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Физика (Шпаргалка)

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Yeaeo?inoaoeea.

Niiniaiinoue e yeaeo?ecaoeee. – niiniaiinoue oae i?eoyaeaaoue e naaa
i?aaeiaou.

Yoe oaea ieac. ca?yaeaiiuie.

Q=ne Q – ca?yae oaea n=1,2,…

Ca?yaeu i?eia?aoaaiua i?e yeaeo?ecaoeee anaaaea e?aoiu a e ca?yaeu yae.
aeene?aoiuie.

Nou. o?e niiniaa yeaeo?ecaoeee oae.

1) Yeaeo?ecaoeey /a?ac o?aiea – o?eaiyeaeo?ecaey.

2) Yeaeo?ecaoeey iaaaaeaieai (yaeaiea yeaeo?inoaoe/aneie eiaeoeoeee).

3)Yeaeo?ecaoeey n iiiiuueth yeaeo?eoe?iaaiey.

Yeaeo?e/ane. ca?yaeu nio?. ia ca?yaeaiiuo oaeao ?acee/iia a?aiy a
caaenaiinoe io niiniaa yeaeo?ecaoeee a1) e 2) – ei?ioeia a?aiy , 3) –
aiaeu e aeanyoee eao.

A caieaooie nenoaia yeaeo?ec oae (iao iaiaia ca?yaeaie n aiaoieie
oaeaie) aeaaa?ae/aneay noiia ye. ca?yaeia inoaaony iinoiyiie i?e ethauo
i?ioeannao i?ienoiaeyueo a yoie nenoaia.

SQi=const

i

Oi/a/iue ca?yae yoi oece/. aano?aeoeey.

Oi/a/iui ca?yaeii i?eiyoi iacuaaoue ca?yae. oaei ?icia?a eioi?iai iaeu
ii n?aaiaieth n ?anno. aei oi/ee enneaaeiaaiey.

Iaeiieiaiiua ca?yaeu iooaeeeaathony, ?aciieiaiiua i?eoyaeaathony.

Cae. Eoeeiia.

Neea acaeiiaeaenoaey iaaeaeooi/a/iuie iaiiaeaeae ca?yaeaie

q1 e q2 i?yiii?iii?oeeaiaeueiu aaee/eia yoeo ca?yaeia e ia?aoiii?iii?oe.
?anno. iaaeaeo ieie.

F=k?((q1q2)/r2

k=1/4pe0 e0=8,85?10-12 O/M

e0 – ooiaeiiaioaeueiay aaciaay iinoiyiiay iaca aaciaie iinoiyiiie.

k=9109 M/O

Cae. Eoeeiia (a ae?oaii aeaea)

F=(1/4pe0)?cq1q2c/r2

aaeooi e=1

F=(1/4pe0)?cq1q2c/er2

aeey n?aaeu e?1

Anee oi/a/i. ca?yae iiianoeouea iaeii?iaei. aaca?aie/.n?aaeo
eoeeiiianeay neea oiaiueoeony a e ?ac ii n?aaiaieth n aaeooiii. e –
aeeyeaeo?. i?iieoeaaiinoue n?aaeu.

O ethaie n?aaeu e?iia aaeooia e>1.

Cae. Eoeeiia a aaeoi?iie oi?ia.

Aeey yoiai ainiieuecoainy aaeeie/iui i?oii ii iai?aaeaieth aaeieue
?annoiyiey iaaeaeo aeaoiy ca?yaeaie.

_ _ _ _

er=r/r r =er?r

_ _

F=(1/4pe0)?(cq1q2c?r)/r3 aaeoi?iay oi?ia

A Ne – neno aaeeieoea ca?yaea 1Ee=1A?n

1Eoeeii – yoi ca?yae, i?ioaeaaiue ca 1 n /a?ac ana iiia?a/iia na/aiea
i?iaiaeieea, ii eioi?iio oa/ao

oi A n neeie 1A.

Cae.Eoeeiia iiaeao auoue i?eiaiai aeey oae cia/eoaeueiuo ?acia?ia anee
eo ?acaeoue

ia oi/a/iua ca?yaeu.

Eoee. neeu – oeaio?aeueiua, o.a.

iie iai?aaeaiu ii eeiee niaae.

oeaio? ca?yaeia.

Cae. Eoeeiia ni?aaaaeeea aeey i/aiue aieueoeo ?annoiyiee aei aeanyoeia
eeeiiao?ia. I?e oiaiueo. ?anno. aei 10-15 i ni?aaaaeeea, i?e iaiueoeo
iani?aaaaeeea.

Yeaeo?inoaoe/. iiea.

Oa?. yeaeo?inoaoe/.iiey.

_ _

(A, D, j)

A i?ino?ainoaa aie?oa ye. ca?yaeia aicieeaao yeaeo?inoaoe/aneia iiea
(ca?yaeu ia iiaeaeae.).

I?eiyoi n/eoaoue, /oi yeaeo?inoaoe/aneia iiea yaeyaony iauaeoeaiie
?aaeueiinoueth. Iaia?oaeeoue iiea iiaeii n iiiiuueth i?iaiuo
yeaeo?e/aneeo ca?yaeia.

I?iai., iieiae., oi/a/iue ca?yae aeieaeai auoue oaeei, /oiau ii ia
eneaaeae ea?oeiu eneaaeoaiiai iiey.

Iai?. yeaeo?inoaoe/. iiey.

_

A – iai?yaeaiiinoue yeaeo?inoaoe/aneiai iiey. Iai?yaeaiiinoue
yeaeo?inoaoe/aneiai iiey yaeyaony neeiaie oa?aeoa?enoeeie.

_ Iai?. iiey a aeaiiie

A=F/q0 oi/ea i?ino?ainoaa

yae. oec. aae. /eneaiii ?aaiay neea (eoeeiiiane.)

aeaenoa. a aeaiiie oi/ea ia aaeeie/iue iaiiaeaeaeiue i?iaiue ca?yae.

[E]=H/Ee [E]=A/i

Neeiaay eeiey – eeiey, a eaaeaeie oi/ea eioi?ie iai?. iiey A iai?aaeaia
ii eanaoaeueiie.

Neeiaua eeiee no?iyo n ii?aae.

aonoioie niioaaonoaothuae iiaeoeth iai?. iiey: /a?ac ieiuaaeeo 1 i2
i?iaiaeyo eiee/anoai eeiee A ?aaiia iiaeoeth A.

I?e a?aoe/aneii i?aaenoaaeaiee aeaeii, /oi a ianoao n aieaa

aonoui ?aniieiae. A iai?. aieueoa.

Auaiae oi?ioe aeey iai?. iiey oi/a/i. ca?yaea.

q – ca?yae nicaeathuee iiea.

q0 – i?iai. ca?yae.

A=(1/4pe0)?(q?q0)/(r2?q0)

E=(1/4pe0)?q/r2

Ec E=(1/4pe0)?q/r2 neaaeoao /oi A caaenao i?yiii?iii?oeeaiaeueii
aaee/eia ca?yaea e ia?aoiii?iii?oe. ?anno. io ca?yaea aei o. enneaaeia.

A iaeii?iaei. aaca?. n?aaea n e?1

(e>1) iai?. iiey oiaiueo. a e ?ac.

E=(1/4pe0)?q/er2

_

E=(1/4pe0)?q2/r3

Yeaeo?e/aneia niauaiea.

_

Ii?aae. oi?ioeie aeey D yae. neaaeouaa a aeaiiie o. n?aaeu yeaeo?e/aneia
niauaiea /eneaiii ?aaii i?iecaaae. aeeyeaeo?. i?iieoeaaiinoe, ye.
iinoiyii. e iai?. iiey.

_

D E D=ee0E

[D]=Ee/i2

Iai?. ye. iiey caanao io e n?aaeu iiyoiio i?e iaee/ee ianeieaeeo
a?aie/aueo aeeyeaeo?eeia ia a?aieoea ?ac?uaa aeaoo n?aae iai?. iiey
iaiyaony nea/eii (eeiee

_

aaeoi?a A oa?iyo ?ac?ua).

_

Aaeoi? D ia caaen. io e n?aaeu o.a. yae. iaeiaeia. ii aaee/eia

_

ai anao n?aaeao o.a. nea/ea D iao , ?ac?uaa iao.

_

Iieaaeai /oi D iacaaen io e.

D=ee0?(kq)/(e0?r2)

D=(1/4p)?q/(e?r2)

Iioaioeaae iiey.

Neeu yeaeo?inoaoe/. iiey eiina?aaoeaiua o.a. iacaaen. io o?ayeoi?ee
aeaeaeaiey ca?yaea.

_

F=- gradI

Fx= -¶I/¶x aiaeiae/ Fy e Fz

1) F= – dI/dr

Aeey yeaeo?inoaoe/. nee F=f(r).

Ainiieuecoainy yoie caaenaiinoueth aeey aaaaeaiey o?aoae oa?aeoa?enoeee
iiey – iioaioeaaea.

I?aia?. 1)

2) dI= – Fdr F – eoeeiiianeay neea acaeiiaeaenoaey iaaeaeo aeaoiy
oi/a/i. ca?yaeaie q e q0.

F=k(/qq0//r2) Iiaenoaaei F a 2) e i?ieioaa?e?oai eaa. e i?aa. /anoue.

3) odI=o -k(/qq0//r2)dr ec 3)

I= -k/qq0/odr/r2=

=k/qq0/?(1/r)+C

?acaeaeei eaa. e i?aa. /anoue 4) ia q0.

5) j=I/q0=(1/4pe0 )?(q/r)+C

6) j=I/q0 Iioaioeaae iiey a aeaiiie oi/ea /eneaiii ?aaai
iioaioeaaeueiie yia?ee i?iaiiai ca?yaea iiiauaiiiai a aeaiioth oi/eo.

[j]=B=Aeae/E

7) j=(1/4pe0 )?(q/r) i?e j=0 r®Y , j ~ d i?e r=const ,

j ~1/r i?e q=const

I?e q>0 j>0 +

I?e q<0 j<0 -Iioaioeaae iiey i?eiyoi ecia?aaeaoue ia ?en. yeaeiioaioeaaeueiuie eeieyie eee iiaa?o.Yeaeiioaioeaae - aaii. ianoi oi/ae ?aaiiai iioaioeaaea iiey.I?eiyoi yeaeiioaioeaae i?iaiaeeoue i?e Dj =constDj=j2 - j1 - ?aciinoue iaaeaeo aeaoiy aeeaeaeoaie yeaeiioaioeaaeaie.Auaiae:_ _ _ _D=e0E DEE=(1/4pe0 )?(q/r2) D=q/4pr2Ea?oeia eeiee A yeaeiioaioe. iiey oi/a/i. ca?yaea.(aeey aaeo-oia)_ _A eee D Dj=const_ _3/4 eeiee D eee A--- yeae._ _Ia?enoai eeiee E e D i?e iaee/ee aeeyeaeo?eea.Aeeyeaeo?e ie?oaeai aaeooiii.A aeeye. e>1 Eae>l , r>>l/2)=(kq2rl)/r4=k(qp/r3)

E=k(2p/r3) E~1/r3

Iiea a o. N ia ia?iaiaeee. ine aeeiiey.

k, q, l, r>>l, p=ql, e=1 , r=OC

E – ?

_

/E/=2I?.A+

A+=A_ a neeo neiiao?ee ca?.

