OECEEA IAI?A?UAIIAI
15. OECE*ANEEA IIEss
15.1. Iienaiea oece/aneeo iieae.
A ainueiie aeaaa auei aaaaeaii iiiyoea iiey, noi?ioee?iaaia eiioeaioeey
aeeceiaeaenoaey, i?eiyoay a nia?aiaiiie oeceea, e ?anniio?aiu /aou?a
aeaea acaeiiaeaenoaey, o.a. /aou?a aeaea iieae. A ianoiyuai ?acaeaea iu
?anniio?ei, /oi oaeia i?eioeei noia?iiceoeee, /ai iienaiea iiey
ioee/aaony io iienaiey aauanoaa, eaeea ia?aiao?u aaiaeyony aeey iienaiey
anao aeaeia iieae.
Niaeanii eiioeaioeee aeeceiaeaenoaey, acaeiiaeaenoaea iaaeaeo oaeaie ia
?annoiyiee inouanoaeyaony iin?aaenoaii iniaiai ninoiyiey iaoa?ee – iiey.
Oaea eee /anoeoeu, o/anoaothuea a acaeiiaeaenoaee, nicaeatho a
ie?oaeathuai eo i?ino?ainoaa iniaia ninoiyiea – iiea.
Iniiaiia ioee/ea iiey io ?anniao?eaaaiuo iaie ?aiaa oae eee /anoeoe
caeeth/aaony a oii, /oi iii eieaeeciaaii ai anai i?ino?ainoaa. Aeey
iienaiey ninoiyiey /anoeoeu o?aaiaaeinue caaeaoue ia?aie/aiiia /enei
ia?aiao?ia ?aaiia /eneo noaiaiae naiaiaeu. (Aeey iaoa?eaeueiie oi/ee yoi
?aaeeon-aaeoi? r, caaeaaaaiue o?aiy i?iaeoeeyie ia ine eii?aeeiao).
Iineieueeo, /enei oi/ae a i?ino?ainoaa aaneiia/ii, aaneiia/ii e /enei
noaiaiae naiaiaeu, a cia/eo, e /enei ia?aiao?ia, eioi?ua ioaeii caaeaoue
aeey iienaiey iiey. Yoi ia icia/aao, /oi a aeaenoaeoaeueiinoe ioaeii
caaeaaaoue aaneiia/iia /enei ia?aiao?ia. Aeinoaoi/ii caaeaoue caeii, ii
eioi?iio iaiyaony iiea a i?ino?ainoaa e ia/aeueiua ia?aiao?u, /oiau
ciaoue ia?aiao?u iiey a ethaie oi/ea i?ino?ainoaa.
Iiea i?iyaeyaony a neeiaii aicaeaenoaee ia oaea eee /anoeoeu, a iaai
iiiauaiiua. O.a. ia /anoeoeo eee oaei a ethaie oi/ea i?ino?ainoaa, aaea
eiaaony iiea, aeaenoaoao neea F. Iaeiie ec aaaeiaeoeo eiee/anoaaiiuo
oa?aeoa?enoee iiey, yaeyaony iai?yaeaiiinoue. Iai?yaeaiiinoue iiey
ii?aaeaeyaony eae ioiioaiea neeu, aeaenoaothuae ia oaei, e aaee/eia oie
eiee/anoaaiiie oa?aeoa?enoeee, eioi?ay o/anoaoao a nicaeaiee iiey e
ii?aaeaeyaony iieai, iiyoiio iai?yaeaiiinoue iacuaatho neeiaie
oa?aeoa?enoeeie iiey. Nouanoaaiii, /oi iai?yaeaiiinoue iiey yaeyaony
aaeoi?iie aaee/eiie, oae aea eae e neea, /a?ac eioi?oth iia
ii?aaeaeyaony.
).
A /ai aea ninoieo i?aeiouanoai iienaiey iieae ia ycuea iai?yaeaiiinoae?
Iiaeao auei au i?iua e oaeiaiaa i?inoi caaeaoue neeo, aeaenoaothuoth ia
oaei a eaaeaeie oi/ea? Aeaei a oii, /oi neea caaeneo eae io
oa?aeoa?enoee iiey, oae e io oa?aeoa?enoee iauaeoa, a iaai iiiauaiiiai
(aai yeaeo?e/aneiai ca?yaea, iannu, i?ioaeathuaai oiea e o.i.).
Iai?yaeaiiinoue aea iiey caaeneo oieueei io naienoa iiey.
Oaeei ia?acii, iiea caaeaii, anee a eaaeaeie oi/ea i?ino?ainoaa ecaanoia
aai iai?yaeaiiinoue. Ia ?enoieao oaeiaii ecia?aaeaoue iiea i?e iiiiue
neeiauo eeiee. Neeiauie eeieyie iiey iacuaathony oaeea eeiee,
eanaoaeueiua e eioi?ui a eaaeaeie oi/ea niaiaaeatho n aaeoi?ii
iai?yaeaiiinoe iiey. Ae?oaeie neiaaie, neeiaay eeiey ii?aaeaeyao
iai?aaeaia iai?yaeaiiinoe iiey a eaaeaeie oi/ea, /a?ac eioi?oth iia
i?ioiaeeo. Neeiaua eeiee iicaieytho ii?aaeaeyoue oaeaea e aaee/eio
iai?yaeaiiinoe iiey. Neeiaua eeiee ?enotho oaeei ia?acii, /oiau /enei
eo, ia?anaeathueo aaeeie/ioth ieiuaaeeo /eneaiii ?aaiyeinue
iai?yaeaiiinoe iiey a aeaiiie oi/ea. Ia ?en. 15.1.a ecia?aaeaiu neeiaua
eeiee iiey, nicaeaaaaiiai iieiaeeoaeueiui yeaeo?e/aneei ca?yaeii Q. Iie
aoua aaeece ca?yaea, aaea iai?yaeaiiinoue iiey aieueoa, e ?aaea aaeaee
io ca?yaea. Ia aieueoeo ?annoiyieyo io ca?yaea ninaaeiea neeiaua eeiee
eaeoo i?aeoe/anee ia?aeeaeueii ae?oa – ae?oao. Oaeia iiea iacuaaaony
iaeii?iaeiui (?en.15.1.a).
?en.15.1
Aaaaeai aua iaeii aaaeiia iiiyoea – iioie aaeoi?a iai?yaeaiiinoe iiey.
Iioie aaeoi?a iai?yaeaiiinoe iiey – ( /a?ac ieiuaaeue S ii?aaeaeyaony
/eneii neeiauo eeiee, ia?anaeathueo /a?ac yoo ieiuaaeue. Ioiaoei, /oi
iioie aaeoi?a iai?yaeaiiinoe – neaey?iay aaee/eia. Nouanoaotho aieaa
no?iaea ii?aaeaeaiey yoiai iiiyoey, ii ia aeaiiue iiiaio aiieia
aeinoaoi/ii, /oi iioie /eneaiii ?aaai /eneo neeiauo eeiee ia?anaeathueo
?anniao?eaaaioth iiaa?oiinoue.
I/aaeaeii, /oi aaee/eia iioiea aaeoi?a ii?aaeaeyaony acaeiiui
iai?aaeaieai neeiauo eeiee e ieiuaaee S. Ia ?en.15.1a ecia?aaeaiu aeaa
ieiuaaee S1 e S2. Ieiuaaee ?acee/iu, ii eiee/anoai neeiauo eeiee, eo
ia?anaeathueo, iaeeiaeiai, neaaeiaaoaeueii iioiee aaeoi?a iai?yaeaiiinoe
iaeeiaeiau. Aaaaeai aaeoi? S, /eneaiii ?aaiue ieiuaaee S, e iai?aaeaiiue
ia?iaiaeeeoey?ii ae. Oiaaea iioie aaeoi?a iai?yaeaiiinoe (A
iaeii?iaeiiai iiey A aoaeao ?aaai neaey?iiio i?iecaaaeaieth aaeoi?ia A e
S:
, aaea ( – oaie iaaeaeo aaeoi?aie A e S. Ec yoiai ii?aaeaeaiey
neaaeoao, /oi iioie aaeoi?a /a?ac ieiuaaeeo, ia?aeeaeueioth neeiaui
eeieyi iiey, ?aaai ioeth.
Ae?oaie aaaeiaeoae oa?aeoa?enoeeie iiey iiaeao auoue aai iioaioeeae. Yoi
iiiyoea iiaeii aaanoe eeoue aeey iieae eiina?aaoeaiuo nee (ni. ?acaeae
11). Iioaioeeae iiey – ( ii?aaeaeyaony eae ioiioaiea iioaioeeaeueiie
yia?aee oaea a iiea, e aaee/eia oie eiee/anoaaiiie oa?aeoa?enoeee,
eioi?ay o/anoaoao a nicaeaiee iiey e ii?aaeaeyaony iieai, iiyoiio
iioaioeeae iacuaatho yia?aaoe/aneie oa?aeoa?enoeeie iiey. Nouanoaaiii,
/oi iioaioeeae iiey – neaey?iay aaee/eia.
Niiaa caaeaaeei naaa aii?in, /ai aea oaeiaii iienaiea iieae ia ycuea
iioaioeeaeia? Iiaeao auei au i?iua e oaeiaiaa aianoi iioaioeeaea i?inoi
caaeaoue aaee/eio iioaioeeaeueiie yia?aee oaea a eaaeaeie oi/ea? Ioaao
ia yoio aii?in aoaeao ii/oe oaeei aea, eae e aeey iai?yaeaiiinoe iiey.
Aeaei a oii, /oi iioaioeeaeueiay yia?aey caaeneo eae io oa?aeoa?enoee
iiey, oae e io oa?aeoa?enoee iauaeoa, a iaai iiiauaiiiai (aai
yeaeo?e/aneiai ca?yaea, iannu, i?ioaeathuaai oiea e o.i.). A oi a?aiy,
eae iioaioeeae caaeneo oieueei io naienoa iiey.
, aaea ( – oaie iaaeaeo iai?aaeaieai neeu F e ia?aiauaiey l. Yoa ?aaioa
iiaeao auoue ?aaiie ioeth eeoue a oii neo/aa, anee F(l, o.a. oaie (( (
90I. Iineieueeo iai?yaeaiiinoue iiey niaiaaeaao ii iai?aaeaieth n neeie,
ia?aiauaiea eaaeeo ia yeaeiioaioeeaeueiie iiaa?oiinoe, neacaiiia
iaicia/aao, /oi eeiee iai?yaeaiiinoe anaaaea i?oiaiiaeueiu
yeaeiioaioeeaeueiui iiaa?oiinoyi.
*ai aeeaea ae?oa e ae?oao ?aniieiaeaiu yeaeiioaioeeaeueiua iiaa?oiinoe,
oai aieueoa iai?yaeaiiinoue iiey. Ia ?en.15.2.a i?eaaaeai i?eia?
yeaeiioaioeeaeueiuo iiaa?oiinoae.
Aniiiiei naycue neeu n iioaioeeaeueiie yia?aeae – oi?ioeo (11.12). Anee
eaaoth e i?aaoth /anoue yoiai ?aaainoaa ?acaeaeeoue ia aaee/eio oie
eiee/anoaaiiie oa?aeoa?enoeee, eioi?ay o/anoaoao a nicaeaiee iiey, oi
iieo/eony oi?ioea, au?aaeathuay naycue iai?yaeaiiinoe iiey n aai
iioaioeeaeii:
.
Aiaeiae/iui ia?acii ec (11.8) iieo/ei oi?ioeo aeey nayce iioaioeeaea
iiey n aai iai?yaeaiiinoueth:
.
Yoe oi?ioeu iicaieytho ii caaeaiiiio a eaaeaeie oi/ea iioaioeeaeo iiey
ainnoaiiyeo aai iai?yaeaiiinoue e iaiai?io.
Ia?aoeiny e i/aiue aaaeiiio a oai?ee iiey i?eioeeio – i?eioeeio
noia?iiceoeee. A iauai neo/aa, i?eioeei noia?iiceoeee – yoi aeiiouaiea,
niaeanii eioi?iio ?acoeueoe?othuee yooaeo neiaeiiai i?ioeanna
aicaeaenoaey yeaeaaeaioai noiia yooaeoia io eaaeaeiai aicaeaenoaey a
ioaeaeueiinoe. ?acoiaaony yoi ii?aaeaeaiea i?aaeiieaaaao, /oi yooaeou ia
aeeytho ae?oa ia ae?oaa. N i?eioeeiii noia?iiceoeee iu noaeeeaaeenue a
oeieueiii eo?na iaoaieee e yeaeo?inoaoeee. Anee ia /anoeoeo, eee oaei
aeaenoaoao ianeieueei nee, oi eo iiaeii caiaieoue iaeiie – aaeoi?iie
noiiie anao nee.
