlileba tolia muSaobisa, romelic sruldeba kondensatoris ganmuxtvisas:

∆Eel=A. (1)

davadginoT, romel fizikur sidideebzea damokidebuli damuxtuli kondensatoris energia. amisaTvis ganvsazRvroT muSaoba, romelsac asrulebs ganmuxtvisas q muxtisa da U Zabvamde damuxtuli kondensatoris eleqtruli veli. kondensatoris ganmuxtvisas misi q muxtis erTi Semonafenidan meoreze gadatanisas eleqtruli velis mier Sesrulebuli muSaoba

A=qUsaS.. (2)

radgan C tevadobis da q muxtis kondensatoris ganmuxtvisas mis Semonafenebs Soris Zabva

U=q/C (3) muxtis pirdapirproporciulad mcirdeba nulamde,

amitom .U U2saS= (4) (4) (2) ⇒ .A

qU2

= (5)

(5) (1) ⇒ D∆Eel

= .EqU2el= (6)

1. ras udris kondensatoris Semonafenebis jamuri muxti ganmuxtvamde? axseniT, ratom fiqrobT ase?

2. ras udris kondensatoris Semonafenebis jamuri muxti ganmuxtvis Semdeg?

3. arsebobs Tu ara eleqtruli veli damuxtuli kondensatoris Semonafenebs Soris?

4. arsebobs Tu ara eleqtruli veli kondensatoris ganmuxtvis Semdeg mis Semonafenebs Soris?

sur. 42.1

+ –


43

(9) formulaSi Sd=V aris eleqtruli velis mier kondensatoris SigniT dakavebuli moculoba. (9) tolobis orive mxare gavyoT V-ze, miviRebT moculobis erTeulSi moqceuli velis energias _ eleqtruli velis energiis simkvrives, aRvniSnoT igi w

el-iT:

.E

2w 0

2

el=ff (10)

es formula marTebulia nebismieri eleqtruli velisaTvis.eleqtruli velis energiis simkvrivis cneba pirvelad maqsvelma

SemoiRo. maqsvelis Teoriis mixedviT, eleqtruli energia ganawilebulia velis mTel moculobaSi. manamde varaudobdnen, rom eleqtruli energia damuxtul sxeulebSi iyo koncentrirebuli.

kondensatoris energia mcirea. igi ramdenime aseul jouls ar aRemateba. muxtis garduvali kargvis gamo kondensatoris energia didxans ar inaxeba. amis gamo kondensators ar SeuZlia Secvalos eleqtruli denis wyaro, magaliTad, akumula-torebi.

kondensators, rogorc energiis damgro-vebels, didi praqtikuli gamoyeneba aqvs misi erT-erTi mniSvnelovani Tvisebis ga mo: masSi energiis dagroveba grZeldeba Seda-rebiT didxans, ganmuxtvisas ki mcire wina Ro-bis wredSi is TiTqmis mey seulad iZleva dagrovil energias. swo red es Tvisebaa praqtikaSi ga mo yenebuli. magaliTad, fotografiaSi gamoyenebuli

mfeTqavi naTura kondensatoris energiiT ikvebeba.

daniSnulebis mixedviT kondensa torebs aqvT sxvadasxva mow yobiloba da garegani saxe. Cveulebrivi teqnikuri konde nsatori Sedgeba aluminis kilitis ori zolisagan, romlebic erTmaneTisagan izolirebulia parafiniT gaJRenTili qaRaldiT (sur. 43.1). aluminisa da qaRaldis zolebi mWidrod aris Sexveuli mcire zomis kompaqtur paketSi (sur. 43.2).

sur. 43.1

5. (6) da (3) formulebis gamoyenebiT miiReT brtyeli

konden satoris energiis sxva saxiT Cawerili formulebi:

,ECq2

2

el= (7) .E CU2

2

el= . (8)

6. gaiTvaliswineT, rom CdS0=

ff da U=Ed da miiReT formula

.EE

Sd20

2

el

ff= (9)

7. daasaxeleT (7),(8)∧(9) formulebSi Semavali fizikuri sidideebi

da TiTo eulis erTeuli SI-Si.

sur. 43.2

44

radioteqnikaSi farTod iyeneben cvladi tevadobis kondensatorebs (sur. 44.1) aseTi kondensatori Sedgeba liTonis firfitebis ori sistemisagan, romlebic saxeluris brunviT erTmaneTSi Sedis. am dros icvleba firfitebis gadamfaravi nawilis farTobi da, maSasadame, maTi tevadoba.

kondensatoris korpusze miTiTebulia eleqtro tevadoba da maqsima luri Zabva, romelzec igia gaTvaliswinebuli. es aucilebelia, radgan konden satoris CarTvam miTiTebul Zabvaze meti Zabvis wredSi SeiZleba gamoiwvios kondensatoris garRveva. es aris movlena, rodesac kondensatoris Semonafenebs Soris gaxteba naperwkali.