A+=A_=k(q/(rc)2)

E+/E_=cosa=l /2rc

I?.A+=I?.A_=A(l /2)

E=2I?.A+=2I?.A

I?.A+=A+nosa=(kq/(rc)2)?

?l/2rc

_

I?.A+/E+=cos aE+

rc~r i?e r>>l

E=2(kq/(rc)2)?l=kql /(rc)3=

=kp/r3

(iai?aaeeueii)

E=k(p/r3)

_ _

Iioiee D e A.

Ionoue yeaeo?inoaoe/aneia iiea aoaeao iaeii?iaeii o.a. oaeia

_

iiea o eioi?. D=const e ana eeiee iiey ii ii iai?aaeaieth , aaaae. a
yoi iiea ieine. iiaa?oiinoue ieiuaaeueth S, no?iai ii?iaeue.

_

I?.D=Dncosa

_

iioie D FD=Dcosa?S

1) FD=Dncosa

_ _

Iioieii D eee E iaca. oec. aae. /ene. = eie – ao. eeiee

_ _

D eee A i?iiecuaathueo enneaaeoaioth iiaa?oiinoue i?e

_ _

oneiaee D eee A ^ iiaa?oiinoe.

FA=AnS 2)

[FD]=Ee [FA]=A?i

Iioie oa?aeoa?enoeea neaey?iay, aeaaa?ae/aneay.

I?e a<900 cosa (+) FD>0

I?e a<900 cosa (-) FD<0Caieoai iauoth oi?ioeo a neo/. eiaaea S eiaao i?ieca. oi?io.A oieii neo/aa ia iiaa?o S iaoiae. o/anoie ieiuaaeueth dS eioi?. iiaeii n/eoaoue ieineei, oiaaea dFD=Dn?dSFD=oDndSSIeiuaaeea dS i?eien. aaeoi?iua naienoaa._ _dS=dS?n_ _FD=o DndSSOai?. Aaonna (eioaa?aeueiay oi?ia).A ?yaea neo/aaa i?eioeei noia?iic. aeey au/eneaiey iai?. iiey i?eiaiyoue o?oaeii, a oaeeo neo/. iai?yaeaiiinoue yeaeo?inoaoe/. iiey au/eneytho n iiiiuueth oai?. Aaonna.Oai?. Aaonna iicaieyao eaaei au/eneyoue A e D i?e neiiao?e/iuo ?aniieiaeaieyo ca?yaea.Iioie aaeoi?a yeaeo?e/. _niauaiey D ceaicue i?iecaieuei. caiei. iiaa?o. S ?aaai aeaaa?ae/. noiia ca?yaeia caeeth/. aioo?e iiaa?o.Caieiooay iiaa?o - oaeay aeioi? iao ioaa?noee.Aeaaa?. noiia - noiia ca?yaea n o/aoii eo ciaeia._ _ n?DdS=Sqi 1)S i=1_ _?EdS=(1/e0)Sqi 2)(aeey aaeooia)S iAeie - ai.1. Ionoue eiaaony iieiae. oi/a/i. ca?yae. q ._ _?DdS=?DdSS S_ _Dn a=0 Dn=DAuianai ca ciae eioaa?.D?dS=D4pr2=(q/4pr2)?4pr2=qS_ _3) ?DdS=qSI/aaeaeii anee oi/a/i. ca?. ?ani. ia a oeaio?a a a etha. o aioo?e iiaa?o. S eiee/. eeiee_D i?iiec. iiaa?o. ia eciai. , o.a. aeey etha. iieiaeaiey oi/a/i. ca?yaea q aioo?e noa?u oi?ioea 3) ni?aaaaeeeaa.Iioie neaicue iiaa?o. ae?oaie oi?iu (i?iecaie.) i?e i?aaeiai ca?yaea q ia eciaieony e 3) ni?aaaaeeeaa.Aioo?e caiei. noa?u iao. ianeieueei ca?yaeia q1, q2 ,q3, ...,qi,...qn 1F i FnAeieaaeai /oi a yoii neo/. oai?. Aaonna aa?ia.Ia iniia. 1)aeey eaaeaeca?. oai?.ni?aaaaeeeaa._ _4) ?DidS=qiSa 4) i?inoiie?oai eaaoth e i?aaoth /anoue._ _S?DidS=Sqii i_ _?(SDi)dS=Sqis i i_ _ n?DdS=Sqi 5)s iOi?ia caiene 5) eiaao iaca. eioaa?aeueiie oi?iu caiene.Eioaa?. oi?i. - iaicia/. /oi a oi?ioea oa?aeoa?enoeee neaaa e ni?aaa ioiinyony e ?aciui oi/eai i?ino?ainoaa.r - ia. ieioiinoue.r=dq/dv (Ee/i3)6)Sqi=ordvi v_ _?DdS=ordv S e V -v niaeani-aaiiu.I?aeoe/. i?eiaiaiea oai?. Aaonna.Iaoiaeeea i?eiaiaiey oai?aiu.Aeaii:Oa? , eo ? 0 , eo>0 , eo=e , ecp=1 , r=const , R – ?aaeeon oa?a 1) r>R
(aia oa?a)

2) rER (nea/ie)

ai ni ai ni

Caaen. A(r)

I?e en?R, oi aioo?ue iiaa?oiinoe iiiaaeaao

aanue ca?yae e ii oai?. Aaonna

4pr2E=Q/e0 , ioeoaea

E=(1/4pe0)?Q/r2 (r ? R)

Anee rcR

2plA=t(l/e0) , io nthaea A=(1/2pe0)(t /r) (r ? R).

Anee r0

_

(+ ca?) div D>0 – enoie ?anoiaeaeaiey. Anee r<0 ( - ca?)_div D<0 aoiaeaeaiea eeiee.Ec3) aaaeiia neaaenoaea:Enoi/ieeii iiey yae. yeaeo?e/. ca?yae.Oai?. Ino?ia?aaene?ai Aaonna.O?. 3) aeiiiiaeei eaa. e i?aa. /anoue ia dV._4) div DdV=r dVi?ieioaa?e?oai 4) ii iauaio_5) odiv DdV=or dVv v_ _or dV=oDdSv s_ _ _6) odiv DdV=?DdS - Ino?. A.v sniaeaniaai «A oai?. Ino?. Aaonna niaea?ae. naycue iaaeaeo aeeaa?aaioeeae e iioieii iaeiiai e oiai aea aaeoi?a.?aaioa nee. yeaeo?inoaoe/. iiey.Iioaioeeae iiey.Neeu yeaeo?inoaoe/. iiey ia?aiauay yeaeo?e/. ca?. niaa?o. ?aaioo.Au/eneei ?aaioo nee yeaeo?inoaoe/. iiey aeey ia?aiauaiey ca?. ii i?iecaieueiie o?aaeoi?ee.q - nicae. iiea.+q0 -ia?aiau. a iiea ca?yaea q.?anniio?ei ia?aiauaiea ca?yaea ia yeaiaioa?. e/anoea dl.0) dA=Fldl =Fcos adl =Fdrr - oae. ?anno. iaaeaeo q eq0.Iaeaeai iieioth ?aaioo.2 2A=odA=oFdr1 1Iineieueeo Fdr cosac=1_ _Fdr=Fdrr 2_ _1) A=oFdrr 1Ainiieuecoainy aeey iieo/. aoi?. oi?ioeu naycueth iaaeaeo_ _ _ _ _ _A e F. E=F/q0 E=q0E_ _2) dA=q0Eldl =q0Edl ==q0Ecos adleioaa?e?oai 2) eaa. e i?aa. /anoue2 _ _3) A=q0oEdl1Iieo/ei aua iaeio oi?ioeo.Ainiieuec. 1) a eioi?. iiaenoaaei o?. Fee.r2A=ok(q0?q/r2)drr1A=q0((kq/r1) - (kq/r2))Ec 4)5) A=q0(j1 - j2)?aaioa i?e ia?aiauaiee ca?. q0 yeaeo?inoaoe/. neeaie ?aaii i?ieca. aae. yoiai ca?yaea ia ?aciinoue iioaioeeaea a ia/aeueiie e eiia/iie oi/ea.Ec 4) neaae. /oi ?aaioa nee iiey iacaaen. io oi?iu o?aaeoi?. Neeu yeaeo?inoaoe/. yae. eiina?aaoeaiuie , iiea yeaeo?inoaoe/aneia yae. iioaioeeaeueiui iieai.Eniieuecoy 5) aeaaeei aoi?ia ii?aae. iioaioeeaea. Aeey yoiai ?anni. ia?aiauaiea iieiae. ca?yaea q0 ec aeaiiie o. a eioi?.j1 = j a aaneiia/iinoue j2=jY=0.Ec 5) AY=q0j6) j = AY/q0Iioaioeeae. iiea a aeaii. o. /ene. =?aaioa niaa?o. neea yeaeo?inoaoe/. iiea i?e ia?aiauaiee aaeeie/iiai iieiae. ca?yaea ec aeaiiie o. a aaneiia/iinoue. Iioaioe. neaey?. oa?aeoa?enoeea. Aeae/Ei=AOai?. i oee?eoeyoeee aaeoi?a iai?.yeaeo?inoaoe/. iiey.Iioaioeeaeueiue oa?aeoa? iiey.?anni. ia?aiau. ca?. q0 a iiea ca?yaea q aaeieue i?iecaieueiie caieiooie o?aaeoi?. A = 0.Aiciai aeey ?aaiou oi?i. 3)_ _q0?Eldl=q0?Edl =0L Lq0 ? 0_1) ?Eldl=0 - oee?eoeyoeey AL _Oee?eoe. A a aeieue i?iecaieuei. oi?iu caiei. eiioo?a=0.Oai?. i oee?eoe. naeaeaoaeuenoaoao i oii /oi yeaeo?inoaoe/. iiea - iioaioeeaeueiia.Anee oee?eoe. ia =0 oi iiea ia iioaioeeaeueii.Oec. niune. oee?eoe. /eneaiii ?aaai ?aaioa ii ia?aiau. aaeeie/i. iieiae. ca?. ii caiei. o?aaeoi?ee.Eaeoeey.Au/eneaiea ?aciinoe iioaioeeaea ii iai?yae. iiey.21)A=q0oEldl12)A=q0(j1 - j2)2j1 - j2=oEldl Naycue iaaeaeo1 ?aciinoueth iioaioeeaea e iai?yaeaiiinoueth iiey.Au/eneei ?aciinoue iioaioeeaea aeey aaneiia/. , ?aaiiia?. ca?yaeaiiie ieoe n eeiaeiie ieioiinoueth t .I?eia?:t =dq/dl [ Ee/i]t1, t2 e=1(j1 - j2) - ?El=Er dl=drr2 r2j1 - j2=oErdr=oEdrr1 r1E=(t/2pe0r) iai?yaeaiiinoue iiey a oi/ea ia ?anno. r io ieoe. 2j1 - j2=(t/2pe0)odr/r1j1 - j2=(t/2pe0)?ln(r2/r1)I?eia? 2:Au/ene. ?aciinoe iioaioeeaea aeey ?aaiiia?. ca?yae. noa?u (i?iaiaeyuee oa?).Noa?a R , q=11) rR

Aeey oi/ae aia noa?u (r>R) ec oai?. Aaonna iai?yaeaiiinoue A au/eneyaony
A=1/2pe0=q/r2

Aioo?e (rR j =(1/4pe0)(q/r)

Aioo?e iai?yaeaiiinoue iiey =0

iiyoiio j1 – j2=0

j1=j2=jR=(1/4pe0)(q/R)

j =const

Ia?en. a?aoeee.