Noi?ioee?iaaiiue i?eioeei ia yaeyaony ooiaeaiaioaeueiui, eee
oieaa?naeueiui. Ii ni?aaaaeeea, anee nenoaia iienuaaaony eeiaeiuie
o?aaiaieyie. E nenoaia, iienuaaaiie iaeeiaeiuie o?aaiaieyie, o.a.
iaiythuaeny iiae aeaenoaeai aiaoieo yooaeoia, i?eioeei noia?iiceoeee
iai?eiaiei.
Iiyniei auoaneacaiiia i?eia?ii. Ionoue a i?ino?ainoaa eiaaony
?aaiiaaniia ?ani?aaeaeaiea yeaeo?e/aneeo ca?yaeia, nicaeathueo anthaeo
aie?oa naay yeaeo?e/aneia iiea. *oi neo/eony, anee a yoi iiea aianoe aua
iaeei yeaeo?e/aneee ca?yae? Anee aianaiiue ca?yae aoaeao i/aiue iae, oi
i?eioeei noia?iiceoeee aeey ?acoeueoe?othuaai iiey aoaeao eiaoue ianoi.
Iaeiaei, anee yoio ca?yae aaeee, oi ii iiaeao i?eaanoe a aeaeaeaiea e
ia?aianoeoue ana eiathueany ca?yaeu. Aneaaenoaea yoiai ieaaeaony, /oi
ia?aiia/aeueiia iiea neeueii eneaceony, e yoi eciaiaiea ia aoaeao
iienuaaoueny a ?aieao i?eioeeia noia?iiceoeee.
A iauai neo/aa iiaeii ooaa?aeaeaoue, /oi i?eioeei noia?iiceoeee
ni?aaaaeeea, anee iaeiaeaiea iieae ia i?eaiaeeo e ia?aiauaieth a
i?ino?ainoaa enoi/ieeia yoeo iiea.
Yeaeo?iiaaieoiia iiea a aaeooia oaeiaeaoai?yao i?eioeeio noia?iiceoeee.
A neeo yoiai i?eioeeia yeaeo?e/aneia eee iaaieoiia iiea, nicaeaaaaiia
nenoaiie ca?yaeia eee oieia, ?aaii noiia iieae, nicaeaaaaiuo yoeie
ca?yaeaie eee oieaie a ioaeaeueiinoe. Aeey yeaeo?iiaaieoiiai iiey a
aauanoaa, i?eioeei noia?iiceoeee iiaeao ia?ooaoueny, iai?eia?, anee
iinoiyiiua, iienuaathuea naienoaa n?aaeu (aeeyeaeo?e/aneay eee
iaaieoiay) caaenyo io aaee/eiu iiey.
I?eia?ii ia?ooaiey i?eioeeia noia?iiceoeee iiaeao neoaeeoue iaaieoiia
iiea a oa??iiaaiaoeea. Ae?oaie i?eia? – naao (neeueiia naaoiaia iiea) a
n?aaea. Oaeia iiea iiaeao aaia?e?iaaoue a n?aaea ca n/ao iaeeiaeiiai
acaeiiaeaenoaey n iae naao ia aeeeia aieiu a aeaa, o?e eee aieaa ?ac
iaiueoae. Neaaia a?aaeoaoeeiiiia iiea n oi?ioae oi/iinoueth iiae/eiyaony
i?eioeeio noia?iiceoeee. Neeueiia aea a?aaeoaoeeiiiia iiea ia
iiae/eiyaony i?eioeeio noia?iiceoeee, iineieueeo iii iienuaaaony
iaeeiaeiuie o?aaiaieyie Yeiooaeia.
?acaeaeu oeceee, eioi?ua eco/atho yaeaiey, a eioi?uo ia?ooaaony i?eioeei
noia?iiceoeee, iau/ii iacuaatho iaeeiaeiuie. Iai?eia?, iaeeiaeiay
iioeea. A aeaeueiaeoai ia?aie/einy ?anniio?aieai neaauo iieae
(a?aaeoaoeeiiiuo e yeaeo?iiaaieoiuo), e eioi?ui i?eioeei noia?iiceoeee
i?eiaiei.
. Iiey oeaio?aeueiuo nee.
A yoii ?acaeaea, iu ?anniio?ei oae iacuaaaiua iiey oeaio?aeueiuo nee.
Yoi iiey , neeu acaeiiaeaenoaey aeey eioi?uo caaenyo oieueei io
?annoiyiey iaaeaeo acaeiiaeaenoaothueie oaeaie e iai?aaeaiu aaeieue
eeiee acaeiiaeaenoaey. Iu aoaeai ?anniao?eaaoue eaacenoaoeeiia?iua iiey,
o.a. oaeea iiey, eioi?ua eeai ia iaiythony ni a?aiaiai, eeai iaiythony,
ii iaaeeaiii ii n?aaiaieth n ?anniao?eaaaiuie yaeaieyie. E
?anniao?eaaaiui iiey a ia?aoth i/a?aaeue ioiinyony a?aaeoaoeeiiiua e
yeaeo?inoaoe/aneea iiey.
Iiaaaeaiea a?aaeoaoeeiiiuo e yeaeo?inoaoe/aneeo iieae iioiaea ae?oa ia
ae?oaa. Oi iauyniyaony oai, /oi a iniiaa iienaiey iaaeo iieae eaaeao
noiaeea caeiiu: caeii anaie?iiai oyaioaiey Iuethoiia e caeii Eoeiia. A
aaeoi?iii aeaea iu caienuaaee eo neaaeothuei ia?acii:
Foya = ( -g) ( M m / r2) (r/r) (15.4)
Feoe = (1/4pe0 ) (Qq/r2) (r/r) (15.5)
Anee ia n/eoaoue eiyooeoeeaioia ia?aae oi?ioeaie (-g) e (1/4pe0)
(eioi?ua iiaoo eiaoue ae?oaie aeae a ae?oaeo nenoaiao aaeeieoe), caeiiu
iioiaee. Neea oyaioaiey Foya (neea i?eoyaeaiey iaaeaeo aeaoiy oaeaie)
i?yii i?iii?oeeiiaeueia iannai M e m oae, ia?aoii i?iii?oeeiiaeueia
eaaae?aoo ?annoiyiey iaaeaeo oaeaie r e iai?aaeaia aaeieue eeiee,
niaaeeiythuae oaea (r/r). Eoeiiianeay neea Feoe (neea acaeiiaeaenoaey
iaaeaeo ca?yaeaie ) i?yii i?iii?oeeiiaeueia ca?yaeai Q e q, ia?aoii
i?iii?oeeiiaeueia eaaae?aoo ?annoiyiey iaaeaeo ca?yaeaie r e iai?aaeaia
aaeieue eeiee, niaaeeiythuae ca?yaeu (r/r).
A aeaeueiaeoai iai aoaeao oaeiaii inoaiiaeony iiae?iaiaa ia iaeiii aeaea
acaeiiaeaenoaey ( yeaeo?inoaoe/aneii eee a?aaeoaoeeiiiii),
iiae?acoiaaay, /oi ana iaoe auaiaeu aoaeoo ni?aaaaeeeau e aeey ae?oaiai
acaeiiaeaenoaey (iiey).
A yeaeo?iaeeiaieea i?e iienaiee yeaeo?e/aneeo iieae eniieuecotho
ae?oaoth oi?io caiene caeiia Eoeiia. Ia iacuaaaony oai?aiie
Ino?ia?aaeneiai-Aaonna. ?anniio?ei aa. Iai?yaeaiiinoue yeaeo?e/aneiai
iiey oi/a/iiai ca?yaea Q ia ?annoiyiee r io iaai ii?aaeaeyaony ec
caeiia Eoeiia e ?aaia:
E = F/q = (1/4pe0)(Q/r )(r/r) (15.6)
Iaeaeai iioie aaeoi?a iai?yaeaiiinoe yeaeo?e/aneiai iiey /a?ac
iiaa?oiinoue, aioo?e eioi?ie iaoiaeeony ca?yae Q , – OA. Ie?oaeei
iiaa?oiinoue noa?ie ?aaeeonii R. Ieiuaaeue noa?u 4pR. Iioie aaeoi?a
iai?yaeaiiinoe /a?ac yoo noa?o /eneaiii ?aaai eiee/anoao neeiauo eeiee,
i?ioiaeyueo /a?ac iaa. Neeiaua eeiee ia?iaiaeeeoey?iu iiaa?oiinoe noa?u,
cos(SE)=1 e, cia/eo, eo /enei ?aaii i?iecaaaeaieth ieiuaaee noa?u ia
iai?yaeaiiinoue iiey ia iiaa?oiinoe noa?u:
OA = (4pR2 ) (1/4pe0 ) (Q/R2 ) = Q/ e0 (15.7)
Anee aianoi noa?e/aneie, iu aicueiai i?iecaieueioth caieioooth
iiaa?oiinoue, /a?ac iaa aoaeao i?ioiaeeoue noieueei aea neeiauo eeiee,
neieueei e /a?ac noa?o. A neeo i?eioeeia noia?iiceoeee oai?aia i?eiaieia
e e i?iecaieueiiio /eneo ca?yaeia aioo?e iiaa?oiinoe. *oiau iaeoe iioie
aaeoi?a iai?yaeaiiinoe i?e i?iecaieueiii /enea ca?yaeia aioo?e
iiaa?oiinoe, iaaei i?inoiie?iaaoue ca?yaeu aioo?e aa. Ae?oaeie neiaaie:
Iioie aaeoi?a iai?yaeaiiinoe /a?ac i?iecaieueioth iiaa?oiinoue ?aaai
aeaaa?ae/aneie noiia ca?yaeia aioo?e yoie iiaa?oiinoe, aeaeaiiie ia
aeeyeaeo?e/aneoth i?iieoeaaiinoue aaeooia.
Oai?aia Ino?ia?aaeneiai-Aaonna eiaao iaaeyaeiue oece/aneee niune. Iia
ooaa?aeaeaao, /oi neeiaua eeiee yeaeo?inoaoe/aneiai iiey ia/eiathony e
caeai/eaathony ia ca?yaeao. Anee aioo?e ?anniao?eaaaiie iiaa?oiinoe
ca?yaeia iao, oi /enei aoiaeyueo a iaa neeiauo eeiee ?aaii /eneo
auoiaeyueo e noiia?iue iioie aaeoi?a iai?yaeaiiinoe ?aaai ioeth.
Yoa oai?aia eniieuecoaony a yeaeo?inoaoeea aeey ?aoaiey iiiaeo caaea/.
?anniio?ei, eae n aa iiiiuueth ii?aaeaeeoue iai?yaeaiiinoue
yeaeo?e/aneiai iiey aaeece ?aaiiia?ii ca?yaeaiiie iiaa?oiinoe. Ionoue o
ian anoue aaneiia/ii aieueoay ?aaiiia?ii ca?yaeaiiay ieineinoue. Anee
ca?yaeu iieiaeeoaeueiu, oi neeiaua eeiee auoiaeyo ec ieineinoe e
?aniieiaeaiu ia?iaiaeeeoey?ii ae (ni.?en.15.2).
?en.15.2
Iaicia/ei /a?ac s=q/s iiaa?oiinoioth ieioiinoue ca?yaea, o.a. ca?yae,
i?eoiaeyueeny ia aaeeieoeo ieiuaaee. Auaeaeei ia ieineinoe ie?oaeiinoue
Ds e iino?iei ia iae eae ia iniiaaiee aeaa oeeeeiae?a ii iaa noi?iiu
iiaa?oiinoe. Aunioa oeeeeiae?ia ?aaia r. Aieiaua noaiee oeeeeiae?ia
ia?iaiaeeeoey?iu iiaa?oiinoe e niaiaaeatho n eeieyie iai?yaeaiiinoe
yeaeo?e/aneiai iiey. Cia/eo iioie aaeoi?a iai?yaeaiiinoe /a?ac ieo ?aaai
ioeth. I?eiaiei oaia?ue e oeeeeiae?o oai?aio Ino?ia?aaeneiai-Aaonna.
