Фізика, збірник задач

111 ?E?DLJHKL:LBD:

?E?DLJHKL:LBQG? IHE? M <:DMMF1

Hkgh\g• nhjfmeb

AZdhg DmehgZ

F = κ		q1q2			=			q1q2			,
		r 2				4πε0 r 2

^_ d 109 Gf2 De2; ε0 = 8,85 10-12N f r – \•^klZgv f•` lhqdh\bfb aZjy^Zfb q1 • q2.

GZijm`_g•klv _e_dljbqgh]h ihey

= F E q0 ,

^_ F – kbeZ a ydhx _e_dljbqg_ ihe_ ^•} gZ ijh[gbc aZjy^ q0 \g_k_gbc m i_\gm lhqdm.

GZijm`_g•klv _e_dljbqgh]h ihey lhqdh\h]h aZjy^m q

E = κ		q		=		q
								.
	r 2				4πε0 r 2

E•g•cgZ ]mklbgZ aZjy^m

τ= GT GO

Ih\_jog_\Z ]mklbgZ aZjy^m

σ= GT G6

H[’}fgZ ]mklbgZ aZjy^m

ρ = dVdq .

51

Ihl•d \_dlhjZ gZijm`_ghkl• ( q_j_a ih\_jogx 6 :

N = ∫ En dS,

S

^_ (3 – ijh_dp•y \_dlhjZ ( gZ ghjfZev ^h _e_f_glZ ih\_jog• dS.

L_hj_fZ Hkljh]jZ^kvdh]h – =ZmkkZ ^ey ihlhdm \_dlhjZ ( q_j_a ^h\•evgm aZfdg_gm ih\_jogx S

∫ (QG6	= ∑1 TL
6	ε L=

GZijm`_g•klv ihey kl\hj_gh]h

Z g_kd•gq_gghx j•\ghf•jgh aZjy^`_ghx iehsbghx

	E =		σ			;
		2ε		0

[ g_kd•gq_ggh ^h\]hx j•\ghf•jgh aZjy^`_ghx gbldhx gZ \•^klZg• U \•^ g_€

	E = κ	2		τ			;
		r

\ j•\ghf•jgh aZjy^`_ghx kn_jbqghx ih\_jog_x jZ^•mkhf R gZ \•^klZg• r \•^ €€ p_gljZ

E = κ		q		, ydsh r ≥ R;
	r 2
E = 0,			ydsh r < R.

] j•\ghf•jgh aZjy^`_ghx dme_x jZ^•mkhf R gZ \•^klZg• r \•^ €€ p_gljZ

E = κ		q				,		ydsh r ≥ R;
	r 2
E = κ		q		r			,	ydsh r < R.
		R3

Ihl_gp•Ze _e_dljhklZlbqgh]h ihey

ϕ= Wp , q0

^_ Wp – ihl_gp•ZevgZ _g_j]•y ijh[gh]h aZjy^m q0 m i_\g•c lhqp•

52

f

Ihl_gp•Ze _e_dljhklZlbqgh]h ihey lhqdh\h]h aZjy^m q gZ \•^klZg• r \•^ gvh]h

ϕ=κ qr = 4πεq0 r .

Jh[hlZ kbe _e_dljhklZlbqgh]h ihey

A = q(ϕ1 −ϕ2 ) .

<aZ}fha\’yahd ihl_gp•Zem ϕ a gZijm`_g•klx E _e_dljbq- gh]h ihey

E = −gradϕ; ϕ1 −ϕ2 = ∫ E d .