Naycue iaaeaeo iai?yaeaiiinoueth iiey e iioaioeeaeii a aeeooa?. oi?ia.

A?aaeeaio iioaioeeae.

Aeey iieo/aiey nayce iaaeaeo A e j a iaeiie oi/ea ainiieuecoainy au?aae.
aeey yeaiaioa?i. ?aaiou i?e ia?aiauaiee q0 ia dl ii i?iecaie.
o?aaeoi?ee.

dA=q0Eldl

A neeo iioaioeeaeueiiai oa?aeoa?a nee yeaeo?inoaoe/aneiai iiey yoa
?aaioa niaa?o. ca n/ao oauee iioaioeeaeueiie yia?aee.

dA= – q0 dj = – I

Eldl = – dj

3) El= – (dj /dl )

I?iyeoeey aaeoi?a iai?yae. iiey ia i?iecaieueiii iai?aaeaiee (l) ?aaia
acyoie n ia?aoiui ciaeii i?iecaiaeiie ii yoiio iai?aaeaieth.

4) Ex= – (dj /dx)

Ey= – (dj /dy) Ez= – (dj /dz)

_ _ _

E= – ( i (¶/¶x)+j (¶/¶y)+

_

+k (¶/¶z))?j

_

E= -grad Iai?yaeaiiinoue

iiey a aeaiiie o. ?aaia acyoiio n ia?. ciaeii
a?aaeeaioo iioaioeaaea a yoie oi/ea.

A?aaeeaio neiey?. ooeoeee yae. aaeoi?ii.

A?aaeeaio iieacuaaao auno?ioo eciaiaiey iioaioeaaea e iai?aaeai a noi?.
oaaee/ iioaioeaaea.

Iai?yae. iiey anaaaea ia?iaiaeeeoey?ia e yeaiioaioeaaeueiui eeieyi.

Ionoue oi/a/iue ca?yae q0 ia?aiauaaony a aeieue yeaeiioaioeaaea j =const
, dl – ia yeaeiioaioeaaee.

dA=q0Eldl dA=0 o.e. Dj =0

El=Ecosa q0Ecosa dl =0

q0?0 E?0 dl?0 cosa=0 a=900

I?iaiaeieee a yeaeo?e/. iiea.

Yeaeo?iaieinoue i?iaiaeieeia.

Eiiaeainaoi?u.

Yia?aey iiey.

§1 Oneiaey ?aaiiaaney ca?yaea ia i?iaiaeieea. Yeaeo?inoaoe/. caueoa.

Aianai a yeaeo?e/. iiea iai?yaeaiiinoueth E0 oaei.

I?e aianaiee i?iaiaeieea ana yeaeo?iiu ieaaeoony a yeaeo?inoaoe/ iiey.

A ioo?e i?iaiaeieea ca ei?ioeia a?aiy i?ecieaeao ?acaeaeaiea ye.
ca?yaeia (yeaeo?inoaoe/ eiaeoeoeey) n iaeiieaieai eo ia eiioeao.

_ _ _

E0 – aiaoiaa E’ ?E0

_

E’ aioo?e i?iaiaeieea

_ _ _ _ _

A=E0+E’=0 E’=E0

E – ?acoeueo. iiea a ioo?e i?iaiaeieea.

A ?acoeueoaoa ?anniio?aiiuuo i?ioeannia.

One. ?aaiiaan. ca?yaea.

1)Iai?. iiey ai anao oi/eao aioo?e i?iaiaeieea A=0 .

2)Iiaa?oiinoue i?iaiaeieea

yae. yeaeiioaioeaaeueiie

j =const.

_

3) Iai?. iiey A ^ yeaeiio.

j =const.

A neeo A=0 i?iaiaeieee etha. oi?iu yae. caueoie io yeaeo?inoaoe/. iiey.

Iiea o iiaa?oi. ca?yae. i?iaiaeieea.

?anni. i?iecaieueioth oi?io i?iaiaeieea ca?yae. ii iiaa?o. n
iiaa?oiinoiie ieioiinoueth s .

Ainiieuec. oai?. Aaonna a eioaa?aeueiie oi?ia.

_ _

?DdS=Sqi

s

Ia ca?yae. iiaa?oiinoe iona/ai e?oa ieiuaaeueth S.

?e0EdS=e0EodS

s s

e0E?S=s?S

a o. A E=s/e0

D=e0E D=s

Iai?. iiey i?yiii?iii?oe. iiaa?o. ieioiinoe ca?yaea i?iaiaeieea a
ie?anoiinoyo yoie oi/ea.

?acaeaeaiea ca?. ii i?iaiaeieeo caaen. io aai iiaa?o. (o ino?uo oaeia
ca?yae aieueoa , iai?yae. neeueiaa).

Yeaeo?iaieinoue i?iaiaeieea.

Aaeeieoea yeaeo?iaieinoe.

?anni. i?iaiaeiee i?ieca. oi?iu. A aeece yoiai i?iaiaeieea ae?oaeo
i?iaiaeieeia iao. oaeie i?iaiaeiee iaca. oaaeeiaiiui i?iaiaeieeii.

Aoaeai ca?yaeaoue oaaeeiaiiue i?iaiaeiee. I?e oaaee/aiee ca?yaea
iioaioeeae i?yii i?iii?oeeiiaeueii caaenao io Q.

Naycue iaaeaeo ca?yaeii Q , iioaioeeaeii j , e oi?iie i?iaiaeieea aeaao
yeaeo?iaieinoue N=Q/j .

Aieinoueth oaaeeiaiiiai i?iaiaeieea – iaca. oec aae. /ene.= aaee/eia
ca?. niiauaaiiai yoiio i?iaiaeieeo i?e oaaee/aiee iioaioeeaea ia 1A.

A Ne 1O – oa?aae.

1O=1Ee/1A

Yeaeo?iaieinoue caaenao io ?acia?ia , oi?iu e aeeyeaeo?e/aneie
i?iieoeaaiinoe n?aaeu.

N=4pee0R

j =(1/4pee0)?(Q/R)

Oaaeeiaiiua i?iaiaeieee i?e i?eaeeaeaiee e iei ae?oaeo i?iaiaeieeia
naith aieinoue nouanoaaiii iaiyao (oiaiueo. ca n/ao acaeiiiai aeeyiey
yeaeo?inoioe/. iieae).

Eaeoeey.

Eiiaeainaoi?u.

Oeiu eiiaeainaoi?ia.

Eiiaeainaoi? – ono?ienoai iicaieythuea iieo/aoue noaaeeueiia cia/aiea
aieinoe iacaaenyuaa io ie?oaeaiey.

Nicaeaiea cae?uoiai iiey ia aeeythuaai ia iaoaeee/. i?aaeiaou
aeinoeaaaony ca n/ao aeaoo iaoaeee/. ?aciieiai. ca?yae. yeaeo?iaeia.

A caaenaiinoe io oi?iu iaeeaaeie ?acee/atho ieineea , oeeeeiae?e/aneea ,
noa?e/aneea eiiaeainaoi?u.

?an/ao aieinoe eiiaeain. ?ace. oeiia.

1)

Aeaii: s , 1/2+ s 1/2=1/2 – s 1/2 ,

e , S , d

C – ?

C=q/j oaaeei. i?iaiaeieea

Aeey eiiaeain.

1) N= q/Dj =q/U

Dj =U – iai?yaeiea

N=sS/Ed=sS/[(s/ee0)?d]=

=ee0S/d 2)

Oeeeeiae?e/. eiiaeainaoi?.

R1 , R2 , l , e

1/2+q 1/2=1/2 – q1/2

+t , -t

C – ?

Ainiieuecoainy 1)

R2

N= tl/(oEdr) E= t/2pee0r

R1

Iai?yaeaiiinoue iiey i?iecaieueiie oi/ee ?aniieiae. iaaeaeo
oeeeeiae?aie ia ?anno. r io ine ii?aaeaeyaony oieueei ca?yaeaie ia
aioo?aiiai oeeeeiae?a (ni. oai?. Aaonna). Aiaeiae/ii aeey oiieie ieoe.

R2

N= tl/(o(t/2pee0r)dr=

R1

= [tl/(t /2pee0?ln R2/R1)]

3) C=[tl/(t /2pee0?ln R2/R1)]

aieinoue oeeeeiae?e/. eiiaeain.

Noa?e/. eiiaeainaoi?.

Noa?e/. eiiaeain. – aeaa eiioeaio?e/aneea noa?u ii?aaeae. ?aaeeona.

Aeaii: e , R1 , R2

1/2+q 1/2=1/2 – q1/2

C – ?

Eniieuec. 1) R2

N=q/= q/Dj =q/(oEdr)=

R2 R1

=q/(o(q/4pee0r2)dr)

R1

C=q/((q/4pee0)?(1/R1 – 1/R2))

C=4pee0R1R2/(R2 – R1)

Aeey anao aeaeia eiiaeain. aeaeii /oi aieinoue caaeneo io ia?aiao?ia
yeaeo?iaeia. Anaaaea n iiiauaieai aeeyeaeo?eea iaaeaeo yeaeo?iaeia
aieinoue oaaee/.

Niaaeeiaiea eiiaeainaoi?ia.

Aaoa?ae eiiaeainaoi?ia.

Eiiaeainaoi?u /anoi i?eoiaeeony niaaeeiyoue aianoa. *anoi aiciee.
iaiaoiaeeiinoue niaae. eo a aaoa?ae (eiaaea ioaeii eiaoue ae?oaoth
aieinoue).

1) Iineaaeiaaoaeueiia niaae. – niaae. i?e eioi?. io?eoeaoaeueiua
yeaeo?iaeu niaae. n iieiae.

O iineaaeiaaoaeueii niaae. Eiiaeainaoi?ia ca?yaeu anao iaeeaaeie ?aaiu
ii iiaeoeth , a ?aciinoue iioaioeeaeia ia caaeeiao aaoa?ae

n

Dj =aj i

i=1

Aeey ethaiai ec ?anniao?eaaaiuo eiiaeain. Dj i=Q/Ci

N ae?oaie noi?iiu ,

n

Dj =Q/C=Qa(1/Ci)

i=1

Ioeoaea

n

1/C=a1/Ci

i=1

2) Ia?aeeaeueiia niaae. – niaae. i?e eioi?. niaaeei. iaaeaeo niaie
iaeeaaeee iaeiiai ciaea.

n

N=aCi

i=1

O ia?aeeae. niaae. eiiaeainioi?ia ?aciinoue iioaioeeaeia ia iaeeaaeeao
eiiaeainaoi?ia iaeeiaeiaa e ?aaia j a -j b. Anee aieinoe eiiaeainaoi?ia
N1 ,N2, …, N3 oi eo ca?yaeu ?aaiu Q1=C1(j a -j b)

Q2=C2(j a -j b)

a ca?yae aaoa?ae eiiaeainaoi?ia

n

Q=aQi=(C1+C2+…+Cn)?

i=1

?(j a -j b)

Iieiay aieinoue aaoa?ae

n

N=Q/(j a -j b)= aCi

i=1

Yia?aey ca?yaeaiiiai i?iaiaeieea e eiiaeainaoi?a.

?anni. oaaeei. i?iaiaeiee i?ieca. oi?iu. I?iaaaeai ca?yaeeo yoiai
i?iaiaeieea , i?e yoii iiaen/eoaai ?aaioo aiao. nee.