Iieiue iioie aaeoi?a iai?yaeaiiinoe yeaeo?e/aneiai iiey ?aaai: OA =
Q/e0=sDs /e0 . N ae?oaie noi?iiu, /oiau iaeoe aai, iaaei i?inoiie?iaaoue
iioiee aaeoi?a iai?yaeaiiinoe /a?ac ana noaiee oeeeeiae?a. *a?acaieiaua
noaiee ii ?aaai ioeth. Iioie aaeoi?a iai?yaeaiiinoe /a?ac oi?oeaaua
noaiee ?aaai: A Ds = s Ds/e0 . Ionthaea iaoiaeei, /oi iai?yaeaiiinoue
iiey ia caaeneo io ?annoiyiey aei iiaa?oiinoe e ?aaia : E = s/e0 .
Yoo aea caaea/o iiaeii, a i?eioeeia, ?aoeoue, eniieuecoy oi?ioeo 15.6.
Ii, aeey ?aoaiey caaea/e n aa iiiiuueth iio?aaiaaeinue au i?eiaiaiea
?acaeaea aunoae iaoaiaoeee, naycaiiiai n aaeoi?iui aiaeecii e
iiaa?oiinoiuie eioaa?aeaie.
Yeaeo?inoaoe/aneia e a?aaeoaoeeiiiia iiea yaeythony iieyie oeaio?aeueiuo
nee, o.a. nee, aaee/eia eioi?uo caaeneo oieueei io ?annoiyiey iaaeaeo
acaeiiaeaenoaothueie oaeaie e iai?aaeaiu aaeieue eeiee, niaaeeiythuae
oaea. Oaeea iiey yaeythony iieyie eiina?aaoeaiuo nee . Iieaaeai yoi ia
i?eia?a a?aaeoaoeeiiiiai iiey aaeece iiaa?oiinoe Caiee. Neeiaua eeiee
a?aaeoaoeeiiiiai iiey aaeece iiaa?oiinoe Caiee ia?aeeaeueiu ae?oa
ae?oao. Iaeaeai ?aaioo, niaa?oaaioth i?e ia?aiauaiee oaea, iannie m ec
oi/ee 1 a oi/eo 2 (ni. ?en. 15.3).
?en.15.3
?annoiyiea iaaeaeo oi/eaie aoaeai n/eoaoue i?aiaa?aaeeii iaeui ii
n?aaiaieth n ?annoiyieai aei oeaio?a caiee. A yoii neo/aa neea oyaioaiey
iaeeiaeiaa ai anao oi/eao o?aaeoi?ee ,?aaia aano oaea ? e iai?aaeaia
aa?oeeaeueii aiec: F = P =mg = m (g M / R 2 ) e, aaea R ?aaeeon Caiee,
e -aaeeie/iue aaeoi? e= -r/r.
Iai?aaei inue eii?aeeiao OZ aaeieue neeiauo eeiee a?aaeoaoeeiiiiai iiey
aa?oeeaeueii aiec. Ii ii?aaeaeaieth, ?aaioa, niaa?oaaiay i?e ia?aiauaiee
oaea iannie m ec oi/ee 1 a oi/eo 2 , ( aaea oi/ea 1 ?aniieiaeaia ia
aunioa H1 , a oi/ea 2 ia aunioa H2 )?aaia:
A12 = F dr = F dr cos(Fdr) = F dZ = F(H1-H2)=P(H1-H2)
(15.8).
?aaioa ia caaeneo io o?aaeoi?ee iooe, a ii?aaeaeyaony ia/aeueiui e
eiia/iui iieiaeaieai oaea. Oai naiui iu aeieacaee, /oi ?anniao?eaaaiua
iiey yaeythony iieyie eiina?aaoeaiuo nee. ?aaioa yoeo iieae ia caieiooie
o?aaeoi?ee ?aaia ioeth.
Aeey iiey eiina?aaoeaiuo nee iiaeii aaanoe iioaioeeaeueioth yia?aeth. A
eaaeaeie oi/ea iiey eiina?aaoeaiuo nee iia ?aaia ?aaioa, eioi?oth ioaeii
cao?aoeoue ia ia?aiauaiea oaea ec aaneiia/iinoe a aeaiioth oi/eo. A
neo/aa yeaeo?e/aneiai iiey ia?aiauaaiui oaeii yaeyaony ca?yae. I?e
iienaiee yeaeo?e/aneeo iieae aianoi iioaioeeaeueiie yia?aee oi/ee /aua
eniieuecotho iiiyoea iioaioeeaea a oi/ea r : j(r) . Iioaioeeae
ii?aaeaeyaony eae ioiioaiea iioaioeeaeueiie yia?aee (Eiio) ca?yaea q a
oi/ea e aaee/eia naiiai ca?yaea:
j(r) = Eiio(r) / q =Ar /q (15.9)
Ec yoiai ii?aaeaeaiey neaaeoao, /oi iioaioeeae yaeyaony neaey?iie
ooieoeeae. I?e/ai, o yoie ooieoeee a?aoiaioii neoaeeo oi/ea a
i?no?ainoaa, eioi?ay iiaeao caaeaaaony aaeoi?ii.
Nayaeai iaaeaeo niaie iioaioeeaeu e ?aaioo ii ia?aiauaieth ca?yaea.
Ionoue iu ia?aiauaai ca?yae q ec oi/ee 1 a oi/eo 2 a yeaeo?e/aneii
iiea. ?aaioa ii ia?aiauaieth oaeiai ca?yaea ?aaia ?aciinoe
iioaioeeaeueiuo yia?aee iiey a oi/eao 1 e 2:
A 12= Eiio(2) – Eiio(1) = [j(2) – j(1)] q=U q (15.10)
Caeanue ?aciinoue iioaioeeaeia iu iaicia/eee eae U , eioi?oth iau/ii
iacuaatho i?inoi iai?yaeaieai.
N ae?oaie noi?iiu, ?aaioa ii ii?aaeaeaieth ?aaia :
A 12= Fdr=qEdr =q Edr=q[j(2)-j(1)] (15.11)
Oai naiui iu naycaee iai?yaeaiiinoue yeaeo?e/aneiai iiey n ?aciinoueth
iioaioeeaeia. Aaee/eio Edr iacuaatho oee?eoeyoeeae aaeoi?a
iai?yaeaiiinoe yeaeo?e/aneiai iiey ia o/anoaa e?eaie 1-2. Anee ca?yae
ia?aiauaaony ii caieiooie e?eaie, o.a. auoae ec oi/ee 1 e aa?ioeny a
oi/eo 1, oi ?aaioa ii aai ia?aiauaieth ?aaia ioeth. Yeaeo?inoaoe/aneia
iiea- iiea eiina?aaoeaiuo nee. Ii yoi icia/aao, /oi oee?eoeyoeey aaeoi?a
iai?yaeaiiinoe yeaeo?e/aneiai iiey ia caieiooie e?eaie ?aaia ioeth. Oai
naiui iu aeieacaee aua iaeio aaaeioth oai?aio yeaeo?inoaoeee i
oee?eoeyoeee aaeoi?a iai?yaeaiiinoe yeaeo?e/aneiai iiey.
A ea/anoaa i?eia?a ?anniio?ei iioaioeeae oi/a/iiai ca?yaea +Q ia
?annoiyiee r0 io iaai. Ionoue i?iaiue ca?yae +q aeaeaaaony ii i?yiie,
i?ioiaeyoae /a?ac ca?yae Q, ec aaneiia/iinoe a oi/eo r0. ?aaioo,
cao?a/aiioth ia ia?aiauaiea ca?yaea iiaeii ii?aaeaeeoue ii oi?ioea 15.5
n o/aoii oiai, /oi ca?yae aeaeaaaony aaeieue neeiaie eeiee, o.a.
neaey?iia i?iecaaaeaiea Fdr =Fdr: A r = Fdr = (1/4pe0) Qq (1/r) dr
= (1/4pe0)Qq(1/r), ioeoaea iioaioeeae oi/a/iiai ca?yaea j(r) =1/4pe0Q
/r.
I?e a?aoe/aneii iienaiee yeaeo?e/aneeo iieae /anoi iieuecothony
yeaeiioaioeeaeueiuie eeieyie eee iiaa?oiinoyie, eioi?ua ii?aaeaeytho
iiaa?oiinoue n iaeeiaeiaui iioaioeeaeii j. Aeey oi/a/iiai ca?yaea eeiee
yeaeiioaioeeaeueiie iiaa?oiinoe ia ieineinoe – i?inoi eiioeaio?e/aneea
ie?oaeiinoe, eae yoi iieacaii ia ?en.15.1. I?e aeaeaeaiee ca?yaea ii
yeaeiioaioeeaeueiie iiaa?oiinoe ?aaioa ia niaa?oaaony, eae yoi neaaeoao
ec oi?ioeu 15.11. Aeey oiai, /oiau ?aaioa i?e ia?aiauaiee ca?yaea a
yeaeo?e/aneii iiea ?aaiyeanue au ioeth, o?aaoaony, /oiau ca?yae
aeaeaaeny ia?iaiaeeeoey?ii neeiaui eeieyi yeaeo?e/aneiai iiey (oiaaea
cos(Fdr)=0 e ?aaioa ?aaia 0). O.a. a iauai neo/aa eeiee
yeaeiioaioeeaeueiie iiaa?oiinoe ia?iaiaeeeoey?iu a eaaeaeie oi/ea eeieyi
iai?yaeaiiinoe yeaeo?e/aneiai iiey.
I?aaeiieiaeei, iu niiaueee iaeioi?ue ca?yae i?iaiaeieeo. *oi aoaeao
i?ienoiaeeoue? Iaeiieiaiiua ca?yaeu aoaeoo iooaeeeaaoueny e no?aieony
?aniieiaeeony ia iiaa?oiinoe i?iaiaeieea. Ii ca?yaeu ia iiaoo
aeaeaaoueny aaneiia/ii aeieai a i?iaiaeieea, eia/a iu iieo/eee au aa/iue
aeaeaaoaeue, o.a. ia?ooeeny au caeii nio?aiaiey yia?aee. Ca?yaeu
?aniieiaeaony oaeei ia?acii, /oiau iai?yaeaiiinoue yeaeo?e/aneiai iiey,
iai?aaeaiiay aaeieue eaaeaeie oi/ee iiaa?oiinoe ii eanaoaeueiie noaea au
?aaiie ioeth. Eeiee iai?yaeaiiinoe yeaeo?e/aneiai iiey a eaaeaeie oi/ea
iiaa?oiinoe aoaeoo ia?iaiaeeeoey?iu ae. Oiaaea aeaeaeaiea ca?yaeia ii
iiaa?oiinoe i?ae?aoeony. Oaeie i?ioeann i?iecieaeao i/aiue auno?i.
Iiaa?oiinoue i?iaiaeieea noaiao yeaeiioaioeeaeueiie, iineieueeo a
eaaeaeie oi/ea iiaa?oiinoe eeiee iai?yaeaiiinoe yeaeo?e/aneiai iiey
aoaeoo ia?aiaiaeeeoey?iu ae.
Aeo?aaua iiey.
Ia?yaeo n iienaiiuie auoa iieyie (yeaeo?inoaoe/aneeie e
a?aaeoaoeeiiiuie) nouanoaoao ae?oaie aeae iieae, neeiaua eeiee eioi?uo
ieaaea ia ia/eiathony e ieaaea ia caeai/eaathony, iie caiueathony naie
ia naay. Oaeea iiey iacuaathony aeo?aauie. Iie iacaaiu oae ec-ca
noiaenoaa neeiauo eeiee a aeaea eiioeaio?e/aneeo ie?oaeiinoae n aeo?ai.
?anniio?ei iniaaiiinoe yoeo iieae. Ia/iai n i?inoaeoaai – iaaieoiiai
iiey. Noaoeeiia?iia iaaieoiia iiea nicaeaaony aeaeaeoueieny ca?yaeaie.
Ec oeieueiiai eo?na oi?ioi ecaanoiu neeiaua eeiee anoanoaaiiuo iaaieoia.