Semonafenebs Soris sivrce gamtari xdeba, kondensatori gamodis

mwyobridan.

moipoveT informacia kondensatorebis klasifikaciisa da maTi

eleqtro teqnikaSi gamoyenebis Sesaxeb.

moam zadeT sakiTxi jer gakveTilze, Semdeg sko lis, qalaqis (raio-

nis), saqarTvelos mos wavleTa SemoqmedebiT konferenciaze warsadgenad.

sakiTxis Sesaswavlad gamoiyeneT TqvenTvis xelmisawvdomi sainfor-

macio wyaro (beWdviTi, audiovizualuri, interneti).

eleqtruli velis energia,

eleqtruli velis energiis simkvrive

damuxtuli kondensatoris eleqtruli velis energia gamoiTvleba

formulebiT:

; ; .EqU

E CU ECq

2 2 2

2 2

el el el= = =

eleqtruli velis energiis simkvrive gamoiTvleba formuliT

.WE

20

2

el=ff

eleqtruli energia ganawilebulia velis mTel moculobaSi.

davaleba

sur. 44.1

45

xSirad kondensatorebs erTmaneTTan aerTeben batareis saxiT. es saSualebas gvaZlevs kondensatorTa mocemuli nakrebidan miviRoT sxvadasxva tevadobis batarea. ganvixiloT kondensatorTa paraleluri da mimdevrobiTi SeerTeba.

1. 45.1 suraTze gamosaxulia paralelurad SeerTebuli C1 da C2 tevadobis kondensatorebi. maTi Semonafenebi erTmaneTTan wyvil-wyviladaa SeerTebuli. ganvsazRvroT kondensatorTa batareis C eleqtrotevadoba.

amoxsna

paraleluri SeerTebisas ∆ϕ=ϕ1-ϕ2≡U (1) potencialTa sxvaoba kondensatoris firfitebs Soris erTianiria orive kondensatorisTvis (sur. 45.1). batareis muxti q=q1+q2, (2) sadac q1 pirveli kondensatoris muxtia, q2 ki _ meorisa.

batareis eleqtrotevadoba ewodeba batareis muxtis Sefardebas kondensatorTa

Semonafenebis potencialTa sxvaobasTan, e. i.

.Cq

={D

(3)

(1)∧(2) (3) ⇒ .CU

q qC

Uq

Uq

C C C1 2 1 21 2& &=

+= + = + (*)

(*)⇒ kondensatorTa paraleluri SeerTebisas batareis eleqtro-

tevadoba calkeul kondensatorTa tevadobebis jamis tolia.

2. 45.2 suraTze gamosaxulia mim devrobiT SeerTebuli C1 da C2 tevadobis konden satorebi. ganvsazRvroT batareis C eleq tro -tevadoba.

amoxsna

mimdevrobiTi SeerTebisas orive kondensa toris muxti erTnairia (sur. 45.2).

Tu pirveli kondensatoris Semonafenis muxti aris +q, maSin mizidvis Sedegad mopirdapire Semonafenze warmoiSoba –q muxti. kondensatorTa Soris arsebuli sadeni da am sadeniT SeerTebuli Semonafenebi mTlianad neitraluria, amitom meore kondensatoris Siga Semonafenis muxti

tolia +q-si, gare Semonafenis ki _ –q-si. kondensatorTa batareis

eleqtrotevadoba ,Cq

Cq

1 21 2&{ { {= - - ={ (1) sadac ϕ1 da ϕ2 gare

SemonafenTa potencialebia. calkeuli kondensatorisaTvis SegviZlia

C1

C2ϕ1 ϕ2

+ –+q1 –q1

+q2 –q2

sur. 45.1

+q –q –q+q

sur. 45.2

ϕ1 ϕ2ϕ′

C1 C2

+ –

amocanis amoxsnis nimuSi 1.16www.physics.ge | saZiebo fraza k10t1p16

46

davweroT ,Cq

11

{ {- =l (2) ,Cq

22

{ {- =l (3) sadac ϕ′ gamtariT SeerTebul

SemonafenTa potencialia.