Ionoue i?e ia?aianaiee dq ec Y , i?iaiaeiee i?eia?ae iioaioeeae j .
Yeaiaioa?. ?aaioa dA=j dq.

Aeiionoei ca?yaeeee aei Q .

N=q/j j=q/C

Any ?aaioa niaa?oaaiay i?e ca?yaeea i?iaiaeieea aei Q ?aaia.

1) A=Q2/2C 2) A=Cj2/2

3) A=Qj/2

A ie?oaeathuai i?ino?ainoaa iinea ca?yaeee i?iaiaeieea aicieeei
yeaeo?inoaoe/aneia iiea, cia/eo ?aaioa i?e ca?yaeea i?iaiaeieea
?anoiaeoaony ia nicaeaiea iiey. Cia/eo ?aaioa ia?aoiaeeo iieiinoueth a
yia?aeth yeaeo?inoaoe/. iiey.

Wye=1) eee 2) eee 3)

Ec 1) , 2) ,3) ia neaaeoao ioaaoa /oi yia?a. Wn eieaeeciaaia a naiii
iiea iineieueeo a oi?ioea noiyo ia?aiao?u ca?yae. i?iaiaeieea.

Eiiaeainaoi?.

?anni. ca?yaeeo eiiaeainaoi?a ninoiyuaai ec aeaoo iaeeaaeie

Ia?aue iooue – dq ia?aiin. ec Y ia iaeio ec iaeeaaeie , oiaaea ia
aoi?ie iaeeaaeea aicieeiao -.

Aoi?ie iooue – yeaiaioa?i. ca?yae dq ia?aianoe ec iaeiie iaeeaaeee ia
aoi?oth.

Iacaaeneii io niiniaa oi?ioeu 1) , 2) , 3) ni?aaaaeeeau (oieueei j
eciaiyaony ia Dj).

Yia?aey yeaeo?inoaoe/aneiai iiey.

Iauaiiay ieioiinoue yia?aee.

Iineoaeai yia?aee yae. naii iiea.

Aeey iiaeoaa?aeaeaiey yoie eaeae aicueiai oi?ioeo 1).

Wye=Q2/2C i?eiaiei aa e ieine. eiiaeainaoi?o. (ia?aiao?u ecaanoiu).

Wye=s2S2d/2ee0S=(s2/2ee0)?Sd=

=(ee0s2/2(ee0)2)?V

1) Wye=(ee0E2/2)?V

Ec 1) neaaeoao /oi iineoaeai yia?aee yae. iiea n iai?yaeaiiinoueth A.

Ec 1) neaaeoao /oi ana noiyuaa ia?aae iauaiii – yoi iauaiiay ieioiinoue
yia?a. yeaeo?inoaoe/aneiai iiey.

2) wye=(ee0E2/2)

2′) wye=DE/2

A oeceea aeieacuaaaony /oi 2) e 2′) iiaeii i?eiaiyoue e aeey
iaiaeii?iaeiiai iiey, aeey eioi?. iieiay yia?a. iiaeao auoue au/aneaiia
ii oi?ioea

3) Wye=owyedV

v

Eaeoeey.

Aeeyeaeo?eee a ye. iiea. Iiey?ecaoeey aeeyeaeo?eeia.

§1 I?iaiaeieee e aeeyeaeo?eee. nouiinoue yae. iiey?ecaoeee.

O i?iaiaeieeia yeaeo?iiu iiaoo naiaiaeii ia?aiauaoueny ii anae oieua
ia?acoea.

yae. yea-

eo?inoaoe/

eiaeoeoeee

Aeeyeaeo?eee – aauanoaa ieioi eee nianai iai?iaiaeyuea ye. oie.

A aeeyeaeo?eea naiaiaeiua ca?yaeu ionoonoaotho. O aeeyeaeo?eea i/aiue
aieueoia nii?ioeaeaiea.

Ai aiaoiai iiea o aeeyeaeo?eeia i?ienoiaeyo i/aiue nouanoaaiiua
eciaiaiey. Ca?yaeu iaoiaeyueany a aoiia ai aiaoiai iiea A0 niauathony
eee iuoathony nianoeoueny. Aeeyeaeo?ee ai aiao. ye. iiea iiey?ecoaony.

iiey?ecoaony

I?e iiey?ecaoeee aeeyeaeo?eea A?0.

O aeeyeaeo?eea ai aiao. ye. iiea ia iiaa?oiinoe ia?acoea iiyae. nayciiua
iaeiiiaine?iaaiiua iiey?eciaaiiua ca?yaeu.

ssae. iiey?ecaoeee caeeth/. a iiyaeaiee yeaeo?e/. iiey A i?e aianaiee ai
aiao. iiea A0 iiyae. naycaiiuo iiaa?oiinoiuo ca?. e iiyaeaiee a oieua
ia?acoea , a eaaeaeie aaeeieoea iauaia aeeiieueiiai iiiaioa.

Aeeiieue ai aiao. ye iiea.

?anni. yeaeo?e/aneee aeeiieue ia?aciaaiiue ca?yaeii q.

_

Yeaeo?e/. iiiaio p=ql , aaea l- iea/i aeeiiey. Aiinei aeeiieue ai aiao.
iiea.

_

A=const

1/2+q1/2=1/2-q1/2=q

Caieoai neeu aeaenoaothuea ia ca?yae.

_ _

Ia +q – F+ , ia -q – F_

_ _ _

1/2F+1/2=1/2F_1/2=1/2F1/2=F

Ia yeaeo?e/. iiiaio aeaenoa. ia?a nee , i?e yoii aiciee a?auathuee
iiiaio I.

I=Fd=Flsina=Eqlsina=

=Epsina

d – iea/i neeu

_

M=[P,E] -a?au. iiiaio

(neiey?. i?ieca.)

A iaeii?iaei. ye iiea yeaeo?e/aneee aeeiieue iiai?a/eaaaony aei oao ii?
iiea ye. iiiaio ia noaiao iai?aaeai ii aiao.

_ _

iieth PE o.a. ye. aeeiieue a iieiae. onoie/eaiai ?aaiiaaey.

A iaiaeii?iaeiii ye. iiea aeeiieue ia?yaeo n iiai?ioii eniuouaaao
iinooiaoaeueiia aeaeae. a iaeanoue iaiaeii?iaeiiai iiey.

Oeiu aeeyeaeo?eeia.

Aeaeu (iaoaieci) iiey?ecaoeee aeeyeaeo?eeia.

A caaeneiinoe io no?oeoo?u iieaeoe ?acee/. aeaa oeia aeeyeaeo?eeia
iiey?. e iaiiey?.

iaiiey?. iiey?iua

O2 , H2 , CO … HCl ,…,CO2

Neiiao?e/. Ia neiiao?e-

no?oeoo?a ia- /iay no?oeoo-

eaeoe. ?a.

Aac aiao. iiey.

(A0=0)

A I oeaio?u Oeaio?u oyae.

oyae. (+) e (-) ia niaiaaeatho

niaiaaeatho.

_ _

Pi=0 Pi?0

aPi=0 aPi=0

i i

A neeo oai-

oe/. aeaeae.

aeeiieae.

O iaiiey?.

aeeye. a iono-

onoa. aiao. ii-

ey iaeaeoeu ia

eiatho nianoa.

ye.iiiaioia.

(aeeiieae iao)

Ai aiao. iiea

_

Pi?0

I?eaioaoeey

_ aeeiiee ii

Pi?0 aiao. iie. A0

aPi?0 aPi?0

i i

aeeiiee

Iiey?ecaoeey a caaen. io aeaea

iaoaiecia iaca.

Aeeoi?iaoeeii- I?eaioaoee-

iay (yeaeo?ii- iiiay iiey-

iay). ?ecaoeey.

Iacaaeneii io aeaea iiey?ecaoeee o ethaiai iiey?eciaaiiiai aeeyeaeo?eea
iiyaeyaony a ye. iiea noiia?iue yeaeo?e/aneee aeeiieueiue iiiaio.

Iiey?eciaaiiinoue.

Aaeoi? iiey?eciaaiiinoe.

Naycue aai n iiaa?oiinoiuie ca?yaeaie.

ssae. iiey?ecaoeee iienuaaaony n iiiiuueth aaaeiie oa?aeoa?enoeee
iiey?eciaaiiinoueth eee aaeoi?a

_

iiey?ecaoeee TH.

Iiey?eciaaiiinoueth aeeyeaeo?eea iaca. oec. aae./eneaiii ?aaioth
noiia?iiio yeaeo?e/aneiio (aeeiieueiiio) iiiaioo iieaeoe caeeth/aiiuo a
aaeeieoea iauaia.

_

1) TH=aPi/DV

i

a /eneeoaea noiia?iue iiiaio anaai ia?acoea , DV – iauai anaai ia?acoea.

A Ne[TH]=Ee/i2

_ _

2) TH=aee0A

ae -aeeyeaeo?e/aneay aini?eei/aainoue aauanoaa.

ae>0 ae>1

Ec 2) ae -const

Iieaaeai /oi aaeoi? iiey?ecaoeee ?aaai (aeey oi/ae acyouo aioo?e
aeeyeaeo?eea).

TH= s ‘

Ionoue ai aiao. iiea A0 iao. ianneaiue ia?acaoe.

DV=Sl

Iacaaeneii io niiniaa iiey?ec. ni?aaa aoaeao +s ‘ , ni?aaa -s ‘.

_

aPi =ql=Ss ‘l=

i

TH=s ‘Sl/Sl =s ‘

Ye. iiea aioo?e aeeyeaeo?eea.

Aaeoi? ye. niauaiey.

?anni. iiey?ecaoeeth iaeii?iaeiiai , ecio?iiiiai aeeyeaeo?eea (ae
-const) aianaiiiai ai aiao. iaeii?iaeiia iiea iiea A0 ia?aciaaiiia
ieineei eiiaeain.

Ia ia?acoea iiyayony iiaa?oiinoiua naycaiiua ca?yaeu.

+ s ‘ , – s ‘. _

Nayc ca?yaeu nicae. iiea A’

_

iai? i?ioeaiiieiae. A0.

_ _ _

A=A0+A’ A= A0+A’

A=A0 – s ‘/e0=E0 – aee0E/e0

E+aeE=E0

(1+ae)= E0

1+ae=e

E=E0/e – iai?yaeaiiinoue iiey a aeeyeaeo?eea aianaiiiai ai aiao. iiea
A0.

Iai?yaeaiiinoue iiey a aeeyeaeo?. Oiaiueoaony a e ?ac i?e oneiaee /oi s
ia iaeeaaeeao eiiaeain. inoathony iinoiyiiuie.

Anee aeeyeaeo?ee aiineony a ieineee eiiaeain. iiaeeeth/aiiue e enoi/ieeo
iai?yaeaiey , iai?yaeaiiinoue inoaaony =A0.

eA=A0

ee0A=e0A0 D0=e0A0

D=D0=s

A oaeii neo/aa ye. niauaiea iaeeiaeiai a aaeooia e a aeeye.

Eaeoeey.

s =const E=A0/e0

E nicae. anaie aeaeaie ca?yaeia eae naiaiaeiuie oae e naycaiiuie.

D = D0

aeeye a aicae

U=const

s =const

A0=E

D=eD0

Naycue iaaeaeo naycaiiuie e naiaiaeiuie e naiaiaeiuie ca?yaeaie (s e s’
).

