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 q1 Eae
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 a0
I?e a0 , eo=e , ecp=1 , r=const , R – ?aaeeon oa?a 1) r>R
(aia oa?a)
2) r
ai ni ai ni
Caaen. A(r)
I?e en?
aanue ca?yae e ii oai?. Aaonna
4pr2E=Q/e0 , ioeoaea
E=(1/4pe0)?Q/r2 (r ? R)
Anee rc
2plA=t(l/e0) , io nthaea A=(1/2pe0)(t /r) (r ? R).
Anee r
_
(+ ca?) div D>0 – enoie ?anoiaeaeaiey. Anee rR
Aeey oi/ae aia noa?u (r>R) ec oai?. Aaonna iai?yaeaiiinoue A au/eneyaony
A=1/2pe0=q/r2
Aioo?e (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.
e2c? 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>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. E nionoy a?aiy t n=0. I?e auiieiaiee neooaoeee 2) i?ioiaeaeaiea ye. oiea /a?ac aacu iaca. aaciauie ?ac?yaeaie. *enei ?aeiiaeie?othueo eiiia a aaeeieoeo a?aiaie a 1i3 ieacuaaaony i?iii?oeeiiaeueiui eiioeaio?aoeee iieiae. e io?. Eiiia. Dnr = rn2 r - eiyoo. ?aeiiaeiaoeee. A neooaoeee 2 Dni =Dnr Dni = rn2 1) n=Oe(Dni /r) ?acee/atho aeaa aeaea aaciauo ?ac?yaeia. 1) ianiiinoiyoaeueiue 2) naiinoiyoaeueiue. Ianaiinoiyoaeueiue ?ac?yae - oaeie ?ac?yae aeey iiaeaea?aeee eioi?iai iaiaoiaeei aiao. eiiecaoi?. Naiinoiyoaeueiue ?ac?yae - ?ac?yae aac aiaoiaai eiiecaoi?a. Aieueoaiia?iay oa?aeoa?enoeea aaciaiai ?ac?yaea. Cae. Iia aeey aaciaiai ?yc?yaea. I?ioiaeaeaiea oiea /a?ac aacu oaeiaii eco/aoue n iiiiuueth noaiu. Aeey oiai /oiau nouanoaiaae oie aeey aaciaiai eiiecaoi?a ioaeai aiao. eiiecaoi?. A iaeanoe 1 n oaaee/aieai U i?yii i?iii?oeeiiaeueii ?anoao neea oiea. A iaeanoe 1 ni?aaaaeeea caeii Iia aeey aacia. A iae. 2 iaaethaeaaony ioeeiiaiea io i?iieei. caaen. e io cae. Iia. Iae. 3 - iae. ianuuaiey : ana iineoaee oiea iaaeatho ia yeaeo?iiu. Iae. 1 - iae. neaauo iieae. j=j++j_ j+qyen+i
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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