(2)∧(3)-is SekrebiT miviRebT .Cq

Cq

1 21 2

{ {- = + (4)

(1) (4) ⇒ .Cq

Cq

Cq

C C C1 1 1

1 2 1 2

&= + = + (*)

amgvarad, mimdevrobiTi SeerTebisas batareis tevadobis Sebrunebuli sidide tolia calkeul kondensatorTa tevadobebis Sebrunebul sidideTa

jamisa. Tu gvaqvs mimdevrobiT SeerTebuli n kondensatori, maSin

.C C1 1

ii

n

2

==

! (5) (*) ⇒ .CC C

C C

1 2

1 2=+

(6)

3. damuxtuli brtyeli kondensatoris firfitebs Soris manZili n=2-jer ga zardes. gansazRvreT, ramdenjer Seicvala: a. kondensatoris mux ti; b. kondensatoris eleqtrotevadoba; g. Zabva fifitebs Soris; d. velis daZabuloba; e. velis energia. ganixileT ori SemTxveva: 1. kondensatori gamorTulia Zabvis wyarodan; 2. kondensatori mier-Tebulia Zabvis wyarosTan.

amoxsna

1. a. radgan kondensatoris firfitebi araferTan ar aris SeerTebuli,

amitom misi muxti ar Seicvleba. b. kondensatoris eleqtrotevadoba

,CdS0=

ff (1) sadac S aris firfitebis urTierTgadamfaravi farTobi, d

_ firfitebs Soris manZili. (1) ⇒ d-s orjer gadidebiT kondensatoris

tevadoba orjer mcirdeba. g. kondensatoris eleqtrotevadoba

,CUq

UCq

&= = (2) sadac q kondensatoris muxtia, U _ Zabva firfitebs

Soris. (2) ⇒ C-s orjer SemcirebiT firfitebs Soris Zabva orjer izrdeba.

d. kondensatoris firfitebs Soris eleqtruli veli erTgvarovania

.EdU= (3) davadgineT, d-s gadidebiT U-c imdenjerve izrdeba. (3)⇒ E ar

icvleba. e. formulidan EqU2el &= damuxtuli kondensatoris eleqtruli

velis energia orjer izrdeba, radganac q ar icvleba, U orjer izrdeba.2. g. rodesac kondensatori CarTulia mudmivi Zabvis wredSi, maSin

Semonafenebze SenarCunebulia mudmivi denis wyaros polusebze arsebuli

Zabva. igi ar icvleba Semonafenebs Soris manZilis cvlilebiT. b.

kondensatoris eleqtrotevadoba CdS0=

ff ar aris damokidebuli imaze

kondensatori mierTebulia Tu ara denis wyarosTan. firfitebs Soris manZilis gadidebiT igi mcirdeba.

a. kondensatoris muxti orjer mcirdeba.d. eleqtruli velis daZabuloba orjer mcirdeba.e. eleqtruli velis energia orjer mcirdeba.

a, d da e SekiTxvebze pasuxebi Tqven daasabuTeT.

47

amoxseniT amocanebi

1. SeadareT ori eleqtronis urTierTganzidvis Zalis moduli maTi gravita ciuli mizidulobis Zalis moduls.

2. gansazRvreT A da B wertilebSi damagrebuli 10 da 20 nk wertilovani muxtebis SemaerTebeli monakveTis SigniT C wertilSi moTavsebul 2 nk muxtze moqmedi Zalebi da maTi tolqmedi, Tu AB=30 sm, AC=10 sm.

3. rogor unda SevcvaloT manZili or muxts Soris, rom wyalSi CaSvebisas maTi urTierTqmedebis Zalis moduli iseTive iyos, rogoric vakuumSi?

4. gansazRvreT eleqtruli velis muSaoba q wertilovani muxtis B wertilidan A wertilSi gadaa-dgilebisas. veli Seqmnilia q1 da q2 werti lovani muxtebiT (sur. 47.1).

5. eleqtruli velis moqmedebiT eleqtronis siCqare 107-dan 3.107 m/wm-mde gaizarda. gansazRvreT potencialTa sxvaoba gadaadgilebis sawyis da saboloo wertilebs Soris.

6. 47.2 suraTze gamosaxuli sqemis mixed-viT gansaz RvreT kondensatorTa batareis eleqtro tevadoba.

q1

q2q

Al

SR

sur. 47.1

B

SeamowmeT Tqveni codna 1.17

C1

BAC3

C2

sur. 47.2

D

testi

1. eleqtruli velis daZabulobis mimarTulebiT velis potenciali a. izrdeba; b. mcirdeba; g. ar icvleba; d. jer mcirdeba, Semdeg

izrdeba.2. Tu eleqtrul velSi muxtis gadaadgilebisas muxtis velTan

urTierTqmedebis potenciuri energia izrdeba, maSin veli a. asrulebs dadebiT muSaobas; b. asrulebs uaryofiT muSaobas; g. muSaobas ar asrulebs; d. jer dadebiT muSaobas asrulebs, Semdeg

uaryofiTs.3. rodesac veli asrulebs dadebiT muSaobas, maSin muxtis

kinetikuri energia a. izrdeba; b. mcirdeba; g. ar icvleba; d. jer mcirdeba, Semdeg

ar izrdeba.4. kondensatoris Semonafenebze Zabvis gadidebiT kondensatoris

eleqtrotevadoba a. izrdeba; b. mcirdeba; g. ar icvleba; d. jer izrdeba, Semdeg

mcirdeba.


Documents

giorgi gedeniZe eTer lazaraSvili