Naycue iaaeaeo s e s’ onoaiaae.ia iniiaaiee au?aae. aeey iai?yae. iiey.

A= A0 – A’

A0/e=A0 – A’

s/e0=s/e0- s ‘/e0

s/e= s – s’

s’=(e – 1/e)?s

_ _ _

Naycue iaaeaeo A , D , TH.

_ _

D= e0eE=(1+ae)?e0E=

_ _

=e0E+aee0E0

_ _

D=e0E+TH – naycue

Oai?. Aaonna i?e iaee/ee aeeyeaeo?eeia.

Aeey aicaeooa e aeey aaeooia aeaa ?aaiua oai?. Aaonna.

1) ?Dnds=aqi

S i

2) oe0Ends=aqi

i

1)=2)

I?e iaee/ee aeayeaeo?eeia cia/eiinoue 1) e 2) ?acee/ia. A oi?ioea 2) i?e
iaee/ee aeeyeaeo?eea a i?aa. /anoue iaaei aeiaaaeoue aeaaa?ae/. noiio
anao naycaiiuo ca?yaeia 2)’ oe0Ends=aqi+

i

+aqi’

i

Aae. naycaiiuo ca?yaeia caaenao io An.

Iioie aaeoi?a ye. niauaiey neaicue i?iecaie. caiei iiaa?o. ?aaai
aeaaa?ae/. noiia anao naiaiae. ca?yaeia caeeth/. aioo?e iiaa?oiinoe.

?Dnds=aqi – oai?. Aaonna

S i i?e iaee/ee aeeyeaeo?eea.

ssaeaiea ia a?aieoea aeaoo aeeyeaeo?eeia .

A?aie/iua oneiaey.

Caeii i?aeiieaiey eeiee iiey.

Aei neo ii? iu ?anni. aeeye. aiineiue a iiea oae /oi iiaa?oiinoue aai
niaiaaeaea n yeaeiioiioe. iiaa?o. , a eeiee

_ _

A e D auee ^ iiaa?oiinoe.

_ _

Eaeiai iai?aaeaiea A e D

_ _

anee A e D ia ^ yeaeiioiioe. iiaa?o.

Aeey iino?iaiey ea?oeiu iiey aieo?e aeeyeaeo?eea ioaeii ciaoue a?aie/iua
oneiaey.

A?aie/iua oneiaey aeey ii?iaeueiuo ninoaaeythueo

_ _

A e D.

?anni. a?aieoeo ?acaeaea aeaoo aeeyeaeo?eeia.

Inoue o 1) – e1

2) – e2

e2 > e1

Ionoue ia a?aieoea ?acaeaea

_

aeaoo aeeyeaeo?ee?eeia D iai?aaeai iiae oaeii a.

_ _

?anneeaaeuaaai D1 e D2 ia ninoiaeythuea ii?iaeueioth e iiaa?oiinoe e
oaiaai-oeeaeueioth.

_ _ _

D1=D1n+D1t

_ _ _

D2=D2n+D2 t

Aeey i?eiaiai. Oai?. Aaonna iaaei iino?ieoue caiai. iiaa?o.

Iooii aua?aoue oeeeeiae?e/ iiaa?oi.

Iaeaeai iioie aaeoi?a ye. niauaiey /a?ac caiei. iiaa?o.

OD=D2nDS – D1nDS

Iaeaeai aeaaa?. noiio ca?. iiiaaoeo aioo?ue.

D2nDS?D1nDS=0

DS?0

1) D2n=D1n

Ciaeanii nayce.

e2e0E2n= e1e0E1n

E1n/E2n = e2/e1

2) – aoi?. a?aie/. one. iieac. eaeiai iiaeaeaiea A ia a?iieoea: En ia
a?aieoea ?acaeaea aeaoo aeeye. eciaiyaony nea/eii.

A?aie/iua oneiaey aeey oaiaaioe. ninoiaeythuae.

Aeey iieo/. yoeo a?aie/. one. ainiieuec. oai?.i oee?eoeyoeee aaeoi?a
iai?yaeaiiinoe yeaeo?e/ iiey.

?Aldl=0

L

Ioaeii iino?ieoue /aoaae aeey

_

A aiaeiae/ii ?en 1.

_ _ _ _

(1) – A1® A1=E1n+E1t

_ _ _ _

(2) – A2® A2=E2n+E2t

Aeey i?eiaiaiey oai?. i oee?eoe. ioaeii aua?aoue caiei. eiioo?. A
ea/anoaa caieiooiai eiioo?a auae?aai i?yiioaieueiee noi?iiu eioi?.
1/21/2 a?aieoea ?acaeaea , aunioa h®0.

AA=CD=a

Iai?aaeaiea iaoiaea ii /aniaie no?aeea.

?Aldl=0 L=ABCD

L

A eaaeaeie oi/ea ia ?anno AB E1t 1/21/2 yoiio o/anoeo.

Iiyoiio oee?eoeyoeey E1t ia AB ?aaia

B D

?Aldl=E1todl – E2todl=0

L A C

E1ta – E2ta=0

a?0

3) E1t=E2t

O aaeoi?a iai?yaeaiiinoe iiey i?e ia?aoiaea /a?ac a?aieoeo ?acaeaea
aeaoo aeeyeaeo?eeia ia iaiyaony oaiaaioeeaeueiay ninoiaey-thuay.

D1t/e1e0=D2t/e2e0

Eniieuecoy 3) e naycue iaaeaeo

_ _

D e E iieo/ei:

D1t/e1e0=D2t/e2e0 – 4-ia oneiaea .

Ia a?aieoea ?acaeaea aeaoo aeeyeaeo?eeia oaiaaioe.

_

nonoaae. D eciaieny.

1,2,3,4 – oneiaey iicaieytho i?aaaeueii iino?ieoue ea?oeio eeiee iiey.

Caeii i?aeiieaiey eeiee iiey.

tga2=D2 t /D2n tda1=D1 t /D1n

tga2/tga1= D2t ?D1n/ D2n?D1t = =D2 t /D1 t = e2/e1

5) tga2/tga1=e2/e1 – cae. i?aeiieaiey eeiee iiey.

Oaie aieueoa a oie n?aaea aaea e aieueoa.

Ec 5) neaaeoao aoua eeiee iiey ?aniieiae. A aeeyeaeo?eea aaea e aieueoa.

e2< e1Iino?ieoue ea?oeio eeiee iiey.Aeoeaiua aeeyeaeo?eee.(aeeyeaeo?eee n iniauie iiey?ecaoeeiiiuie naienoaa-ie.)Iu ?anniao?eaaee iiey?eca-oeeth iaeii?iaeiuo , ecio?ii-iuo aeeyeaeo?eeia._ _TH=aee0Aae=constI?e A=0 o aieueoainoaa aeeye. TH =0. (iiey?ecaoeey en/acaao)Nou. aeeyeaeo?eee n iaeeiaeiie caaenaiinoueth._ _TH io A._ _TH ?aee0A2) TH = f(E)Yoi ia?aue oei aeeye. n iniauie naienoaaie i?aaenoa-aeyao niaie eeann neaia-ioiaeeyeaeo?eeia.O neaiaioiaeeyeaeo?eeia 2) i?aaenoaaeyao niaie iaoeth aenoa?acena.Iaoey aenoa?acena 1,2,3,4,5,6,1Iaeanoue 0,1 - iaeanoue ia?ae/-iie iiey?ecaoeee._ _I?e oiaiueoaiee A aaeoi? THoauaiao ii e?eaie 1,2,3._I?e A=0 a aeeyeaeo?eea nio-?aiyaony inoaoi/iay iiey?e-_caoeey TH 0._TH =0 a o. 3 o.a. i?e aiao. iiea ia?aoiiai iai?aaeaiey.Eaeoeey.Iinoiyiiue oie.I?iaiaeeiinoue iaoaeeia e aacia.Yeaeo?e/aneee oie - iai?aaeaiiia aeaeaeaiea ca?yaeia.Iineoaee ca?yaea - ca?yaeu nicaeathuea oie.A yeaeo?ieeoao - eiiuiaoaeeao - yeaeo?iiuaacao - eiiu e yeaeo?iiu.I?ioiaeeiinoueth oiea - iaca. i?ioiaeaeaiea ca?yaeia /a?ac aauanoai.Oeiu i?iaiaeeiinoe - eiiiay , yeaeo?iiiay , niaoaiiay.Iacaaeneii io aeaea i?iaiaeeiinoe aeey oiea i?eiyou neaaeothuea oa?aeoa?enoeee:I - neea oiea.j - ieioiinoue oiea.Neea oiea - oec. aae. /eneaiii ?aaiay ca?yaeo ia?aiineiiio /a?ac iiia?a/iia na/aiea i?iaiaeieea ca 1 n. (neaey?iay aae.)[ I ]=AI=q/A1A = neea oiea i?e i?ioiaeaeaiee eioi?iai /a?ac iiia?a/iia na/aiea i?iaiaeieea a 1 n ia?aiineony ca?yae a 1 Ee.A - /aoaa?oay iniiaiay aaeeieoea a Ne.Iai?aaeaieai oiea n/eoatho iai?aaeaiea iieiaeeoaeueiuo ca?yaeia.Anee neea oiea iinoiyiia e iai?aaeaiea iinoiyiii , oi aiai?yo i iinoiyiiii oiea.(1) - ni?aaaaeeeaa aeey iinoiyiiiai oiea.Anee neea oiea iaiyaony ni a?aiaiai oi (1) caien. neaaeothuoth 2) i=dq/dt.Ia iniiaaiee (2) iiaeii iieo/eoue eie- ai ca?yaea ia?aiineiiai /a?ac iiia?a/iia na/aiea i?iaiaeieea ca aaeeieoeo a?aiaie dq=idt.t3) q=oi(t)dt0Ieioiinoue oiea - aaeoi?iay oa?aeoa?enoeea.Ii ii?aaeaeaieth iinoiyiiiai oiea ieioiinoue oiea ?aaia_4) 1/2j1/2=I/S^ S^- ^ oieoIeioiinoue oiea - oec. aae. /eneaiii ?aaiay ca?yaeo ia?aiineiiio ca 1n /a?ac aaeeie/ioth ieiuaaeeo iiia?a/iiai na/aiey ?aniieiaeaiiiai ^ oieo.Anee oie iaiyaony 5) j=di/dS^oi?ioea 5) aeaao aiciiaeiinoue iaoiaeeoue neeo oiea.6) di=jdS^=jndSeioaa?e?oai eaa. e i?aa. /anoue._ _7) i=ojndS =ojdSS SEc 7) neaaeoao /oi neea iaiythuaainy oiaa /eneaiii = iioieo aaeoi?a ieioiinoe oiea /a?ac ieiuaaeue iiia?a/iiai na/aiey.Aaeeieoeae ieioiinoe oiea yae. A/i2.Naycue iaaeaeo ieioiinoueth oiea e nei?. iai?aaeaiiiai aeaeaeaiey iineoaeae oiea.A ethaii aauanoaa i?iaiaeyuai oie iineoaee oiea o/aanoaotho a iai?a?uaiii /aioe/. aeaeae.uo=c? uo- oaieiaay nei?.

Iai?aaeaiiia aeaeae. yoi aeaeaeaiea eioi?ia iaeaaaaony ia oaioe/. oaie.
aeaeae. e auioaeaeaao iineoaeae aeaeaaoueny a ii?aaeaeaiiii iai?aaeaiee.

c?- n?. cia/. nei?. iai?aaeaiiiai aeaeae.