Eo aeae ecia?aaeai ia ?en.15.4a. Oaeie aea aeae iieae iiaeii iieo/eoue,
eniieuecoy caieiooue i?iaiaeiee, ii eioi?iio oa/ao oie. Iiea e?oaiaiai
aeoea n oieii ecia?aaeaii ia ?en.15.4a. Neeiaua eeie iiey
?en.15.4
ia?acotho caieiooua e?eaua. Eo iai?aaeaiea ii?aaeaeyaony ii i?aaeeo
i?aaiai ao?aa/eea. Anee ?o/eo ao?aa/eea a?auaoue ii iai?aaeaieth oiea a
aeoea, oi ino?ea iieacuaaao iai?aaeaiea neeiauo eeiee. Noaoeeiia?iia
iaaieoiia iiea nicaeaaony aeaeaeoueieny ca?yaeaie. Ia ?en.15.5 iieacaiu
neeiaua eeiee aaneiia/ii aeeeiiiai i?iaiaeieea n oieii. Iie
i?aaenoaaeytho eiioeaio?e/aneea ie?oaeiinoe. Iai?aaeaiea neeiauo eeiee
oaeaea iiaeii ii?aaeaeeoue n iiiiuueth i?aaeea ao?aa/eea. Aeey yoiai
iaaei iai?aaeoue ino?ea ao?aa/eea ii iai?aaeaieth oiea, oiaaea
iai?aaeaiea a?auaiey ?o/ee ao?aa/eea niaiaaeao n iai?aaeaieai neeiauo
eeiee.
?en.15.5
I?aaeei ao?aa/eea – iiaiiie/aneia i?aaeei, iicaieythuaa i?inoi
ii?aaeaeyoue iai?aaeaiea neeiauo eeiee iaaieoiiai iiey. Nouanoaotho
no?iaea caeiiu, iicaieythuea ii?aaeaeyoue aaee/eio e iai?aaeaiea neeiauo
eeiee i?iecaieueiiai ii oi?ia i?iaiaeieea n oieii.
Iai?yaeaiiinoue iaaieoiiai iiey ii?aaeaeyaony caeiiii
Aei-Naaa??a-Eaieana. Iu ia aoaeai ?anniao?eaaoue a yaiii aeaea yoio
caeii. A i?eioeeia, n aai iiiiuueth iiaeii ?ann/eoaoue iai?yaeaiiinoue
iaaieoiiai iiey, nicaeaaaaioth ethaui i?iaiaeieeii n oieii. Oae
iai?yaeaiiinoue iaaieoiiai iiey aaneiia/ii aeeeiiiai i?iaiaeieea n oieii
ia ?annoiyiee r io iaai ?aaia: H=I/2pr.
Ia aeinoaoi/ii oaeaeaiiii ?annoiyiee io i?iaiaeieea n oieii iaaieoiia
iiea iiaeii n/eoaoue iaeii?iaeiui. O.a. neeiaua eeiee oaeiai iiey
?aniieiaeaiu ia?aeeaeueii ae?oa io ae?oaa. Ia i?iaiaeiee n oieii,
iiiauaiiue a iaeii?iaeiia iaaieoiia iiea aeaenoaoao neea. Aaee/eia neeu
ii?aaeaeyaony ii caeiio Aiia?a. Aeey o/anoea i?iaiaeieea n oieii,
aeeeiie L aai iiaeii caienaoue a aaeoi?iii aeaea a nenoaia aaeeieoe NE
eae:
F = m0 I [ H L ] (15.12)
Caeanue m0 – iinoiyiiay , iaoneiaeaiiay auai?ii nenoaiu aaeeieoe
(NE), L -i?iaiaeiee n oieii I , eioi?ue caaeaaony a aaeoi?iii aeaea, oae
eae eiaao iai?aaeaiea a i?ino?ainoaa. Aai iai?aaeaiea niaiaaeaao n
iai?aaeaieai aeaeaeaiey oiea, o.a. iieiaeeoaeueiuo ca?yaeia.
Ec 15.12 neaaeoao, /oi ia i?iaiaeiee n oieii a iaeii?iaeiii iaaieoiii
iiea aeaenoaoao neea, iai?aaeaiiay ia?iaiaeeeoey?ii aaeoi?o
iai?yaeaiiinoe iaaieoiiai iiey H e iai?aaeaieth aeaeaeaiey oiea
(i?iaiaeieea n oieii L ). A yoii caeeth/aaony i?eioeeieaeueiia ioee/ea
neeiaiai aicaeaenoaey aeo?aaiai iaaieoiiai iiey ia i?iaiue yeaiaio io
iiey eiina?aaoeaiuo nee.
Aeo?aauie auaatho ia oieueei iaaieoiua, ii e yeaeo?e/aneea iiey.
Aeaenoaeoaeueii, aicueiai i?iaiaeiee n oieii a aeaea eieueoea e iinoaaei
aioo?ue iaai aaoa?aeeo. Ca?yaeu (iineoaeyie ca?yaeia a i?iaiaeieeao
yaeythony yeaeo?iiu) aoaeoo aeaeaaoueny ii eieueoeo, nicaeaaay oie.
Aaee/eia oiea I ii?aaeaeyaony ecaanoiui aai caeiiii Iia:
I = E / (ra +R) (15.13),
aaea A – yeaeo?iaeaeaeouay neea (YAeN) aaoa?ae, R e ra – nii?ioeaeaiea
i?iaiaeieea e aioo?aiia nii?ioeaeaiea enoi/ieea YAeN.
?anniio?ei, /oi i?ienoiaeeo a i?iaiaeieea. Eae iu ciaai, yeaeo?iiu
aeaeaathony aaeieue neeiauo eeiee yeaeo?e/aneiai iiey. A
?anniao?eaaaiii iaie i?iaiaeieea yeaeo?iiu aeaeaathony ii caieiooie
e?eaie, ia?acoaiie i?iaiaeieeii. Cia/eo a i?iaiaeieea ?aaeecoaony oaeia
yeaeo?e/aneia iiea, eioi?ia canoaaeyao aeaeaaoueny yeaeo?iiu ii
caieiooie e?eaie.
Neaaeiaaoaeueii, e neeiaua eeiee yeaeo?e/aneiai iiey oiaea
i?aaenoaaeytho ec naay caieiooua e?eaua. O.a. yeaeo?e/aneia iiea a
i?iaiaeieea oaeaea yaeyaony aeo?aaui iieai. Yeaeo?inoaoe/aneia iiea
niiniaii ia?aiauaoue ca?yaeu, ii oieueei aei oiai iiiaioa, iiea
ia?a?ani?aaeaeaiea ca?yaeia ia neiiiaine?oao iiea. Iinea yoiai ca?yaeu
aoaeoo inoaaaoueny iaiiaeaeaeiuie. Iiea a i?iaiaeieea n oieii
noaoeeiia?ii e aucuaaao noaoeeiia?iia aeaeaeaiea ca?yaeia. Cia/eo yoi ia
yeaeo?inoaoe/aneea iiey, a eaeea-oi ae?oaea. Oaeea iiey, niiniaiua
nicaeaaaoue noaoeeiia?iia aeaeaeaiea ca?yaeia, a ioee/ea io
yeaeo?inoaoe/aneeo, iau/ii iacuaatho yeaeo?e/aneeie iieyie,
nicaeaaaaiuie noi?iiieie neeaie. Noi?iiieie, iioiio, /oi yeaeo?e/aneea
ca?yaeu naie ia niiniaiu nicaeaoue oaeea iiey. Niioaaonoaaiii, neeu,
aucuaathuea noaoeeiia?iia aeaeaeaiea ca?yaeia – noi?iiieie neeaie.
Yeaeo?e/aneia iiea noi?iiieo nee niaa?oaao ?aaioo i?e ia?aaeaeaeaiee
ca?yaeia ii caieiooiio eiioo?o. Iia ?aaia i?iecaaaeaieth oiea a eiioo?a
ia YAeN e ia a?aiy, a oa/aiee eioi?iai oae oie: A=IEDt.
Yeaeo?e/aneea iiey noi?iiieo nee iiao auoue nicaeaiu ca n/ao ?acee/iuo
aeaeia yia?aee. Iaoaie/aneie, oaieiaie , oeie/aneie , yaea?iie e
ae?oaeo. Iaoaie/aneay yia?aey, a?auathuay aaia?aoi?u n oieii
i?aa?auaaony a yeaeo?e/aneoth. Aaoa?aeee eee aeeoioeyoi?u ?aaioatho ca
n/ao oeie/aneeo ?aaeoeee. ssaea?iua aaoa?aeee ?aaioatho ca n/ao yaea?iie
yia?aee, aunaiaiaeaeaaiie i?e ?aniaaea eee i?aa?auaiee iaeieo yaea? a
ae?oaea.
Aica?aoeiny oaia?ue iacaae e aeaaeei ii?aaeaeaiea YAeN. YAeN ,
aeaenoaothuay a eiioo?a n oieii, /eneaiii ?aaia ?aaioa A, niaa?oaaiie
i?e ia?aiauaiee aaeeie/iiai ca?yaea q0 ii eiioo?o :
E=A/q0 (5.14)
Iiaeii aeaoue aua iaeii, ii?aaeaeaiea YAeN. Yeaeo?e/aneia iiea,
nicaeaaaaiia noi?iiieie neeaie, iiaeii iaicia/eoue eae Ano. ?aaioa,
niaa?oaaiay i?e ia?aiauaiee ca?yaea ii eiioo?o A ?aaia:
A= Fdr = q0 Eno dr = q0 Eno dr.
Caeanue eioaa?e?iaaiea aa?aony ii eiioo?o, ii eioi?iio oa/ao oie.
A niioaaonoaee n ii?aaeaeaieai YAeN (15.14.), YAeN A ?aaia:
E = A/q0 = Ano dr .
Ae?oaeie neiaaie, YAeN ?aaia oee?eoeyoeee aaeoi?a iai?yaeaiiinoe
yeaeo?e/aneiai iiey noi?iiieo nee. A ioee/ea io yeaeo?inoaoe/aneiai
iiey, iia ia ?aaia ioeth ia caieiooii eiioo?a, a ?aaia YAeN,
aeaenoaothuae ia aeaiiii eiioo?a. Iineieueeo oee?eoeyoeey aaeoi?a
iai?yaeaiiinoe yeaeo?inoaoe/aneiai iiey ?aaia ioeth, aeiaaaeaiey 0 a
aeaeueiaeoai iu ia ao
Iu oaeaeaee, /oi ?aaioa, niaa?oaaiay yeaeo?e/aneei iieai ia ?aaia
ioeth ia caieiooii eiioo?a, anee a iai aeaenoaotho noi?iiiea neeu,
caaeathuea YAeN. Oaeei ia?acii , yeaeo?e/aneea iiey noi?iiieo nee,
eioi?ua yaeythony aeo?aauie iieyie – iaeiina?aaoeaiua iiey.
Oi aea naiia iiaeii neacaoue e i iaaieoiuo iieyo. Anee ?aniieiaeeoue
i?iaiae n oieii a iaaieoiii iiea oae, /oiau neea, aeaenoaothuay ia iaai
ni noi?iiu iaaieoiiai iiey niaiaaeaea au n iai?aaeaieai ia?aiauaiey, oi
?aaioa ii ia?aiauaieth oaeiai i?iaiaeieea, niaa?oaeanue au
iaeiina?aaoeaiuie neeaie.
Aeo?aaua yeaeo?e/aneea iiey iiaoo ?aaeeciauaaoueny ca n/ao ae?oaeo iieae
– iaaieoiuo. Aiaeeeneee o/aiue I.Oa?aaeae a 1831 aiaeo e iacaaeneii io
iaai aia?eeaineee o/aiue Aeae.Aai?e a 1832 aiaeo ioe?uee caeii
yeaeo?iiaaieoiie eiaeoeoeee. Nae/an aai iacuaatho caeiiii
yeaeo?iiaaieoiie eiaeoeoeee Oa?aaeay. Noi?ioee?oai aai a oii aeaea,
eioi?ue iai oaeiaai a aeaeueiaeoai. Anee iaiyoue iioie eiaeoeoeee
iaaieoiiai iiey OI, i?ioiaeyuaai /a?ac i?iaiaeiee, oi a i?iaiaeieea
aicieeaao YAeN, eioi?oth i?eiyoi iacuaaoue YAeN eiaeoeoeee.