1−2

12.1.AZjy^ q1 fdDe j•\ghf•jgh jhaih^•e_gbc ma^h\` lhgdh]h kljb`gy ^h\`bghx L f GZ ijh^h\`_gg• hk• kljb`gy gZ

\•^klZg• • f \•^ ch]h k_j_^bgb agZoh^blvky lhqdh\bc aZjy^

q2	gDe <bagZqblb kbem F	a ydhx aZjy^ kljb`gy \aZ}fh^•} •a
aZjy^hf q2. fG
12.2. Lhgdbc kljb`_gv ^h\`bghx L		f fZ} j•\ghf•jgh jhaih^•-
e_gbc aZjy^ a e•g•cghx ]mklbghx 2			gDe f GZ ijh^h\`_gg•
hk•	kljb`gy gZ \•^klZg• •		f \•^ [eb`qh]h ch]h d•gpy

f•klblvky lhqdh\bc aZjy^ q1 ydbc \aZ}fh^•} a kljb`g_f •a kbehx

F fdG AgZclb \_ebqbgm aZjy^m q1. gDe

12.3.Lhgdbc kljb`_gv ^h\`bghx L f fZ} aZjy^ ydbc j•\ghf•jgh

jhaih^•e_gbc ih ^h\`bg• kljb`gy a e•g•cghx ]mklbghx 2 fdDe f. GZ \•^klZg• • \•^ kljb`gy agZoh^blvky lhqdh\bc aZjy^ q1 gDe ydbc j•\gh\•^^Ze_gbc \•^ d•gp•\ kljb`gy <bagZqblb kbem F \aZ}fh^•c aZjy^m q1 •a aZjy^hf kljb`gy fG

12.4. Lhgdbc g_kd•gq_ggh ^h\]bc ^j•l a•]gmlbc i•^ dmlhf α = 90h >j•l

j•\ghf•jgh aZjy^`_gbc a e•g•cghx ]mklbghx 2

fdDe f.

Lhqdh\bc aZjy^ q = 0,2 fdDe jhaf•s_gbc gZ ijh^h\`_gg• h^g•}€ •a

klhj•g • \•^^Ze_gbc \•^ \_jrbgb dmlZ gZ • f H[qbkeblb kbem F sh ^•} gZ lhqdh\bc aZjy^ fG

53

f d< f d< f

12.5.	Lhgd_ d•evp_ jZ^•mkhf R = 0,0 f fZ} j•\ghf•jgh jhaih^•e_gbc
	aZjy^ q1 gDe GZ i_ji_g^bdmeyj• ^h iehsbgb d•evpy ydbc ijh-
	\_^_gbc •a p_gljZ d•evpy agZoh^blvky lhqdh\bc aZjy^ q2	gDe gZ
	\•^^Ze• h f \•^ p_gljZ <bagZqblb kbem F sh ^•} a [hdm
	aZjy^`_gh]h d•evpy gZ aZjy^ q2. fdG
12.6.	LhgdZ ^jhlbgZ j•\ghf•jgh aZjy^`_gZ aZjy^hf q gDe AgZclb
	gZijm`_g•klv _e_dljbqgh]h ihey ? \ lhqp• ydZ jhaf•s_gZ gZ
	\•^klZg• • f \•^ d•gp•\ ^jhlbgb • gZ \•^klZg• •0	f \•^ €€
	k_j_^bgb < f

12.7.D•evp_ a lhgdh]h ^jhlm j•\ghf•jgh aZjy^`_g_ g_]Zlb\gbf aZjy^hf q = – gDe JZ^•mk d•evpy R f <bagZqblb gZijm`_g•klv ?

_e_dljbqgh]h ihey gZ hk• d•evpy \ lhqdZo sh jhalZrh\Zg• \•^ p_gljZ d•evpy gZ \•^klZgyo h1 f • h2 f. < f < f

12.8.D•evp_ a lhgdh]h ^jhlm j•\ghf•jgh aZjy^`_g_ i_\gbf aZjy^hf JZ^•mk d•evpy R f <bagZqblb gZ yd•c \•^klZg• hm \•^ p_gljZ d•evpy agZoh^blvky lhqdZ gZ hk• d•evpy \ yd•c gZijm`_g•klv _e_dljbqgh]h ihey [m^_ fZdkbfZevghx f