Ieioiinoue oiea yae. ooieoeeae. j=f(n, qye, )

1) j= qye?n

Aeey aeie. ?anniio?ei i?iaiaeiee iinoiyiiiai na/aiey oeeeeiae?e/. oi?iu.

n – /enei iineoaeae oiea

qye- ecaanoii

j=I/S=q/St

q – aae. ca?yaea ia?aiineiiai /a?ac iiia?a/. na/aiea S ca a?aiy t.

l=

V=lS=S

qv= qyenV – /a?ac S^ ca 1n.

q=qv?t

Iiaenoaaei a 2)

i= qyenV?St/St _ _

Ionthaea neaaeoao j=qyen

Oneiaey nouanoaiaaiey oiea.

Enoi/ieee oiea.

Y.Ae.N. enoi/ieea oiea.

Iaiaoiaeeiua one. nou. oiea.:

1) iaee/ea iineoaeae oiea

2) iaee/ea nee auioaeaeathueo iineoaeae oiea aeaeaaoueny

3) iaee/ea ?aciinoe iioaioeeaeia aaeieue iiaa?oiinoe i?iaiaeieea.

?anni. io?acie i?iaiaeieea.

Aeey aeeeoaeueiiai iiaeaea?aeaiey oiea iaiaoiaeeii eaeeioi ia?acii
iieiaeeoaeueiua iineoaee oiea n eiioea 2 ia?aianoe ia oi?aoe 1.

Aeaeaeaiea iineoaeae oiea aioo?e ia?acoea i?ienoiaeeo iiae aeaenoa. neeu
yeaeo?e/. i?e?iaeu.

Aeaeaeaiea ca?yaeia i?ae?aoeony i/aiue auno?i: iieiaeeoaeueiua
neaieeaathony ia eiioea 2.

Ia?aiin ca?yaeia ec 2 a 1 inouanoaeoue iaaiciiaeii (yoi icia/aei au
aeaeaeaiey (+) i?ioea A ).

Oaeie ia?aiin iiaeii inouanoaeoue oieueei n iiiiuueth neeu ae?oaie
i?e?iaeu ia yeaeo?e/. i?ienoiaeaeaiey.

Yoio ia?aiin ?aaeecoao ono?ienoai iacuaaaiia enoi/ieeii oiea.

Ca n/ao aeaenoaey enoi/ieea oiea aioo?e i?iaiaeieea iiyae. yeaeo?e/.
iiea iai?yaeaiiinoueth A.

Iineieueeo A iiaa?o. i?iaiaeieea , oi iiaa?o. i?iaiaeieea ia yae.
yeaeiioiioe.

j2< j 1j2 - j 1= DjEnoi/. oiea iacaaen. io i?eioeeia ?aaiou oa?aeoa?ecoao e - Y.Ae.N. e r - aioo?. nii?ioeae.Y.Ae.N. - iacuaatho ?aaioo niaa?oaaioth noi?iiieie neeaie ii ia?aiauaieth aaeeie/. iieiae. ca?. ia caieiooii o/anoea oeaie.1) e=A*/q[e]=BAoi?. ii?aaeaeaiea Y.Ae.N.2A=q(j2 - j 1)=qoAldl122) A*=A1,2*= qoAl*dl1E* - iai?yaeaiiinoue iiey noi?iiieo nee.E*=F*/qIiaenoaaei 2 a 1.23) e=oAl*dl1Aeey caiei. oeaie a 3) ioaeii acyoue eiioo?iue eioaa?ae.4) e=?Al*dlLY.Ae.N. - a caieiooie oeaie = oee?eoeyoeee aaeoi?a iai?yaeaiiinoe iiey noi?iiieo nee.Cae. Iia a eioaa?aeueiie oi?ia.(iaiauaiiue caeii)I=(j2 - j 1)/R=U/RR=r?(l/S) aeey oeeeeiae?e/ i?iaiaeieeia.r - oaeaeueiia nii?ioeaeaiea.U=j2 - j 1 niaiaaeatho oieueei aeey iaeii?iaeiiai o/anoea oeaie.Ia ini. cae. nio?. yia?a. iiaeii iieo/eoue cae. Iia aiauae oi?ia, ec eioi?iai neaaeotho /anoiua neo/ae.Iaiauaiiue caeii Iia -caeii aeey iaiaeii?iaeiiai o/anoea oeaie.Iaiaeii?iaeiue o/anoie - o/anoie niaea?aeauee enoi/iee oiea.I=((j2 - j 1)±e)/R1,2 - iaiauaiiue caeii.R1,2=R+ rNi ciaeii + e aa?aony oiaaea eieaea neea oiea io + e - .Ni ciaeii - e oiaaea eiaaea i - e +.(j2 - j 1)±e =U?anni. /anoiue neo/ae.1) neo/ae e=0I=(j2 - j 1)/R=U/R2) neo/ae: caieiooay oeaiuej1=j2 j2 - j 1=03) I=e/(R+r)Cae. Iia a aeeooa?aioeeaeueiie oi?ia.?anni. i?iaiaeiee ia?aiaiiiai na/aiey.Auaeaeei aioo?e yeaiaioa?iue iauai , aeeeiia - dl , ieiuaaeue iiia?a/i. na/aiey dS.dR=r?(dl/dS)Auaeaeei iauai niioaaonoaothuae iaeii?iaeiiio o/anoeo oeaie.dI=dU/dRdI=dU/(r?(dl/dS))dI/dS=(1/r)?(dU/dl)j=(1/r)?E1/r =g - oaeaeueiay i?iaiaeeiinoue._ _J=gE ieioiinoue oiea a aeaii. oi/ea i?iaiaeieea = i?iecaaaeaieth oaeae. I?iaiaeeiinoe yoiai i?iaiaeieea ia iai?yaeaiiinoue a yoie aea oi/ea. C o/aoii noi?iiieo nee aeey iaiaeii?iaei. o/anoea oeaie cae. Iia aoaeao:_ _ _j=g(E+E*)Eaeoeey.Aeiiieieoaeueiua iai?aaeaeaiey Y.Ae.N.Aeey caiei. oeaie cae. Iia aoaeaoI=e/(R+r)III) e=IR+IrIR - iaaeaiea aiao. iai?yaeaiey.Ir - iaaeaiea aioo?. iai?yaeaiey.Yeaeo?iaeaeaeouay neea enoi/ieea oiea = noiia iaaeaiee iai?yaeaiey ia aiao. nii?. e ia aioo?. o/anoea.Ec III iiaeii i?eeoe e caeeth/aieth /oi anee R>>r (enoi/iee oiea
?aciieioo) R®Y.

IV) e=IR Y.Ae.N.= iai?yaeaieth ia eeaiao ?aciieiooiai oiea.

Aaciaue ?ac?yae.

Eiiecaoeey. ?aeiiaeiaoeey aacia.

Aacu yae. aeeyeaeo?eaie , e a iau/iuo oneiaeyo ia i?iaiaeyo ye. oie.

Ana aacu nino. ec iaeo?aeueiuo aoiiia e iaeaeoe.

Anee eaeei eeai ia?acii nicaeaoue iineoaee oiea a aacao , oi iie noaioo
i?iaiaeieeaie.(eiiecaoeey).

: OO , R – eo/e , g – ece. , a , b /anoeoeu – aiaoiea eiiecaoi?u.

Eiiecaoeey – yoi i?aa?auaiea iaeo?aeueiuo aoiiia e iaeaeoe a eiiu.

Yeaeo?iiu a aoiiao oaea?aeeaathony neeaie eoeeiiiane. i?eoyaeaiey.

Aeey oaeaeaiey yeaeo?iia iaiaoiaeeii niiaueoue yia?aeth ?aaioth eee
i?aauoathuoth yia?aeth aai nayce n yae?ii (eia?aey eiiecaoeee Ei).

Ei =io 5 aei 20 yA

Yeaeo?ii e eii iiaoo ia?aiauaoueny iiae aeaenoa. ye. iiey.

Naiaiaei. yeaeo?iiu noaeeeaaynue n iaeo?aeueiuie aoiiaie iiaeao aieoe a
aai ninoaa nicaeaaay io?eoeaoaeueiue eii.

A ?acoeueoaoa eiiecaoeee aiciee. 3 aeaea iineoaeae oiea: +eii , -eii ,
yeaeo?ii.

Aicieeatho aeaa iai?aaeaiiuo ae?oa e ae?oao ano?a/iuo iioiea ia?acothuea
ye. oie.

Iaeiia?aiaiii n eiiecaoeeae a aaca i?ienoiaeeo ?aeiiaeiaoeey aaca
caeeth/athuayny a en/aciiaaiee iineoaeae oiea.

Iiae aeaenoaeai aiaoiaai eiiecaoi?a iiuiinoueth Dn.

(iieacaaaao neieueei yeaeo?iiia ia?acoaony a 1 i3 ca 1n.)

1) A ia/. iiiaio a?aiaie E>?.

2) Nionoy iaeioi?ia a?aiy E=? n+=n_ onoaiaaeeaaaony ?aaiiaanea
eiioeao?aoeee iineoaeae oiea n.

3) Iinea aueeth/aiey. Ei

A ?aaiiaanee qye(+)=(-)=e a neeo i?aeiouanoaa iaeiie?aoiie eiiecaoeee.

n+=n_=n

j=en(+)

Iiuo iieacuaaao /oi nei?. iai?. aeaeae. caaeneo io aae. iai?yaeaiiinoe
ye. iiey e iiaeaeaeiinoe.

u+=b+E

u_=b_E

u+,u_ – iiaeaeaeiinoue iineoaeae oiea.

u+>b_ b=u/E

Iiaeaeaeiinoue – yoi oec. aae. /ene. = nei?. oii?yaei/. aeaeae.
iineoaeae oiea iiae aeaenoaeai ye. iiey aaeeie/iie iai?yaeaiiinoe.

[b]=i2/(A?n)

1) j=e?n(b++b_ )E – cae. Iia.

I?iecaaaeaiea ?aaiiaaniie eiioeaio?aoeee ia yeaiaioa?. ca?yae iineoaeae
oiea ia noiio iiaeaeaeiinoae e ia iai?. ye. iiey.

2) j=gE

g=e?n(b++b_ ) g=1/r

g – oaeaeueiay i?iaiaeeiinoue

3) ji=e?Dni?d

d – ?anno. iaaeaeo yeaeo?iaeaie.

Dni – iiuiinoue eiiecaoi?a.

Oaea?iay eiiecaoeey.

Naiinoiyoaeueiue aaciaue ?ac?yae.

I?e aieueoeo iai?. iiey naiaiae. yeaeo?iiu onei?ythony aei oaeeo yia?aee
eioi?uo aeinoaoi/ii aeey yeaeo?iiiui oaea?ii.

A iae. 4 a ioo?e aaca iiyae. nianoaaiiue enoi/iee eiiecaoeee , oaea?iie
eiiecaoeee.

*enei yeaeo?iiia ?acei aic?anoaao.

Eaaeiiia?aciue i?ioeann.

A iae. 4 iaee/ea aiao. eiiecaoeee iaiaoiaeeii aeey iiaeaeaiaeaiey
ca?yaea.

I?e aeaeueiaeoai oaaee/aiee iai?. iiey a iae. 5 yia?aeth aeinoaoi/ioth
aeeyeiiecaoeee iieo/atho eiiu.