Iaoaiaoe/aneay oi?ioee?iaea aai oaeiaa:
E = – m0 dOI / dt = Edr = – m0 dOI / dt (15.15)
YAeN naiieiaeoeoeee i?iii?oeeiiaeueia nei?inoe eciaiaiey iioiea
eiaeoeoeee iaaieoiiai iiey, acyoie n ia?aoiui ciaeii. N ae?oaie noi?iiu,
YAeN ?aaia oee?eoeyoeee aaeoi?a iai?yaeaiiinoe yeaeo?e/aneiai iiey e iu
iiaeai iaienaoue: E= Edr = – m0dOI / dt. Yoa oi?ia caiene caeiia
yeaeo?iiaaieoiie eiaeoeoeee Oa?aaeay auea aaaaeaia Ae.E. Iaenaaeeii e
aoiaeeo a nenoaio o?aaiaiee Iaenaaeea, iienuaathueo yeaeo?iiaaieoiua
iiey.
Caeii yeaeo?iiaaieoiie eiaeoeoeee ia aiai?eo i oii, ca n/ao /aai
iaiyaony iioie eiaeoeoeee iaaieoiiai iiey. Ii iiaeao iaiyony eae ca n/ao
aaee/eiu iaaieoiiai iiey, oae e ca n/ao eciaiaiey ieiuaaeee, /a?ac
eioi?oth i?ioiaeeo iaaieoiue iioie.
Iiyniei auoaneacaiiia i?eia?aie. Ia ?en.15.6 ia?eniaai aeoie i?iaiaea,
iiiauaiiue a iaaieoiia iiea . Aeoie i?eniaaeeiai e oieinuaiieeai. Anee
iu aoaeai a?auaoue aeoie, oi a caaeneiinoe io aai iieiaeaiey, iioie
eiaeoeoeee iaaieoiiai iiey aoaeao iaiyoueny e a iai aaia?e?oaony YAeN.
Yoa YAeN nieiaaony n oieinuaiieeia e iu iieo/aai aaia?aoi? ia?aiaiiiai
oiea.
Aoi?ie i?eia?. Ionoue iu eiaai a i?ino?ainoaa ia?aiaiiia iaaieoiia iiea
H=H0coswt. Yoi iiea aaia?e?oao aie?oa naay ia?aiaiiia yeaeo?e/aneia iiea
E =E0 coswt. Ia?aiaiiia yeaeo?e/aneia iiea oaeaea aeo?aaia. Aai neeiaua
eeiee ia?acotho eieueoea, eae yoi iieacaii ia ?en.15.7. A naith
i/a?aaeue, eae iu ?anniio?ei ianeieueei iicaeiaa, ia?aiaiiia
yeaeo?e/aneia iiea aaia?e?oao ia?aiaiiia aea iaaieoiia iiea e yoa
oeaii/ea i?iaeieaeaaony a i?ino?ainoaa. Ia?acoaony iiaue aeae iiey-
yeaeo?iiaaieoiia iiea, eioi?ia ?ani?ino?aiyaony a i?ino?ainoaa eae
yeaeo?iiaaieoiua aieiu.
?en.15.6 ?en.15.7
A caeeth/aiee yoiai ?acaeaea ?anniio?ei nenoaio o?aaiaiee Iaenaaeea,
eioi?ay iienuaaao aaeeiui ia?acii ana yeaeo?e/aneea e iaaieoiua yaeaiey.
Yoa nenoaia auea iieo/aia Ae.E. Iaenaaeeii a 60 aiaeao i?ioeiai noieaoey
ia iniiaa iaiauaiey yiie?e/aneeo caeiiia yeaeo?e/aneeo e iaaieoiuo
yaeaiee e eaeae I.Oa?aaeay, /oi acaeiiaeaenoaea iaaeaeo ca?yaeaie
inouanoaeyaony iin?aaenoaii yeaeo?iiaaieoiuo iieae. Oaeoe/anee iu oaea
?anniio?aee aieueooth /anoue o?aaiaiee.
Ia?auie aeaoiy o?aaiaieyie yaeythony ?anniio?aiiua iaie o?aaiaiey i
iioieao eiaeoeoeee yeaeo?e/aneiai e iaaieoiiai iiey. Iioie eiaeoeoeee
yeaeo?e/aneiai iiey /a?ac caieioooth iiaa?oiinoue ?aaai ca?yaeo aioo?e
yoie iiaa?oiinoe , aeaeaiiiio ia aeeyeaeo?e/aneoth iinoiyiioth aaeooia.
Iioie eiaeoeoeee iaaieoiiai iiey /a?ac caieioooth iiaa?oiinoue ?aaai
ioeth. Yoe o?aaiaiey auee iaiauaiu Ae.Iaenaaeeii ia neo/ae ia?aiaiiuo
iieae. O.a. iie ni?aaaaeeeau e iiaoo auoue i?eiaiaiu eae e iinoiyiiui,
oae e e ia?aiaiiui iiey. Oece/aneee niune yoeo o?aaiaiee aeinoaoi/ii
iaaeyaeai. Yeaeo?e/aneea iiey iiaoo ia/eiaoueny e caeai/eaaoueny oieueei
ia ca?yaeao. Yeaeo?e/aneia iiea iiaeao auoue oeaio?aeueiui e aeo?aaui.
Iaaieoiua iiey anaaaea ia/eiathony e caeai/eaathony naie ia naaa. Iie
anaaaea aeo?aaua.
O?aouea o?aaiaiea Iaenaaeea – iaiauaiea caeiia yeaeo?iiaaieoiie
eiaeoeoeee Oa?aaeay. Iii naycuaaao iaaieoiia e yeaeo?e/aneia iiea. Aai
neaaenoaeai yaeyaony aicieeiiaaiea aeo?aaiai ia?aiaiiiai yeaeo?e/aneiai
iiey i?e iaee/ea iaiythuaainy iioiea eiaeoeoeee iaaieoiiai iiey.
*aoaa?oia o?aaiaiea Iaenaaeea aace?oaony ia ?anniio?aiiie iaie oai?aia i
oee?eoeyoeee aaeoi?a iai?yaeaiiinoe iaaieoiiai iiey: oee?eoeyoeey
aaeoi?a iai?yaeaiiinoe iaaieoiiai iiey ii caieiooiio eiioo?o ?aaia oieo
(oieo i?iaiaeeiinoe), i?ioiaeyuaio /a?ac yoio eiioo?. Oai?aia
ni?aaaaeeeaa eae aeey iinoiyiiuo, oae e aeey ia?aiaiiuo iaaieoiuo iieae.
Iaeiaei, a neo/aa ia?aiaiiuo iaaieoiuo iieae , Iaenaaee aaae ia?yaeo n
oieii i?iaiaeeiinoe oie niauaiey. Oie niauaiey i?iii?oeeiiaeai nei?inoe
eciaiaiey iioiea eiaeoeoeee yeaeo?e/aneiai iiey. Oaeoe/anee yoi
icia/aao, /oi , anee eiaaony ia?aiaiiia yeaeo?e/aneia iiea, oi iii
aaia?e?oao ia?aiaiiia iaaieoiia iiea. Oa naiui o?aouea e /aoaa?oia
o?aaiaiey Iaenaaeea naycuaatho iaaeaeo niaie ia?aiaiiua yeaeo?e/aneea e
iaaieoiua iiey.
Nenoaia o?aaiaiee Iaenaaeea eaaeeo a iniiaa ?yaea ?acaeaeia oeceee. A
ia?aoth i/a?aaeue – eeanne/aneie yeaeo?iaeeiaieee. Yeaeo?iaeeiaieea
iienuaaao iiaaaeaiea e acaeiiaeaenoaea iinoiyiiuo e ia?aiaiiuo oieia e
ca?yaeia, ?ani?ino?aiaiea iieae ( yeaeo?e/aneeo, iaaieoiuo e
yeaeo?iiaaieoiuo) a i?ino?ainoaa.
N?aaee anao ecaanoiuo aeaeia acaeiiaeaenoaey yeaeo?iiaaieoiia caieiaao
ia?aia ianoi ii oe?ioa e ?aciiia?aceth. Yoi naycaii n oai, /oi ana oaea
ninoiyo ec iieiaeeoaeueii e io?eoeaoaeueii ca?yaeaiiuo /anoeoe,
yeaeo?iiaaieoiia acaeiiaeaenoaea iaaeaeo eioi?uie ia iiiai ii?yaeeia
neeueiaa a?aaeoaoeeiiiiai , e eiaiii iii ioaaonoaaiii ca iiiaiia?acea
oece/aneeo e oeie/aneeo i?ioeannia iaaeaeo aoiiaie e iieaeoeaie.
16.EIEAAAIEss E AIEIU
16.1. Eieaaaiey, aeaeu eieaaaoaeueiuo i?ioeannia.
A i?e?iaea e a aieaa neiaeiuo no?oeoo?ao, oaeeo eae iauanoai, iu /anoi
ano?a/aainy n i?ioeannii eciaiaiey eaeiai eeai ia?aiao?a ai a?aiaie. Iu
iaaethaeaai niaio aeiy e ii/e, naciiia a aiaeo, ia?eiaee/aneeo eciaiaiee
noieiinoe aeoeee e oae aeaeaa. Anee eciaiaiey eaeiai-eeai ia?aiao?a
iiaoi?ythony ai a?aiaie, eo i?eiyoi iacuaaoue eieaaaoaeueiuie
i?ioeannaie. Eiathueany o ian /oanoaa – c?aiea e neoo oaeaea naycaiu n
eieaaaieyie. Aieaa 90( eioi?iaoeee /aeiaae iieo/aao i?e iiiiue c?aiey e
neooa, o.a. i?e iiiiue aini?eyoey eieaaaiee yeaeo?iiaaieoiiai iiey –
naaoa e eieaaaiee aeaaeaiey aicaeooa – caoea.
Ia?aeaeai e aieaa no?iaei ea/anoaaiiui e eiee/anoaaiiui oi?ioee?iaeai
eieaaaiee. Eieaaaoaeueiui iacuaaaony oaeie i?ioeann, i?e eioi?ii
ninoiyiea nenoaiu, eciaiyynue, iiiaie?aoii iiaoi?yaony ai a?aiaie.
Iaeaieaa ?ani?ino?aiaiu e aeaoaeueii eco/aiu ia?eiaee/aneea
eieaaaoaeueiua i?ioeannu. A yoeo i?ioeannao nenoaia /a?ac ii?aaeaeaiiue
i?iiaaeooie a?aiaie, iacuaaaiui ia?eiaeii eieaaaiee (O), aica?auaaony a
enoiaeiia ninoiyiea. I?eia?ii ia?eiaee/aneiai eieaaaoaeueiiai i?ioeanna
iiaoo neoaeeoue aeaeaeaiey iayoieea, ea/aeae, i?uaathuaai iy/a e o.ae.
A iauai neo/aa eieaaaiea iiaeao niaa?oaoue iaoa?eaeueiia oaei,
oece/aneee ia?aiao?, oa?aeoa?ecothuee iiea eee n?aaeo, a oaeaea, ethaie
ia?aiao?, iienuaathuee neiaeioth nenoaio, iai?eia?, iauanoai.
Anee oece/aneay aaee/eia X eciaiyaony ii caeiio:
aaea A – aiieeooaea, (0(2((O ( e?oaiaay /anoioa eieaaaiee, (0 –
ia/aeueiay oaca, oi oaeea eieaaaiey iacuaathony aa?iiie/aneeie.
?anniio?ei yeaiaiou aeeiaieee aa?iiie/aneeo eieaaaiee. Aeey i?inoiou
nia/aea inoaiiaeiny ia iaoaie/aneeo eieaaaieyo, aeey eioi?uo O eiaao
niune niauaiey iaoa?eaeueiie oi/ee ec iieiaeaiey ?aaiiaaney. Ec (18.1)
aeeooa?aioee?iaaieai iaeaeai nei?inoue e onei?aiea yoie iaoa?eaeueiie
oi/ee.
Iaeaeai neeo, iiae aeaenoaeai eioi?ie niaa?oathony aa?iiie/aneea
eieaaaiey. Aoi?ie caeii Iuethoiia, iienuaathuee aeaeaeaiea oi/ee aaeieue
ine (io), i?eieiaao aeae:
Oi?oaea e eaaceoi?oaea neeu anaaaea yaeythony oeaio?aeueiuie, oae eae
caaenyo oieueei aaee/eiu niauaiey oaea. Neaaeiaaoaeueii, yoe neeu
yaeythony eiina?aaoeaiuie. Aeey ieo ieacuaaaony aiciiaeiui aaanoe
iioaioeeaeueioth yia?aeth, eioi?ay ?aaia iioaioeeaeueiie yia?aee oi?oaie
(eaaceoi?oaie) aeaoi?iaoeee.
. Caieoai au?aaeaiea aeey eeiaoe/aneie yia?aee eieaaethuaainy oaea.