12.9.>bkd jZ^•mkhf R f aZjy^`_gh j•\ghf•jgh a ih\_jog_\hx ]mklbghx 1 fdDe f2 AgZclb gZijm`_g•klv ? ihey \ lhqp• ydZ agZoh^blvky gZ i_ji_g^bdmeyj• ^h ^bkdZ sh ijhoh^blv q_j_a ch]h p_glj gZ \•^klZg• h f \•^ ^bkdZ. d< f

12.10.GZ ^\ho g_kd•gq_ggbo iZjZe_evgbo iehsbgZo j•\ghf•jgh jhaih-

2	•	=
^•e_g• aZjy^b a ih\_jog_\bfb ]mklbgZfb 11 gDe f	12

gDe f2 <bdhjbklh\mxqb l_hj_fm Hkljh]jZ^kvdh]h – =ZmkkZ jhajZom\Zlb gZijm`_g•klv ? ihey f•` iehsbgZfb d< f

12.11. GZ ^\ho dhZdk•Zevgbo g_kd•gq_ggh ^h\]bo pbe•g^jZo a jZ^•mkZfb

R1 f • R2 f j•\ghf•jgh jhaih^•e_g• aZjy^b a ih\_jog_- \bfb ]mklbgZfb 11 fdDe f2 • 12 fdDe f2 AZklhkh\mxqb

l_hj_fm Hkljh]jZ^kvdh]h – =ZmkkZ h[qbkeblb gZijm`_ghkl• ?

_e_dljbqgh]h ihey \ lhqdZo yd• \•^^Ze_g• \•^ hk• pbe•g^jZ gZ \•^klZg• r1 f • r2

12.12. GZ ^\ho dhZdk•Zevgbo g_kd•gq_ggh ^h\]bo pbe•g^jZo sh fZxlv jZ^•mkb R1 f • R2 f j•\ghf•jgh jhaih^•e_g• aZjy^b a

54

• 12 = - gDe f2.

2

gDe f

ih\_jog_\bfb ]mklbgZfb 11

<bdhjbklh\mxqb l_hj_fm Hkljh]jZ^kvdh]h – =ZmkkZ jhajZom\Zlb

gZijm`_g•klv _e_dljbqgh]h ihey ? \ lhqp• ydZ \•^^Ze_gZ \•^ hk• pbe•g^jZ gZ \•^klZgv r f d< f

12.13. >\• ^h\]• j•aghcf_ggh aZjy^`_g• ^jhlbgb a e•g•cghx ]mklbghx

aZjy^m 21 = –22 fdDe f jhaf•s_g• gZ \•^klZg• •				f h^gZ
\•^ h^gh€ AgZclb \_ebqbgm gZijm`_ghkl• ? _e_dljbqgh]h ihey \
lhqp• sh agZoh^blvky gZ \•^klZg• r		f \•^ dh`gh€ ^jhlbgb
d< f
12.14. GZ ^\ho dhgp_gljbqgbo kn_jZo jZ^•mkb ydbo R1				f • R2 =
f j•\ghf•jgh jhaih^•e_g• aZjy^b a ih\_jog_\bfb ]mklb-
gZfb 11 gDe f2 • 12 gDe f2		<bdhjbklh\mxqb l_hj_fm
Hkljh]jZ^kvdh]h – =ZmkkZ jhajZom\Zlb gZijm`_g•klv ihey ? \
lhqdZo yd• \•^^Ze_g• \•^ p_gljZ gZ \•^^Ze• r1			f • r2		f
d< f d< f
12.15. IZjZn•gh\Z dmevdZ jZ^•mkhf R	f j•\ghf•jgh aZjy^`_gZ
aZjy^hf a h[¶}fghx ]mklbghx !	fdDe f3 <bagZqblb gZijm-
`_ghkl• ? _e_dljbqgh]h ihey gZ \•^klZgyo r1			f • r2		f
\•^ p_gljZ dmevdb >•_e_dljbqgZ ijhgbdg•klv iZjZn•gm 0					.