A iae. 5 ?ac?yae noaiiaeony naiinoiyoaeueiui. i?e yoii neea oiea oaaee/.
I?aeoe/anee aac eciaiaiey A.

Iai?yaeaiiinoue i?e eioi?. i?ienia?aoiae ec ianiiino. A naiino. ?ac?yae.
?ac?yae iaca. iai?yaeaieai caaeeaaiey eee i?iaiy.

Oeiu naiinoiyoaeueiuo aaciauo ?ac?yaeia.

1) oeathuee

2) ene?iaie

3) aeoaiaie

4) ei?iiiue

(a O?aoeiiaie)

Cae. Aeaeioey – Eaioea a eioaa?aeueiie e aeeooa?. oi?ia.

Ia aiao. nii?ioeaeaiee a ethaie yeaeo?e/aneie oeaie auaeaeyaony eie –
ai oaieiou.

1) Q=I2Rt

Ca a?aiy t i?e i?ioaeaiee neeu oiea i?e i?ioaeaiee neeu oiea a iai
auaeaeeony eie-ai oaieiou Q. (eioaa?aeueiay oi?ia)

Iieo/ei cae. a aeeooa?. oi?ia.

Aeey yoiai ?anni. aioo?e i?iaiaeieea n nii?. R yeaiaioa?iue iauai
dV=dS?dl

dR= r dl/dS

Caieoai aianoi 1) eie-ai oaieiou auaeae. a yoii iauaia ca a?aiy dt.

2) dQ=j?(dS)2?r?(dl/dS)?dt

(dQ/dVdt)=rj2

3) wo=rj2 j=gE

wo =r?g2E2=(1/g)g2E2

3c ) wo =gE2

?aaioa e iiuueiinoue oiea, EIAe oiea.

e=A*/q A=qe=eIt

iieiay iiuiinoue enoi/ieea oiea P=A*/t=Ie

P=I( IR+Ir)=I2R+I2r

P=Piieac+Paaciieaci

h=Piieac/P

Iniiaiua iieiaeaiey EYO.

1) I?e e?enoaeeecaoeee iaoaeeia ec ?anieaaa aoiiu eo oa?ytho yeaeo?iiu.
I?e yoii aicieeatho iieiae. ca?yae. eiiu e naiaiaeiua yeaeo?iiu. Anee
eaaeae. aoii oa?yao ii ye-io, oi nao=nye=(D/m)·Na. Naia. ye-iu niiniaiu
ia?aiauaoueny ii anaio iau?io iaoaeea.

2) Ana iaoaeeu eiatho e?enoaeee/. no?oeoo?o, a iniiaa eioi?ie eaaeeo
e?enoaeee/. ?ao?oea eoae/. oi?iu n iieiaeeo. eiiaie a oceao. Oaeei
ia?acii ?ao?oea i?ic?a/. aeey ye-iia.

3) Naia. ye-iu, ioi?aaiiua io aoiiia, noaiiayony eieeaeoeaiie
nianoaaiiinoueth anaai iaoaeea. Iie niaa?o. oaioe/. oaie. aeaeaeaiea.
I?e yoii ye-iu aaaeoo naay iiaeiaii iaeiiaoiiiui iie-eai eaeaae. aaca,
iiae/eiyynue noaoenoeea Iaenaaeea. Naia. ye-iu i?eiyoi iacua.
“yeaeo?iiiui aacii”. Aeey ye-iia ii o-ea, ecaanoiie ec IEO iiaeii
ii?aaeaeeoue n?aae. nei?. oaieiaiai aeaeaeaiey:

aVon=Oe(8KT)/(pm)»105i/c. 4) Naia. ye-iu, noaeeeaaynue n eiiaie,
?aniieiaeaiiuie a oceao ?ao?oee, ioaeatho ei naith eeiao. yia?aeth. Yoei
iaoneiaeaii nii?ioeaeaiea i?iaiaeieeia.

5) I?e i?eeiaeaiee aiaoi. ye. iiey iai?yae?iiinoueth E ia oaioe/. oaie.
aeaeaeaiea ye-iia iaeeaaeuaaaony oii?yaei/aiiia aeaeaeaiea. I?e yoii
aicieeaao ye. oie. aVn « aVTn

Ioeaiei aVn ii o-ea j=qyenaVn=enaVnTH

TH aVn=j/(en); n~1029i-3, j(Cu)=107A/i2TH

TH aVn~10-3i/n. Noiia?i. nei?.aVSn=aVn+aVTn

Iineieueeo aVn « aVTn, oi aVSn » aVTn

Caeii Iia a EYO

Iniiaiua iieiaeaiey EYO iicaieytho auaanoe o-eo caeiia Iia eae o-oeeth
ia?aiao?ia iineoaeae oiea. Aeey auaiaea eniieuecoai niioiioaiea j=enaVn.
Ionoue e i?iaiaeieeo i?eeiaeaii aiaoiaa iiea E. Naia. ye-iu i?eaeoo a
aeaeaeaiea. Ia ye-iu aoaeao aeaenoa. neea ni noi?iiu iiey
F=eE.E=constTHa=const.

F=eE=ma (ii II c-io Iuetho.). a=(eE)/m

Aeey ?aaiione. aeaeae. Vt=V0+at

n?. aeeeia naia. i?iaaaa aln~d ?anno. iaaeaeo eiiaie; t-a?aiy naia.
i?iaaaa.

Nei?inoue yeaeo?iia

Vt=Vmax=at – aei noieeiiaaiey n eiiii

V0=0 – iinea noieeiiaaiey n eiiii

aVn=(V0+Vmax)/2=Vmax/2=(at)/2=(eEt)/2m;

t = aln/aVSn = aln/aVTn;

aVn = [(eE)/2m] · aln/aVTn;

j=enaVn=[(e2nE)/2m]·aln/aVTn c-i Iia a EYO

j=gE TH g=(ne2aln) / (2maVTn)

Caeii Aeaeioey-Eaioea a EYO

Iaa?aaaiea i?iaiaeieea, niaeanii EYO, iauyniyaony noieeiiaaieai
yeaeo?iiia n eiiaie e?enoae. ?ao?oee. ?ann/eoaai eeiao. yia?aeth
ioaeaeueiiai ye-iaia?aae noieeiiaaieai n eiiii, iieo/aiioth ei ca n/?o
iiey: W1=(mV2max)/2.

Ca 1 nae. ye-i iiaeao eniuouaaoue Z nioaea?aiee, aaea Z = 1/t =aVTn /
aln. Anee a 1 i3 /enei ye-iia = n, oi eeiao. yia?aey, ia?aaeaiiay
?ao?oea anaie n ye-iaie ca Z noieeiiaaiee eaaeaeiai ec ieo W=naZnW1=wT.

wT=[(mV2max)/2]·n·aZn=[ne2aln/2maVTn]E2

Cao?oaeiaiey EYO

1) Oaiia?aoo?iay caaeneiinoue i?iaiaeieeia. Niaeanii yenia?. aeaiiui
nii?. iaoaeeia oaaee/. n oaiia?aoo?ie ii c-io R=R0+aT, aaea R0-nii?. i?e
T=273K, a=1/273 a?aae-1. Aeey r o-ea aiaeiae/ia r=r0+aT. Niae. iiuoa
r~T. r=2maVTn/(ne2aln)THr~aVTn. Ia ini. EYO neaae. r=OeT, o.a. oai?ey
?anoiaeeony n iiuoii.

2) Oaiei?ieinoue iaoaeeia e aeeyeaeo?eeia. Niae. iiaoia aoiiiay
oaiei?ie. iaoaeeia e aeeye-eia iaeeiaeiaa (C=3R, aaea R-aaciaay
iinoiyiiay). Yoi iieiaeaiea iac. c-i Aetheiiaa e Ioe. Niae. EYO iaoaee
nino. ec e?enoae. ?ao?oee e naia. ye-iia, a aeeyeaeo?ee naia. ye-iia ia
eiaao. Neaaeoao iaeeaeaoue, /oi oaiei?ie. iaoaeeia=o.?. e?enoae.
?ao?oee+o.?. naia. ye-iia (Ciao=R+3/2R=4,5R), /aai iao ia iiuoa.

Yeaeo?iiiue aac, ia naiii aeaea iiae/eiyaony ia eeanne/aneie noaoenoeea
Iaenaaeea, a eaaioiaie noaoenoeea. Cao?oaeiaiey ono?aiythony a eaaioiaie
oai?ee i?iaiaeeiinoe. Ianiio?y ia cao?oaeiaiey, EYO iia i?inoa e oe?iei
i?eiaiyaony i?e aunieeo oaii-?ao e iaeuo eiioeaio?aoeeyo.

Yeaeo?iiaaiaoeci

Iaai. iiea. Aeaeae. ca?yaeu a ie?oae. i?ino?ainoaa nicaeatho iaai. iiea,
eioi?ia yae. iaeiie ec oi?i nou. iaoa?ee. A ioee/ea io ye. noaoe/aneiai
iiey, iaaieoiia aeaenoaoao oieueei ia aeaeae. ca?yaeu. I?iaiaeieee n
oaeoueie ii iei oieaie a ie?oae. i?-aa nicaeatho iaai. iiea. I?eiyoi
?acee/aoue iae?i- e iee?ioiee. Iae?ioiee-yoi oiee, oaeouea ii
i?iaiaeieeai. A ethaii aau-aa yeaeo?iiu aeaeaeoony ii e?oaiaui i?aeoai.
Aeaeaeaiea ye-iia a aoiia ii e?oaiaui i?aeoai oiaea i?eaiaeeo e
nicaeaieth iaai. iiey. Oiee, nicaeaaaaiua a aauanoaao aeaeaeoueieny
ye-iaie iacuaatho iee?ioieaie.

Aeiioaca Aiia?a: a eaaeaeii aau-aa ca n/?o aeaeaeaiey yeaeo?iiia
aicieeatho iee?ioiee.

Aeey enneaae. iaai. iiey i?eiaiytho iaai. no?aeee (iiuo Ynoa?aea). Iaai.
no?aeea i?aaeno. niaie iaaieo, iaeaoue ia ino?e?. I?e i?iioneaiee oiea
/a?ac i?iaiaeiee no?aeea eniuouaaao neeiaia aicaeaenoaea
(onoaiaaeeaaaony ia?iaiae. i?iaiaeieeo). 2e iaoiae enneaae. iaa. iiey –
n iiiiuueth ieineiai eiioo?a n oieii. Oi?ia eiioo?a ia ea?aao ?iee.

Iaiaoiaeeii, /oiau ?acia? eiioo?a aue ianoieueei iae, /oiau ia eneaaeae
enneaaeoaiia iiea. Eiioo?u, aiineiua a iaai. iiea eniuouaatho
i?eaioe?othuaa aeaenoaea ni noi?iiu yoiai iiey. ?aiee i?eiyoi
oa?aeoa?eciaaoue iieiaeeo. ii?iaeueth. Iieiaeeoaeueiie iac. ii?iaeue,
i?iaaae?iioth e oeaio?o i?iaiaeieea, oaeiaeaoai?ythuaai i?aaeeo i?aaiai
aeioa ii iai?. oiea. Ia iniiaaiee aeaenoaey nee ia ?aieo aeaeatho
auaiae: iaaieoiia iiea – neeiaia e aai iaaei oa?aeoa?eciaaoue ii?aae.
iai?aaeaieai. Ca iai?. iaai. iiey i?eieiatho iai?. iieiae. ii?iaee a
aeaiiii ianoa ?aniie. eiioo?a n oieii.