Ia?aoei aieiaiea ia oi, /oi iaa aeaea yia?aee eciaiythony a i?aaeaeao io
ioey aei iaeneiaeueiiai cia/aiey, i?e/ai iaeneiaeueiua cia/aiey
eeiaoe/aneie e iioaioeeaeueiie yia?aee oaea iaeeiaeiau. Eeiaoe/aneay e
iioaioeeaeueiay yia?aey iaiythony a i?ioeaioaca. A iiiaiou a?aiaie,
eiaaea oaei i?ioiaeeo iieiaeaiea ?aaiiaaney, any aai yia?aey
ii?aaeaeyaony eeiaoe/aneie yia?aeae. A iiiaiou a?aiaie, eiaaea
aiieeooaea oaea noaiiaeony iaeneiaeueiie, aai yia?aey ii?aaeaeyaony
iioaioeeaeueiie yia?aeae. Iieiay iaoaie/aneay yia?aey ?aaia:
Iieiay iaoaie/aneay yia?aey, eae e neaaeiaaei iaeeaeaoue, ieacaeanue
iinoiyiiie.
E?iia eiina?aaoeaiuo nee, a ?aaeueiie nenoaia iiaoo aeaenoaiaaoue e
iaeiina?aaoeaiua neeu, iai?eia? neeu o?aiey. I?e eo iaee/ee iaoaie/aneay
yia?aey nenoaiu ia?aoiaeeo ai aioo?aiithth yia?aeth, o.a. eaeao ia
iaa?aa oaea. Iieiay iaoaie/aneay yia?aey a yoii neo/aa ia nio?aiyaony,
iia oauaaao ni a?aiaiai. Cia/eo, aeieaeia oiaiueoaony e aiieeooaea
eieaaaiee nenoaiu A. Anee neeu o?aiey i?yii i?iii?oeeiiaeueiu nei?inoe
oaea Fo?(b(( (ayceia o?aiea), aiieeooaea eieaaaiee A(t) caaeneo io
a?aiaie neaaeothuei ia?acii:
.
Aiieeooaea eieaaaiee oauaaao ii yeniiiaioa, ia?aiao?u eioi?ie
ii?aaeaeythony ia/aeueiie nei?inoueth e neeaie o?aiey. Iieo/eaoeany
eieaaaiey iacuaathony caoooathueie. Ioiaoei, /oi caoooathuea eieaaaiey
i?ioaeatho iaaeeaiiaa, /ai eieaaaiey a oie aea nenoaia aac o?aiey. Eo
/anoioa iaiiiai iaiueoa, a ia?eiae, niioaaonoaaiii, iaiiiai aieueoa.
.
?en.18.1 ?en.18.2
Aeey oiai, /oiau aiieeooaea eieaaaiee ia oiaiueoaeanue iiae aneaaenoaea
iioa?ue yia?aee, a nenoaio iaiaoiaeeii aeiaaaeyoue yia?aeth ecaia.
Aeiaaaeyaiay yia?aey aeieaeia eiiiaine?iaaoue iioa?e. Nouanoaotho ?aciua
niiniau ia?aaea/e yia?aee a nenoaio. *aua anaai a oaoieea eieoeee?otho
oae iacuaaaiua auioaeaeaiiua eieaaaiey. Auioaeaeaiiua eieaaaiey
aicieeatho iiae aeaenoaeai aiaoiae ia?eiaee/aneie neeu n /anoioie (. Yoa
/anoioa iiaeao ia niaiaaeaoue n /anoioie nianoaaiiuo (() eee caoooathueo
((() eieaaaiee. Eieaaaiey ia/eiathony n?aco ia aeaoo /anoioao:
auioaeaeaiiua ia /anoioa ( e caoooathuea ia /anoioa ((. Caoooathuea
eieaaaiey auno?i caoooatho, e inoathony oieueei iacaoooathuea
auioaeaeaiiua eieaaaiey. Aiieeooaea auioaeaeaiiuo eieaaaiee yaeyaony
ooieoeeae /anoiou auioaeaeathuae neeu (. Yoa caaeneiinoue i?eaaaeaia ia
?en.18.2 aeey nenoai n aieueoei (1) e iaeui o?aieai (2). Anee /anoioa
auioaeaeathueo eieaaaiee – ( aeecea e /anoioa nianoaaiiuo eieaaaiee
nenoaiu – (, oi ianooiaao oae iacuaaaiia yaeaiea ?aciiaina. I?e
?aciiaina aiieeooaea eieaaaiee nenoaiu iaeneiaeueia.
Anee iioa?e, aucaaiiua neeaie o?aiey, aeinoaoi/ii iaeu, oi aiieeooaea
eieaaaiee iiaeao noaoue oaeie aieueoie, /oi nenoaia iiaeao aeaaea
?ac?ooeony. Ecaanoai neo/ae ?ac?ooaiey iinoa iiae aeaenoaeai aao?a,
aucaaaoaai neeueiua eieaaaiey. A aaeaoeee ecaanoai oa?iei, iacuaaaiue
oeaooa?ii, eiaaea aiieeooaea eieaaaiee aeaoaeae naiieaoia noaiiaeony
ianoieueei aieueoie, /oi naiieaou ?ac?ooathony a aicaeooa.
Nouanoaotho e ae?oaea niiniau ia?aaea/e yia?aee nenoaia aeey
inouanoaeaiey ia?eiaee/aneeo iacaoooathueo eieaaaiee. A i?inoaeoai
neo/aa, eioi?ue eiaao ianoi a iaoaie/aneeo /anao, yia?aey iaoaie/aneie
i?oaeeiu ia?eiaee/anee n /anoioie 1 Aoe iiaeaiaeeony e iayoieeo.
Eioa?anai neo/ae aicaoaeaeaiey iacaoooathueo eieaaaiee a nenoaia, n
iiiiuueth yia?aee, iiaeaiaeeiie iai?a?uaii. I?eia?ii aicieeiiaaiey oaeeo
eieaaaiee – aaoieieaaaiee iiaoo neoaeeoue o?oau i?aaiia e ae?oaeo
iocueaeueiuo eino?oiaio eia. Iioie aicaeooa i?ioiaeeo n iinoiyiiie
nei?inoueth /a?ac i?aaiioth o?oao e ia?aaeaao ae yia?aeth, ca n/ao
eioi?ie o?oaa ecaeaao caoee ii?aaeaeaiiie oiiaeueiinoe. Eae iiaeii a
yoii neo/aa iauynieoue i?ioeann aicieeiiaaiey ia?eiaee/aneeo eieaaaiee?
Aaoieieaaaiey aiciiaeiu oieueei oiaaea, eiaaea yia?aey, ia?aaeaaaaiay
nenoaia iaeeiaeii caaeneo io eaeiai-oi ia?aiao?a, iai?eia? io nei?inoe
nenoaiu. A ?aciua iiiaiou a?aiaie nei?inoue noaiie o?oau, n eioi?ie
nii?eeanaaony iioie aicaeooa, ?acee/ia. E iioie aicaeooa n ?aciie neeie
«o?aony» i noaiee, o.a. ia?aaeaao ae ?acioth yia?aeth. Eieaaaiey noaiie
o?oau iienuaathony iau/iuie o?aaiaieyie eieaaaiee (18.1-18.3)
Neaaeiaaoaeueii, yia?aey, ia?aaeaaaaiay iioieii aicaeooa i?aaiiie o?oaa
oaeaea aoaeao iaiyoueny ii caeiio aa?iiie/aneiai eieaaaiey. A eiia/iii
n/aoa i?ioeann ia?aaea/e yia?aee io iioiea aicaeooa e noaieai o?oau
oaeaea aoaeao iineoue ia?eiaee/aneee oa?aeoa?. Ia?eiae yoiai i?ioeanna
ii?aaeaeyaony nianoaaiiuie /anoioaie eieaaaiee o?oau. Eiaao ianoi
yaeaiea ?aciiaina, i?e eioi?ii aiieeooaea eieaaaiee noaiiaeony i/aiue
aieueoie i?e n?aaieoaeueii iaaieueoeo cao?aoao yia?aee. Eiaiii yoei
yaeaieai iauyniyaony «oeaooa?» e ?ac?ooaiea iinoa neeueiui iioieii
aicaeooa.
18.2 ?ani?ino?aiaiea eieaaaiee, caoeiaua e yeaeo?iiaaieoiua aieiu.
Oi?oaie iacuaaaony n?aaea, eioi?ay iiaeao nii?ioeaeyoueny aeaoi?iaoeee.
Aicueiai, iai?eia?, iaoaeee/aneoth eeiaeeo. Cae?aiei iaeei aa eiiaoe, a
ia aoi?ie iiaeaenoaoai n iaeioi?ie neeie. Aeey oiai, /oiau niaiooue
eeiaeeo o?aaoaony i?eeeaaeuaaoue neeo, eioi?ay o?aaiiaaoeaaaony neeaie,
aeaenoaothueie ni noi?iiu ninaaeieo o/anoeia eeiaeee. *a?ac iaeioi?ia
a?aiy iinea i?ae?auaiey aeaenoaey aiaoiae neeu eeiaeea ?aciaiaony e
ia?aeaeao a i?yiia ninoiyiea. Yoi i?eia? aeaenoaey oi?oaeo nee a
oaa?aeuo oaeao. A aacao oaeaea nouanoaotho oi?oaea neeu. Aicueiai
ii?oaiue a oeeeeiae?a e iiiuoaainy naeaoue aac a oeeeeiae?a. Oi?oaea
neeu, aicieeathuea ec-ca ecauoi/iiai aeaaeaiey aaca, aoaeoo no?aieoueny
aa?iooue ii?oaiue a iieiaeaiea ?aaiiaaney. AEeaeeinoe oiaea yaeythony
oi?oaeie n?aaeaie, a ieo oiaea aicieeatho oi?oaea neeu.
Ioee/ea oi?oaeo nee a oaa?aeuo oaeao io oi?oaeo nee a aeeaeeinoyo e
aacao, caeeth/athony a oii, /oi, a oaa?aeuo oaeao oi?oaea neeu
aeaenoaotho ai anao iai?aaeaieyo, iacaaeneii io oiai, eoaea iu no?aieiny
i?eeiaeeoue neeo. A aacao oi?oaea neeu aicieeatho oieueei oiaaea eiaaea
iu no?aieiny eciaieoue ia?aiia/aeueiue iauai aaca. Ae?oaeie neiaaie,
oaa?aeia oaei nii?ioeaeyaony eciaiaieth naiaai iauaia e naiae oi?iu, a
aeeaeeinoe e aacu – oieueei eciaiaieth iauaia.
Anee canoaaeoue eieaaaoueny o/anoie oi?oaie n?aaeu, oi iiae aeaenoaeai
oi?oaeo nee yoe eieaaaiey aoaeoo ia?aaeaaaoueny ninaaeiei o/anoeai
n?aaeu. I?ioeann ?ani?ino?aiaiey eieaaaiee a oi?oaie n?aaea iacuaatho
aieiaie. A iauai neo/aa aieia – yoi i?ioeann ?ani?ino?aiaiey eieaaaiee
eaeiai-oi ia?aiao?a (niauaiey aoiiia a oaea, aeaaeaiey a aacao,
iai?yaeaiiinoe yeaeo?e/aneiai iiey eee aua /aai-ieaoaeue) a
i?ino?ainoaa. A aeeaeeinoyo e aacao eieaaaiey iiaoo auoue iai?aaeaiu
oieueei aaeieue iai?aaeaiey ?ani?ino?aiaiey aieiu. Oaeea aieiu
iacuaathony i?iaeieueiuie.
A oaa?aeuo oaeao eieaaaiey iiaoo niaa?oaony eae aaeieue iai?aaeaiey
?ani?ino?aiaiey aieiu, oae e iiia?ae. Aieiu, o eioi?uo eieaaaiea
niaa?oaaony ia?iaiaeeeoey?ii iai?aaeaieth ?ani?ino?aiaiey iacuaathony
iiia?a/iuie. I?eia?ii i?iaeieueiuo aiei a aacao yaeyaony caoe. I?eia?ii
iiia?a/iuo aiei yaeythony yeaeo?iiaaieoiua aieiu, o eioi?uo eieaaethony
iai?yaeaiiinoe yeaeo?e/aneeo e iaaieoiuo iieae.
aa?aaee aoaeao naiy. Ii aa?aaea aoaeao ?ani?ino?aiyoueny eieaaaiea,
o.a. aicieeiao oae iacuaaaiay aaaouay aieia.