d< f d< f

12.16.Lhgdbc kljb`_gv j•\ghf•jgh aZjy^`_gbc a e•g•cghx ]mklbghx

aZjy^m 2 fdDe f <bagZqblb ihl_gp•Ze 3 _e_dljhklZlbqgh]h ihey \ lhqp• ydZ \•^^Ze_gZ \•^ d•gp•\ kljb`gy gZ \•^klZgv sh ^hj•\gx} ^h\`bg• kljb`gy <

12.17. Lhgdbc kljb`_gv ^h\`bghx • f j•\ghf•jgh aZjy^`_gbc aZjy^hf q = – gDe AgZclb ihl_gp•Ze 3 m lhqp• ydZ e_`blv gZ hk• kljb`gy gZ \•^klZg• L f \•^ k_j_^bgb kljb`gy (– <

12.18. D•evp_ a lhgdh]h ^jhlm j•\ghf•jgh aZjy^`_g_ aZjy^hf q gDe. JZ^•mk d•evpy R f <bagZqblb ihl_gp•Ze 3 ihey m p_glj• d•evpy • gZ i_ji_g^bdmeyj• ^h iehsbgb d•evpy \ lhqp• ydZ \•^- ^Ze_gZ \•^ p_gljZ d•evpy gZ h f. d< f d< f

12.19.>•_e_dljbd ^•_e_dljbqgZ ijhgbdg•klv ydh]h 01 = 7 fZ} nhjfm dme• jZ^•mkhf R f • j•\ghf•jgh aZjy^`_gbc aZjy^hf q = 6 gDe. Dmey

55

gDe f

i_j_f•klblvky gZ

f•klblvky \ k_j_^h\bs• a ^•_e_dljbqghx ijhgbdg•klx 02 = 2,2. H[qbkeblb ihl_gp•Zeb 3 _e_dljbqgh]h ihey gZ \•^klZgyo r1 f • r2 f \•^ p_gljZ dme• < <

12.20.?e_dljhg jhaf•s_gbc gZ hk• lhgdh]h d•evpy jZ^•mkhf R = kf gZ \•^klZg• h kf \•^ ch]h p_gljZ D•evp_ hljbfm} ^h^Zlgbc aZjy^ q gDe • ihqbgZ} ijbly]Zlb _e_dljhg A ydhx r\b^d•klx v ijhe_lblv _e_dljhg q_j_a p_glj d•evpy" (355 106 f k

12.21. Qhlbjb dmevdb yd• fZxlv h^gZdh\• aZjy^b q	gDe jhaf•s_g•
\a^h\` h^g•}€ ijyfh€ <•^klZgv f•` dmevdZfb d	f <bagZqblb
jh[hlm : ydm g_h[o•^gh \bdhgZlb sh[ jhalZrm\Zlb dmevdb m
\_jrbgZo d\Z^jZlZ •a klhjhghx d. fd>`
12.22. Qhlbjb dmevdb yd• fZxlv h^gZdh\• aZjy^b q	gDe jhaf•s_g•

gZ \•^klZg• d f h^gZ \•^ h^gh€ \a^h\` h^g•}€ ijyfh€ AgZclb

jh[hlm : ydm lj_[Z \bdhgZlb sh[ jhaf•klblb dmevdb m \_jrbgZo l_ljZ_^jZ a j_[jhf d. fd>`