Ii?aaeaeaiea oa?aeoa?enoee iaa. iiey naycaii n ii?aaeaeaieai iiaaaeaiey
eiioo?a n oieii a iiea. A iaeii?. iiea aian?i eiioo? oiea oaeei ia?acii,
/oiau aaeieue eeiee iiey auea iai?aaeaia ieineinoue.

Ia?a nee nicaea?o a?auathuee iiiaio M. Iiuo iieacuaaao, /oi a?au. iiiaio
caaeneo io iaeio. neeiaie oa?-ee iiey e io neeu oiea a ?aiea (M~B;
|M|~|I|). Aeey anao ?aiie aaiaeeony oa?-ea, naycaiiay n ?acia?aie ?anie
e neeie oiea, oaeouae a ieo. Pm – iaaieoiue iiiaio. Pm=I·S [A·i2]. Iaai.
iiiaio yae. aaeoi?ii. Pm=n·I·S, aaea n – i?o iieiae. ii?iaee, o.a. Pm ||
n. Iiuo iieac., /oi M=[Pm , B] – iaoaie/aneee a?au. iiiaio ?aaai
aaeoi?iiio i?iecaaaeaieth iaaieoiiai iiiaioa ?aiee ia aaeoi? eiaeoeoeee
iaai. iiey. M=Pm·B·sina (a=Pm^B). Ec yoie o-eu aeaeii, /oi M=max, anee
a=90° (iieiaeaiea I ia ?en.) Mmax=Pm·B(1). M=0 i?e a=0 (iieiae II).
Iieiae. II niioaaonoaoao onoie/eaiio ?aaiiaaneth ?aiee.

Eiaeoeoeey iaai. iiey – iniiaiay neeiaay oa?-ea yoiai iiey. Niae. o-eu
(1) B=Mmax / Pm. Eiaeoeoeeae iaai. iiey a aeaiiie oi/ea iac. oece/aneay
aaee/eia, /eneaiii ?aaiay iaen. a?auathuaio iiiaioo, aeaenoaothu. a
aeaiiie oi/ea ia ?aieo n oieii, eiathuoth aaeeie/iue iaai. iiiaio.
[B]=I/(A·i)=Oe (Oanea). Ei-oeey iaai. iiey i?aaeno. niaie oa?-eo
?acoeueoe?othuaai iiey, nicaeaiiiai iae?i- e iee?ioieaie. Eiaeoeoeeth
iiaeii ecia?aceoue neeiauie eeieyie (aiaeia iai?yae?i. ye. noao. iiey).

Iai?yae?iiinoue iaai. iiey

Eniieuec. aaeoi? B ia anaaaea oaeiaii, iineieueeo i?iyae. caaeneiinoue
io naienoa N?aaeu. Aaiaeeony aniiiiaao. oa?-ea, ia caaen. io naienoa
N?aaeu – iai?yae?iiinoue iaaieoiiai iiey H (aiaeia D a ye. noaoeea).
B=mm0H, aaea m-iaai. i?iieoeaaiinoue. Aeey aaeooia m=1. m0-iaaieoiay
iinoiyiiay. m0=4p·107 Ai/i. [H]=A/i. Aeey aaeooia H=B/m0. Ca aae. (A/i)
iai?yae. iaai. iiey i?eieiatho iai?yae. oaeiai iiey, o eioi?iai
eiaeoeoeey B=4p·107Oe. H ii?aaeaeyaony oieueei iae?ioieaie e ia caaen.
io iee?ioieia. Iineieueeo H – yoi aaeoi?, aeey iaai i?eiyoi no?ieoue
eeiee iai?yae?iiinoe.

Aeo?aaie oa?aeoa? iaa. iiey. A ioee/ea io ye. noao. iiey, iaa. iiea
yaeyaony aeo?aaui: eeiee iaai. iiey anaaaea caieioou, i?aaenoaaeytho
niaie ie?oaeiinoe (aeo?e), ioaaouaathuea i?iaiaeieee n oieii.

Iaai. iiea ia yae. iioaioeeaeueiui. Eeiee iiey B no?iyo niaeanii
i?aaeeo i?aaiai aeioa. Aaeoi?u B e H iai?aaeaiu ii eanaoaeueiie a
eaaeaeie oi/ea eeiee.

I?eioeei noia?iiceoeee

iaaieoiuo iieae

Anee a i?-aa eiaaony iane. i?iaiaeieeia n oieaie, oi a eaaeaeie oi/ea
i?-aa iaai. iiea nicaea?ony eaaeaeui ec i?iaiaeieeia a ioaeaeueiinoe
iacaaen. io iaee/ey inoaeueiuo. ?acoeueoe?. iiea a yoie oi/ea
oa?aeoa?ecoaony aaeoi?aie B e H. Bi e Hi – aaeoi?u, ii?iaeaeaaiua i-ui
i?iaiaeieeiin oieii.

B=SBi; H=SHi;

Caeii Aei-Naaa?a-Eaieana

Ini. caaea/a iaaieoinoaoeee ninoieo a oiaiee ?ann/eo. oa?-ee iieae.
Caeii A-N-E n eniieueciaaieai i?eioeeia noia?iiceoeee aea?o i?inoaeoee
iaoiae ?an/?oa iieae.

dB-eiaeoeoeey, nicae. a oi/. A.

dB=(mm0 /4p)·(I·dl·sina/r2) [1]

dH=(I·dl·sina)/(4pr2) [2]

Eiaeoeoeey iaai. iiey, nicaeaiiay yeaiaioii i?iaiaeieea dl n oieii I a
oi/ea A ia ?annoiyiee r io dl i?iii?oe. neea oiea, dl, neiono oaea
iaaeaeo r e dl e ia?. i?iii?oeeii. eaaae?aoo ?annoiyiey r.

___ ____ __

dB=(mm0 /4p)·(I·[dl,r] /r3)

Cia/aiea c-ia A-N-E caeeth/aaony a oii, /oi ciay dH e dB io dl iiaeii
au/eneeoue H e B i?iaiaeieea eiia/. ?acia?ia ?ace. oi?i.

I?eiaiaiea c-ia A-N-E

Iiea i?yiiai io?acea eiia/iie aeeeiu n oieii.

m=1, m0=4p·10-7Ai/i, H?, B?

dH=I·dl·sina/4pr2

Ii i?aaeeo i?aa. aeioa iaeae?i iai?aae. dH

____ ____

H=SdH. Iineieueeo ana dH iai?. iaeeiaeiai, iiaeii caienaoue H=odH.
Ia?aiaiiie eioaa?e?iaaiey auae-?aai oaie a.

rda/dl=sina TH dl=rdl/sina.

dH=I·r·da·sina/sina·4pr2=

=I·da /4pr

ec o?aoa. DOATH b/r=sinaTH

THr=b/sina.

dH=I·sinada/4pb

a1

H=o I·sinada/4pb=

a2

a1 a1

=I/4pbo sinada=-I/4pbcosa|

a2 a2

H=I/4pb(cosa1-cosa2) (2)

B=m0I/4pb(cosa1-cosa2) (2’)

Iiea i?yiiai aaneii. oiea.

Aeey aane. oiea a1=0, a2=p

A (2): cosa1-cosa2=1-(-1)=2

H=I/2pb; B=m0I/2pb.

Iiea e?oaiaiai oiea

H=odH; r=R; a=90°

2pR

H=o I·dl/4pR2=I·2pR/4pR2=

0

=I/2R; B=Im0/2R (4)

Ea?oeia eeiee iiey aeey e?oaiaiai oiea:

Iiea iiaeiaii ye. noaoe/. iieth aeeiiey. A nayce n yoei e?oaiaie oie
ia?aeno. niaie iaai. aeeiieue. Iieaaeai, /oi e?oa. oie iiaeao neoaeeoue
iaai. aeeiieai. Aeey yoiai a o-ea (4) aeiiiiaeei /eneeoaeue e
ciaiaiaoaeue ia pR2.

B=m0·I·4pR2/2RpR2

pR2=S; I·S=Pm

B=m0·Pm /2pR3

Caeii Aiia?a

Ia iiuoa onoai., /oi ia i?iaiaeiee n oieii a iaai. iiea aeaenoa. neea.
Aeey i?yiieei. i?iaiaeieeia aeeeiie l: F=IBl·sina. I?e a=90° F=IBl. Aeey
i?iaiaeieeia neiaeiie oi?iu c-i Aiia?a caien. a aeeooa?aioe. oi?ia:
dF=IBdl·sina;

___ ___ ___

dF=I[B,dl]-aaeoi?iay oi?ia.

____ ____

F=SdF

Acaeiiae. ia?aee. oieia

?anni. 2 i?iaiaeieea, ?aniieiaeaiiuo ia?aee. ae?oa e ae?oao.

Aoaeai n/eoaoue, /oi 1 nicaea?o iaai. iiea, a 2 iaoiaeeony a iiea 1-ai.
Oiaaea eiaeoeoeey iaa. iiey B1 a oi/eao iaoiaeaeaiey 2: B1=m0I1/2pd.

F2=I2B1l2sina=mI1I2l2/2pd.

Iiaeii aiaeia. ?anni. neeo F1, aeaenoaothu. ia i?iaiaeiee 1 ni noi?iiu
iiey oiea I2. F1=F2, anee l1=l2=l. Ia?ae. oiee i?eoyaeaathony,
aioeia?ae. – iooaeeeaathony.

I?e ?anni. ia?ae. i?iaiaeieeia aaiaeyo neeo, aeaenoa. ia aaeeieoeo
aeeeiu i?iaiaeieea:

faae.aee.=m0I1I2/2pd. (1)

Yoa o-ea iicaie. aaanoe aaeeieoeo neeu oiea a NE “1 Aiia?”.

Ii?aae. aae. neeu oiea-Aiia?

Iieaaay, /oi I1=I2=I ec (1) eiaai: I2=faae.aee.·2pd/m0=
faae.aee.·d/2·10-7. Aa??i d=1i, faae.aee.=2·10-7I/i.

Ca aaeeieoeo neeu oiea 1A i?eiei. neeo oaeiai oiea, eioi?ue i?ioaeaao ii
2-i ia?ae. i?iaiaeieeai, ?ani. ia ?anno. 1 i a aaeooia, aucuaaao neeo
acaeiiaeaenoaey iaaeaeo ieie, ?aaioth 2·10-7I ia eaaeae. aae. aeeeiu.

Neea Ei?aioea.

Ye. oie i?aaeno. niaie oii?yaei/aii. aeaeaeaiea ye. ca?yaeia. Ia oiee a
iaai. iiea aeaenoaoao neea Aiia?a, o.a. ni noi?. iaai. iiey ia eaaeae.
iineoaeue ca?yaea aeaenoa. oiaea neea. Yoo neeo iac. neeie Ei?aioea.

____ ____

Fe=qVBsina; a=B^V

___ _ ____

Fe=q[V,B] – a aaeo. oi?ia.

Ia iieiyuaeany ca?yaeu neea Ei?aioea ia aeaenoa. Ia ca?yaeu, aeaoathuea
a iiea ia?aee. eeieyi iiey neea Ei?. oiaea ia aeaenoa.

Anee iaeiia?ai. aeaenoa. yeaeo?. e iaai. iiey, oi ni?aaaaeeaa o-ea
Ei?aioea:

-___ ___

F=qE+Fe

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