Aaaaeai ia?aiao?u, oa?aeoa?ecothuea aieio. Ieieiaeueiia ?annoiyiea
iaaeaeo aeaoiy o/anoeaie aa?aaee, eieaaethueieny a iaeeiaeiaie oaca
iaciaai aeeeiie aieiu (, ni.?en.18.3. O/anoee aa?aaee n iinoiyiiie oacie
eieaaaiey ia?aiauathony neaaa iai?aai. Nei?inoue ia?aiauaiey iinoiyiiie
oacu eieaaaiey iacuaatho oaciaie nei?inoueth – (. Ca a?aiy, ?aaiia
iaeiiio ia?eiaeo eieaaaiee(((T, aieia ii?iaaaaao ?annoiyiea, ?aaiia aa
aeeeia((((.
.
Iiaa?oiinoue, ana oi/ee eioi?ie eieaaethony a iaeeiaeiaie oaca,
iacuaaaony aieiiaie iiaa?oiinoueth. Aaiiao?e/aneia ianoi oi/ae, eioi?uo
aeinoeaei aiciouaiea io enoi/ieea iacuaaaony aieiiaui o?iioii. Yoe
iiiyoey i/aiue iioiaee, ii ia oiaeaeanoaaiiu. Aieiiaie o?iio
ia?aiauaaony ni nei?inoueth aieiu, a aieiiaua iiaa?oiinoe iaiiaeaeaeiu
eeoue a iaeei iiiaio a?aiaie iie niaiaaeatho ae?oa n ae?oaii. Anee,
iai?eia?, eieiiia iaoei aaeao ii aei?iaa, oi ia?aoth iaoeio iiaeii
oiiaeiaeoue aieiiaiio o?iioo, a ano?a/athueany ia iooe eeeiiao?iaua
noieau – aieiiaui iiaa?oiinoyi. Ionoue aieia ?ani?ino?aiyaony ec oi/ee I
aaeieue ine (oz). Iaeaeai oaco aieiu a i?iecaieueiie oi/ea z
(ni.?en.18.4).
?en.18.3 ?en.18.4
eiaai:
Caeanue k – aieiiaia /enei, eioi?ia iieacuaaao neieueei aeeei aiei (
oeeaaeuaaaony ia io?acea, aeeeiie 2(.
Iieo/aiiia au?aaeaiea iacuaaaony o?aaiaieai aaaouae aieiu. Iii
ii?aaeaeyao eieaaaiea aieiu a eaaeaeie oi/ea i?ino?ainoaa, yaeyynue
ooieoeeae eii?aeeiaou z e a?aiaie t.
*anoi, e?iia e?oaiaie /anoiou eieaaaiee ((2(/T eniieuecotho
oeeeee/aneoth /anoioo ((1/T. *anoioa ecia?yaony a Aa?oeao, 1 Aoe – yoi 1
eieaaaiea a naeoiaeo. A iauai neo/aa aianoi niauaiey oi/ee n?aaeu ec
iieiaeaiey ?aaiiaaney iiaeii aaanoe ethaie “eieaaethueeny” ia?aiao?.
Aeey caoeiauo aiei oaeei ia?aiao?ii yaeyaony aeaaeaiea aaca a aeaiiie
oi/ea i?ino?ainoaa. Caoeiaua aieiu – i?iaeieueiua aieiu e oece/anee
naiaeyony e i?ioeanno ?ani?ino?aiaiey a aaca eieaaaiee aeaaeaiey. Yoe
eieaaaiey iau/ii nicaeatho iooai eieaaaiee iaia?aiu ia?iaiaeeeoey?ii aa
ieineinoe. Aicieeathuea ia?aiaaeu aeaaeaiey e i?aaenoaaeytho niaie
caoeiaoth aieio. Iaeanoue /anoio, eioi?ua neuoeo /aeiaa/aneia ooi eaaeeo
a aeeaiaciia 20-20000 Aoe.
Ae?oaei /?acau/aeii aaaeiui aeaeii aiei yaeythony yeaeo?iiaaieoiua
aieiu. Yeaeo?iiaaieoiua aieiu iiaoo aicieeaoue e ?ani?ino?aiyony a
ionoii i?ino?ainoaa, o.a. a aaeooia. Ec o?aaiaiee Iaenaaeea neaaeoao,
/oi ia?aiaiiia iaaieoiia iiea nicaeaao aie?oa naay a i?ino?ainoaa
ia?aiaiiia yeaeo?e/aneia iiea. A naith i/a?aaeue, ia?aiaiiia
yeaeo?e/aneia iiea nicaeaao aie?oa naay a i?ino?ainoaa ia?aiaiiia
iaaieoiia iiea. Yoio i?ioeann i?eaiaeeo e iiyaeaieth a i?ino?ainoaa
iaeioi?ie aieiu – yeaeo?iiaaieoiie aieiu. Yoa aieia yaeyaony iiia?a/iie.
Iai?yaeaiiinoe yeaeo?e/aneiai e iaaieoiiai iieae aieiu ia?iaiaeeeoey?iu
ae?oa ae?oao e iai?aaeaieth ?ani?ino?aiaiey aieiu. Ia ?en.18.5 iieacaiu
iai?yaeaiiinoe yeaeo?e/aneiai e iaaieoiiai iieae a aaaouae aieia.
?en.18.5
Iniaaiiinoueth yeaeo?iiaaieoiuo aiei yaeyaony oi, /oi aeey eo
?ani?ino?aiaiey ia o?aaoaony ieeaeie n?aaeu. Ia?aiaiiua yeaeo?iiaaieoiua
iiey iiaoo ?ani?ino?aiyoueny a aaeooia.
Aeey eiee/anoaaiiiai iienaiey aiei aaiaeyo aeaa iiiyoey: eioaineaiinoue
aieiu e iauaiioth ieioiinoue yia?aee aieiu. Eioaineaiinoue aieiu – yoi
n?aaeiyy ii a?aiaie yia?aey, ia?aiineiay aieiaie /a?ac aaeeie/ioth
ieiuaaeue, ia?aeeaeueioth aieiiaiio o?iioo, ca aaeeieoeo a?aiaie.
Iauaiiay ieioiinoue yia?aee – yoi yia?aey aiei, i?eoiaeyuayny ia
aaeeieoeo iauaia. Aieia – yoi i?ioeann ?ani?ino?aiaiey eieaaaiee a
i?ino?ainoaa (a oi?oaie n?aaea , eae yoi eiaao ianoi aeey caoeiauo aiei,
eee a aaeooia, eae yoi eiaao ianoi aeey yeaeo?iiaaieoiuo aiei). Yia?aey
eieaaaiee ii?aaeaeyaony aiieeooaeie e /anoioie. Iia i?iii?oeeiiaeueia
eaaae?aoo aiieeooaeu eieaaaiee. A nenoaia NE eioaineaiinoue aieiu
au?aaeaaony a Ao/i2.
Aac auaiaea i?eaaaeai au?aaeaiey aeey eioaineaiinoe e nei?inoe caoeiaie
e yeaeo?iiaaieoiie aiei. Aeey caoeiaie aieiu:
aaea A – aiieeooaea eieaaaiee n?aaeu, ( –
/anoioa, (, (//, (( – nei?inoue aieiu, i?iaeieueiie e iiia?a/iie, ( –
ieioiinoue n?aaeu, a eioi?ie ?ani?ino?aiyaony caoeiaay aieia, ( –
eiooeoeeaio THiaa, G – eiyooeoeeaio naeaeaa.
?ani?ino?aiaiea caoea a oi?oaie n?aaea naycaii n iauaiiie aeaoi?iaoeeae.
Iiyoiio aeaaeaiea a eaaeaeie oi/ea n?aaeu iai?a?uaii eieaaeaony n
/anoioie ( aie?oa iaeioi?iai n?aaeiaai cia/aiey. Aeaaeaiea, aucaaiiia
caoeiaie aeaoi?iaoeeae n?aaeu iacuaaaony caoeiaui aeaaeaieai.
Iaoa ooi aini?eieiaao caoeiaua aeaaeaiey iaiaeeiaeiai ia ?aciuo
/anoioao. Iaeanoue /anoio ,eioi?ua aini?eieiaao ooi eaaeeo a aeeaiaciia
20 – 20000 Aoe. Iaeaieueoae /oanoaeoaeueiinoueth ooi iaeaaeaao a
aeeaiaciia /anoio ieiei 1000 Aoe. Ia yoeo /anoioao ooi niiniaii
aini?eieiaoue caoee, caoeiaia aeaaeaiea a eioi?uo ioee/aaony ia 7
ii?yaeeia.
Aeey eioaineaiinoe yeaeo?iiaaieoiie aieiu ni?aaaaeeeai:
, aaea Ei e Hi aiieeooaeu iai?yaeaiiinoe yeaeo?e/aneiai e
iaaieoiiai iieae, ( e ( aeeyeaeo?e/aneay e iaaieoiay i?iieoeaaiinoe
n?aaeu, (i e (i aeeyeaeo?e/aneay e iaaieoiay i?iieoeaaiinoe aaeooia –
iinoiyiiua, aaaaeaiiua a nenoaia NE. Nei?inoue ?ani?ino?aiaiey
yeaeo?iiaaieoiuo aiei a n?aaea ?aaia
, iiyoiio nei?inoue yeaeo?iiaaieoiie aieiu a aaeooia aoaeao ?aaia
.
Eae aeaeii, iia ?ania nei?inoe naaoa a aaeooia – n, /oi ia
oaeeaeoaeueii, iineieueeo naao yaeyaony yeaeo?iiaaieoiuie aieiaie.
18.3 Aieiiaua yaeaiey: iiey?ecaoeey, eioa?oa?aioeey, aeeo?aeoeey e
aeenia?ney.
?ani?ino?aiaiea aiei a i?ino?ainoaa e eo acaeiiaeaenoaea ni n?aaeie
i?eaiaeeo e iiyaeaieth oeaeiai eeanna yaeaiee, eioi?uo iao i?e
iaoaie/aneii aeaeaeaiee oae. ?anniio?ei iniiaiua ec ieo aeey caoeiauo e
yeaeo?iiaaieoiuo aiei.
A iiia?a/iuo aieiao (e eioi?ui ioiinyony yeaeo?iiaaieoiua) eieaaaiey
i?ienoiaeyo ia?iaiaeeeoey?ii iai?aaeaieth ?ani?ino?aiaiey aieiu. Yoe
eieaaaiey iiaoo auoue eae oii?yaei/aiiuie, oae e iaoii?yaei/aiiuie.
Iai?eia?, eieaaaiey iiaoo i?ienoiaeeoue oieueei a iaeiii auaeaeaiiii
iai?aaeaiee. Aieiu, o eioi?uo eieaaaiey niaa?oathony a iaeiie ieineinoe,
iacuaathony ieinei iiey?eciaaiiuie.
A eaaeaeie oi/ea i?ino?ainoaa aieia i?aaenoaaeyao niaie eieaaaiea n
ii?aaeaeaiiie ia/aeueiie oacie. Aeaa eieaaaiey a aua?aiiie oi/ea
i?ino?ainoaa neeaaeuaathony ae?oa n ae?oaii. Ia?aie/einy neo/aai, eiaaea
neeaaeuaathony aieiu n iaeeiaeiauie /anoioaie. Anee neeaaeuaathony aeaa
eieaaaiey a iaeeiaeiaie oaca, oi aiieeooaea ?acoeueoe?othuaai eieaaaiey
iaeneiaeueia e ?aaia noiia aiieeooae. Anee aea neeaaeuaathony aeaa
eieaaaiey a i?ioeaioaca, oi ?acoeueoe?othuay aiieeooaea aoaeao
ieieiaeueia e ?aaia iiaeoeth ?aciinoe aiieeooae yoeo eieaaaiee. I?e
i?iecaieueiie ?aciinoe oac neeaaeuaathueony eieaaaiee aiieeooaea
?acoeueoe?othuaai eieaaaiey iiaeao iaiyoueny io ioey aei iaeneioia.