12.23. ?e_dljbqg_ ihe_ kl\hj_gh g_kd•gq_ggh \_ebdhx j•\ghf•jgh aZjy^-

`_ghx iehsbghx a ih\_jog_\hx ]mklbghx aZjy^m 1	gDe f2.
<bagZqblb j•agbpx ihl_gp•Ze•\ 3 ^\ho lhqhd ihey	h^gZ a ydbo

jhaf•s_gZ gZ iehsbg• Z ^jm]Z gZ \•^klZg• r f \•^ g_€ <

12.24.;•ey aZjy^`_gh€ g_kd•gq_ggh \_ebdh€ iehsbgb jhalZrh\Zgh lhqdh\bc aZjy^ q gDe I•^ ^•}x ihey \•g i_j_f•sZ}lvky

\a^h\` e•g•€ gZijm`_ghkl• gZ \•^klZgv d f ijb pvhfm \bdhgm}lvky jh[hlZ : fd>` <bagZqblb ih\_jog_\m ]mklbgm 1 aZjy^m gZ iehsbg• fdDe f2)

12.25. >\Z _e_dljbqg• aZjy^b q1 gDe • q2 gDe jhaf•s_g• \ ih\•lj• gZ \•^klZg• r0 f h^bg \•^ h^gh]h KihqZldm h[b^\Z aZjy^b aZdj•ie_g• g_jmohfh Z ihl•f aZjy^ q2 a\•evgy}lvky • i•^ ^•}x kbeb \•^rlh\om\Zggy ihqbgZ} i_j_f•sm\Zlbkv \•^ aZjy^m q1 Ydm jh[hlm \bdhgZ} kbeZ \•^rlh\om\Zggy dheb aZjy^ q2

\•^klZgv r f g>`

12.26. Lhgdbc kljb`_gv a•]gmlbc m i•\dheh • j•\ghf•jgh aZjy^`_gbc a e•g•cghx ]mklbghx aZjy^m 1 M p_glj• i•\dheZ

56

f•klblvky lhqdh\bc aZjy^ q gDe H[qbkeblb jh[hlm ydm

ihlj•[gh \bdhgZlb ^ey i_j_f•s_ggy aZjy^m a p_gljZ i•\dheZ m g_kd•gq_gg•klv fd>`

12.27.GZ \•^klZg• r1 f \•^ g_kd•gq_ggh ^h\]h]h aZjy^`_gh]h ^jhlm f•klblvky lhqdh\bc aZjy^ q gDe I•^ ^•}x _e_dljbqgh]h ihey

aZjy^ i_j_f•sm}lvky ih e•g•€ gZijm`_ghkl• gZ \•^^Zev r2 =

f ijb pvhfm \bdhgm}lvky jh[hlZ : fd>` <bagZqblb e•g•cgm ]mklbgm 2 aZjy^m ^jhlm fdDe f

?E?DLJH/FG1KLV DHG>?GK:LHJB

Hkgh\g• nhjfmeb

?e_dljh}fg•klv \•^hdj_fe_gh]h ijh\•^gbdZ

& = ϕT

^_ ϕ – ihl_gp•Ze ijh\•^gbdZ ydbc fZ} aZjy^ q.

?e_dljh}fg•klv kn_jb jZ^•mk ydh€ R

&= πεε 5

^_ ε – ^•_e_dljbqgZ ijhgbdg•klv k_j_^h\bsZ yd_ hlhqm} kn_jm?e_dljh}fg•klv dhg^_gkZlhjZ

C = ϕ1 −q ϕ2 = Uq ,

^_ U = ϕ1 – ϕ2 – j•agbpy ihl_gp•Ze•\ f•` h[deZ^dZfb dhg^_gkZlhjZ

?e_dljh}fg•klv

Z iehkdh]h dhg^_gkZlhjZ

& = εεG 6

^_ ε – ^•_e_dljbqgZ ijhgbdg•klv ^•_e_dljbdZ sh } f•` h[deZ^dZfb dhg^_gkZlhjZ S – iehsZ dh`gh€ ieZklbgb dhg^_gkZlhjZ G – \•^klZgv f•` gbfb

57

[ kn_jbqgh]h dhg^_gkZlhjZ

& = πεε 5 5 5 − 5

^_ R1, R2 – jZ^•mkb kn_jbqgbo h[deZ^hd dhg^_gkZlhjZ \ pbe•g^jbqgh]h dhg^_gkZlhjZ

& = πεε /

OQ 5 5

^_ L – ^h\`bgZ pbe•g^jbqgbo h[deZ^hd jZ^•mkb ydbo 5 • 5 .?e_dljh}fg•klv ihke•^h\gh a’}^gZgbo dhg^_gkZlhj•\

1	n
	= ∑	1	.
C
		C
	i=1 i

?e_dljh}fg•klv iZjZe_evgh a’}^gZgbo dhg^_gkZlhj•\

C= ∑Ci .

i=1

?g_j]•y aZjy^`_gh]h dhg^_gkZlhjZn

W	=	CU 2	=		q2	= qU .
		2			2C
						2
H[’}fgZ ]mklbgZ _g_j]•€ _e_dljbqgh]h ihey
w =	εε0 E 2		=	ED		=	D2		,
		2		2			2εε	0
^_ D – _e_dljbqg_ af•s_ggy

13.1. Iehkdbc dhg^_gkZlhj aZih\g_gbc ljvhfZ rZjZfb ^•_e_dljbd•\ lh\-

sbgb ydbo ^hj•\gxxlv \•^ih\•^gh d1 ff d2	ff d3 ff,
Z ^•_e_dljbqgZ ijhgbdg•klv ε1 = 7,0, ε2 = 2,0 • ε3 = 5,0		>h dhg^_g-
kZlhjZ ijbdeZ^_gh j•agbpx ihl_gp•Ze•\ U	<	<bagZqblb

gZijm`_g•klv _e_dljbqgh]h ihey ? \ dh`ghfm rZj• d<

d< d<

58

ff,

13.2. <•^klZgv f•` ieZklbgZfb iehkdh]h dhg^_gkZlhjZ d0

j•agbpy ihl_gp•Ze•\ U < GZ gb`g•c ieZklbg• e_`blv iebldZ iZjZn•gm lh\sbghx d ff >•_e_dljbqgZ ijhgbdg•klv iZjZn•gm ε = 2 AgZclb ih\_jog_\m ]mklbgm 1´ a\¶yaZgbo aZjy^•\ iZjZn•gh\h€ iebldb fdDe f2)

13.3.Ijhkl•j f•` ieZklbgZfb iehkdh]h dhg^_gkZlhjZ aZih\g_gbc ^•_e_dljbdhf a ^•_e_dljbqghx ijhgbdg•klx ε = 6 <•^klZgv f•` ieZklbgZfb d ff F•` ieZklbgZfb kl\hj_gh j•agbpx ih- l_gp•Ze•\ U < <bagZqblb gZijm`_g•klv ? ihey \ ^•_e_d-

ljbdm ih\_jog_\m ]mklbgm 1 aZjy^m gZ ieZklbgZo dhg^_gkZlhjZ ih\_jog_\m ]mklbgm 1´ aZjy^m gZ ^•_e_dljbdm ^•_e_dljbqgm kijbc- gyleb\•klv χ. d< f fdDe f2 fdDe f2; 5)