Anee, iai?eia?, neeaaeuaathony aeaa eieaaaiey n iaeeiaeiauie
aiieeooaeaie e iaeeiaeiauie oacaie, oi ?acoeueoe?othuay aiieeooaea
oaeaieony, a eioaineaiinoue aic?anoao a /aou?a ?aca. Anee aea eieaaaiey
n ?aaiuie aiieeooaeaie neiaeaony a i?ioeaioaca, oi eieaaaiey iieiinoueth
iiaanyo ae?oa ae?oaa, e eioaineaiinoue ?acoeueoe?othuaai eieaaaiey
ieaaeaony ?aaiie ioeth. Eioaineaiinoue aeaoo neeaaeuaathueony aiei ia
?aaia noiia eo eioaineaiinoae. ssaeaiea noaoeeiia?iiai ai a?aiaie
oaaee/aiey eioaineaiinoe aiei a iaeieo oi/eao i?ino?ainoaa e
oiaiueoaiey a ae?oaeo iacuaaaony eioa?oa?aioeeae. Aua ?ac iiae/a?eiai,
/oi aeey iaaethaeaiey eioa?oa?aioeee iaiaoiaeeii, /oiau /anoiou
eieaaaiee auee iaeeiaeiauie. Oaeea aieiu iacuaathony eiaa?aioiuie.
Ia?yaeo n ieineeie aieiaie, eioi?ua iu ?anniao?eaaee aei neo ii?,
nouanoaotho e ae?oaea oeiu aiei, iai?eia?, noa?e/aneea eee
oeeeeiae?e/aneea. Iaiiiiei, /oi oei aieiu eee oi?ia aieiiaie iiaa?oiinoe
ii?aaeaeyaony oi?iie enoi/ieea e caeiiii aai eieaaaiey. Noa?e/aneee
enoi/iee, eae i?aaeei, nicaeaao noa?e/aneea aieiu. Oaeea aieiu ia eiatho
auaeaeaiiiai iai?aaeaiey e ?ani?ino?aiythony ai anao iai?aaeaieyo
iaeeiaeiai. Anee a n?aaea iao iaeiina?aaoeaiuo nee, oi aiieeooaea
eieaaaiee oaeeo aiei oauaaao ia?aoii i?iii?oeeiiaeueii ?annoiyieth, a
eioaineaiinoue, niioaaonoaaiii, ia?aoii i?iii?oeeiiaeueii eaaae?aoo
?annoiyiey.
Aaaaeaiea noa?e/aneeo aiei iaiaoiaeeii aeey iiieiaiey aua iaeiiai /enoi
aieiiaiai yaeaiey – aeeo?aeoeee. Iiae aeeo?aeoeeae iiieiatho iaeaaiea
aieiaie i?aiyonoaey e eo caoiaeaeaiea a iaeanoue aaiiao?e/aneie oaie.
I?aaenoaaei naaa neaaeothuoth neooaoeeth. O ian anoue cae?uoay eiiiaoa a
iaeiie ec noai eioi?ie anoue ieii. Iai?ioea noaiu n ieiii noieo no?aeie
e no?aeyao a iaai. Anoanoaaiii, anee ioee ia ?eeioaoyo, ana iie iiiaaeoo
a noaieo ca ieiii e ieeiaaea ia aeinoeaioo aieiauo noai. Anee iu
?anniao?eaaai aeaeaeaiea iaoa?eaeueiuo oae, oi yoe oaea (a ionoonoaea
neeiauo aicaeaenoaee) a niioaaonoaee n ia?aui caeiiii Iuethoiia
aeaeaathony i?yiieeiaeii. Anee ia eo iooe ano?a/athony i?aiyonoaey, oaea
ia iaeaatho eo.
t aoaeao iaeaathuay yoeo noa?e/aneeo o?iioia.
r, eae yoi iieacaii ia ?enoiea. Iaeaathuay noa?e/aneeo aiei oaea ia
aoaeao ieineie aieiie. I?iaeieaeei yoio i?ioeann. Anee acyoue
aeinoaoi/ii aieueoie i?iiaaeooie a?aiaie t, o.a. ?anniao?eaaoue aieiiaua
iiaa?oiinoe ia aieueoii ii n?aaiaieth n ?acia?aie ioaa?noey ?annoiyiee,
oi i?ioaaeoay /a?ac iaai ieineay aieia i?aa?aoeony a noa?e/aneoth aieio.
Aieia ca ioaa?noeai aoaeao ?ani?ino?aiyony ai ana noi?iiu, a oii /enea
e a iaeanoue aaiiao?e/aneie oaie.
?en.18.5
?anniio?ei ae?oaie i?eia?, eeethno?e?othuee i?eioeei Atheaaina. Ionoue
ieineay aieia iaaeaao ia a?aieoeo ?acaeaea n?aae (1) e (2), eae yoi
iieacaii ia ?en.18.6. Oaie iaaeaiey iaicia/ei /a?ac (1. Nei?inoue
?ani?ino?aiaiey aieiu a ia?aie n?aaea ?aaia (1, ai aoi?ie (2. Iaeaeai,
iiae eaeei oaeii (2 aoaeao ?ani?ino?aiyony aieia ai aoi?ie n?aaea.
A niioaaonoaee n i?eioeeiii Atheaaina eaaeaeoth oi/eo ia a?aieoea aeaoo
n?aae iu iiaeai n/eoaoue enoi/ieeii aoi?e/iuo noa?e/aneeo aiei. Nenoaia
neiiao?e/ia e iai aeinoaoi/ii acyoue aeaa oi/ee A e A, eioi?ua
ia?aie/eaatho o?iio iaaeathuae aieiu. I?iaaaeai ec oi/ee A i?yioth,
ia?iaiaeeeoey?ioth iai?aaeaieth ?ani?ino?aiaiey o?iioa aieiu AC. Yoa
i?yiay niaiaaeaao n o?iioii aieiu a iiiaio a?aiaie t.
V
V A
N
D
A
1
2
?en. 18.6
Oi/ea N o?iioa aieiu aeinoeaiao oi/ee B a iiiaio a?aiaie ti. A?aiy t-
to =CB/V =AB sin( y 1 )/V1 . Ca a?aiy t – to ec oi/ee A
?ani?ino?aieony noa?e/aneay aieia n ?aaeeonii AD = (t -to ) V. O?iio
aieiu ai aoi?ie n?aaea aoaeao i?ioiaeeoue /a?ac oi/eo A e aoaeao
eanaoaeai e noa?a ?aaeeonii AD. Ethaay oi/ea io?acea AA iiaeao
?anniao?eaaoueny eae enoi/iee aoi?e/iuo noa?e/aneeo aiei. Ca a?aiy t –
t iie ?ani?ino?aiyony a n?aaea 2 ia iaeioi?ua ?annoiyiey. Eanaoaeueiua
e ie?oaeiinoyi yoeo oi/ae e aeaaeoo i?yioth AD. Ai aoi?ie n?aaea
oaeaea ?ani?ino?aiyaony ieineay aieia.
Iineieueeo AD = AB sin =V(t – t ) n iaeiie noi?iiu e n ae?oaie
noi?iiu AA sin =V ( t – t ) , i?e?aaieaay AA ec yoeo
o?aaiaiee e nie?auay ia (t – t ), iieo/aai o?aaiaiea i?aeiieaiey aiei
ia a?aieoea aeaoo n?aae:
.
Nei?inoue ?ani?ino?aiaiey naaoiauo aiei a n?aaea ( ii?aaeaeyaony
eiyooeoeeaioii i?aeiieaiey n yoie n?aaeu e nei?inoueth naaoa a aaeooia
n:
.
Iiaenoaaea yoi niioiioaiea a o?aaiaiea (18.18), iieo/ei caeii
i?aeiieaiey naaoa:
.
Caeii i?aeiieaiey naaoa aue noi?ioee?iaai a o?oaeao A?oeiaaea ieiei
aeaoo n iieiaeiie ouny/ eao iacaae. Ia?yaeo n caeiiii i?yiieeiaeiiai
?ani?ino?aiaiey naaoa e caeiiii iaacaeiiaeaenoaey naaoiauo aiei, ii
yaeyaony iaeiei ec iniiaiuo caeiiia iioeee. Iiaeaaeythuaa aieueoeinoai
?an/aoia iioe/aneeo nenoai (i/eia, aeiieeae, oioiaiia?aoia e o.ae.)
aace?oaony ia yoeo caeiiao.
Cia/aiea iieacaoaey i?aeiieaiey n iiaeii iaeoe ainiieueciaaaoenue
o?aaiaieyie (18.16) e (18.17).
.
.
A caeeth/aiea ?acaeaea ?anniio?ei yaeaiea aeenia?nee. I?iyaeaiea aai
ecaanoii n iacaiaiyoiuo a?aiai. Ana iu iaaethaeaee ?aaeoao a iaaa iinea
aeiaeaey, ethaiaaeenue ea?ie naaoa a ae?aaioeaiiuo eaiiyo. Ana yoe
yooaeou naycaiu n yaeaieai aeenia?nee. Iiae yaeaieai aeenia?nee
iiieiatho caaeneiinoue nei?inoe ?ani?ino?aiaiey aiei eee eiyooeoeeaioa
i?aeiieaiey n?aaeu io aeeeiu aieiu eee /anoiou eieaaaiee.
?anniio?ei iiuo Iuethoiia ii iaaethaeaiee aeenia?nee naaoa (ni. ?en.
18.7). Ii iai?aaeye ia?aeeaeueiue io/ie aaeiai naaoa ia noaeeyiioth
i?ecio I e iaaethaeae aai i?ioiaeaeaiea ia noiyuai aaeaee ye?aia Y.
I?ecia i?aeiieyao io/ie naaoa , ii ii ?aciiio aeey ?aciuo aeeei aiei, e
ia ye?aia Y iaaethaeaaony ia iaeii aaeia iyoii, a niaeo?,
aeeth/athuee ana oeaaoa ?aaeoae io neiaai aei e?aniiai.
Ia a?aiyo i?eciu a niioaaonoaee n caeiiii i?aeiieaiey naao i?aeiieyaony.
Eiyooeoeeaio i?aeiieaiey noaeea n ?acee/ai aeey ?aciuo aeeei aiei, o.a.
n(((n((). Iieacaoaeue i?aeiieaiey aeey neiaai naaoa aieueoa, /ai aeey
e?aniiai, iiyoiio, a niioaaonoaee n caeiiii i?aeiieaiey (18.20) neiee
naao i?aeiieyaony neeueiaa, /ai e?aniue.
I
Y
E
N
?en.18.7.
E?iia e?aniiai e neiaai oeaaoia a anoanoaaiiii naaoa i?enoonoaotho ana
inoaeueiua oeaaoa, e eiyooeoeeaiou i?aeiieaiey aeey eaaeaeiai ec ieo
?acee/iu. Eaaeaeue ec yoeo eo/ae aoaeao i?aeiieyoueny ia ?aciue oaie. Ia
ye?aia aoaeoo iaaethaeaoueny ana oeaaoa ?aaeoae, ia?aoiaeyuea ae?oa a
ae?oaa io e?aniiai aei oeieaoiaiai.
Yoio aea yooaeo iu iaaethaeaaony i?e i?ioiaeaeaiee naaoa /a?ac a?aie
iooeeoiaaiiiai aeiaca – a?eeeeaioa. I?e?iaeiue aeiac eiaao i/aiue
aunieoth aeenia?neth e aieueoia cia/aiea eiyooeoeeaioa i?aeiieaiey
n(((2,4. Eiaiii iiyoiio aaeue naao, i?aeiieyynue ia a?aiyo aeiaca,
oi?ioi ?acaeaeyaony ia ana oeaaoa ?aaeoae.
A caeeth/aiea iiae/a?eiai aua ?ac iniiaiia ioee/ea aeaeaeaiey aiei io
aeaeaeaiey iaoa?eaeueiuo oae. Aieia – yoi ia iaoa?eaeueiia oaei, a
i?ioeann ?ani?ino?aiaiey eieaaaiee a i?ino?ainoaa. Iia ia eieaeeciaaia a
eaeie-eeai oi/ea i?ino?ainoaa e iaeaaeaao aaneiia/iui /eneii noaiaiae
naiaiaeu. Aieia iiaeao iaeaaeaoue oa?aeoa?enoeeaie, ia eiathueie
aiaeiaia aeey iaoa?eaeueiuo oae, iai?eia?, iiey?ecaoeeae. I?ioiaeaeaiea
aiei a n?aaea eee i?ino?ainoaa nii?iaiaeaeaaony yaeaieyie,
ionoonoaothueie i?e aeaeaeaiee iaoa?eaeueiuo oae: eioa?oa?aioeeae,
aeeo?aeoeeae, aeenia?neae.
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