13.4. M ]Zk• ^•_e_dljbqgZ ijhgbdg•klv ydh]h ε = 2 gZ ]eb[bg• h						kf \•^
	ih\_jog• f•klblvky lhqdh\bc aZjy^ q		gDe H[qbkeblb ]mklbgm
	1 aZjy^•\ gZ ih\_jog• ]Zkm gZ^ aZjy^hf • gZ \•^klZg• •					kf \•^
	aZjy^m fdDe f2 fdDe f2)
13.5.	<•^klZgv f•` ieZklbgZfb iehkdh]h dhg^_gkZlhjZ d				ff ieh-
	sZ ieZklbg S	kf2 < ijhklhj• f•` ieZklbgZfb dhg^_gkZlhjZ
	jhaf•s_gh ^\Z rZjb ^•_e_dljbd•\ Lh\sbgZ i_jrh]h d1					ff •
	^•_e_dljbqgZ ijhgbdg•klv ε1 = 5,0, lh\sbgZ ^jm]h]h d2					ff •
	^•_e_dljbqgZ	ijhgbdg•klv ε2 = 7,0	<bagZqblb }fg•klv K dhg-
	^_gkZlhjZ iN
13.6.	Ijh\•^gZ dmevdZ jZ^•mkhf R ff f•klblvky \ ]Zk• ^•_e_dljbqgZ
	ijhgbdg•klv ydh]h ε = 2 AZjy^ dmevdb q			gDe <bagZqblb
	]mklbgm 1´ a\¶yaZgbo aZjy^•\ m ]Zk• [•ey ih\_jog• dmevdb • ih\gbc
	aZjy^ q´. fdDe f2 gDe
13.7.	Ijhkl•j f•` h[deZ^dZfb pbe•g^jbqgh]h dhg^_gkZlhjZ					^h\`bgZ
	ydh]h • kf jZ^•mk \gmlj•rgvh€ h[deZ^db R1				kf jZ^•mk

ah\g•rgvh€ h[deZ^db R2 kf aZih\g_gh ^•_e_dljbdhf /fg•klv dhg^_gkZlhjZ K = iN <bagZqblb ^•_e_dljbqgm ijhgbdg•klv ε

^•_e_dljbdZ ydbc aZih\gx} ijhkl•j f•` h[deZ^dZfb dhg^_g- kZlhjZ (2)

59

13.8. Kn_jbqgbc dhg^_gkZlhj kdeZ^Z}lvky a ^\ho dhgp_gljbqgbo f_lZe_\bo

kn_j jZ^•mkZfb R1	kf • R2	kf Ijhkl•j f•` h[deZ^dZfb
dhg^_gkZlhjZ aZih\g_gh ]Zkhf		^•_e_dljbqgZ ijhgbdg•klv ydh]h

ε = 2,0 <bagZqblb }fg•klv K pvh]h dhg^_gkZlhjZ iN)

13.9.F_lZe_\Z dmey jZ^•mkhf R1 kf hlhq_gZ kn_jbqgbf rZjhf

^•_e_dljbdZ a ^•_e_dljbqghx ijhgbdg•klx ε = 7 • aZ\lh\rdb d kf lZ ^jm]hx f_lZe_\hx ih\_jog_x jZ^•mkhf R2 kf ydZ dhg- p_gljbqgZ a i_jrhx <bagZqblb }fg•klv K lZdh]h dhg^_gkZlhjZ

iN

13.10.<bagZqblb }fg•klv K; [ZlZj_€ dhg- ^_gkZlhj•\ ydZ ah[jZ`_gZ gZ jbkmg- dm /fg•klv dh`gh]h dhg^_gkZlhjZ

K fdN. fdN

13.11. Iehkdbc ih\•ljygbc dhg^_gkZlhj aZjy^beb ^h j•agbp• ihl_gp•Ze•\

U	< • \•^¶}^gZeb \•^ ^`_j_eZ gZijm]b IehsZ ieZklbgb
S	kf2 \•^klZgv f•` gbfb d kf IeZklbgb dhg^_gkZlhjZ

jhaf•s_g• \_jlbdZevgh Agbam i•^ghkylv ihkm^bgm a g_ijh\•^ghx j•^bghx ε = 2 lZd sh \hgZ aZih\gx} iheh\bgm dhg^_gkZlhjZ

<bagZqblb }fg•klv K dhg^_gkZlhjZ gZijm`_g•klv ihey ? m ih\•l- jyg•c qZklbg• ijhf•`dm f•` ieZklbgZfb • \ qZklbg• aZih\g_g•c

j•^bghx af•gm _g_j]•€ dhg^_gkZlhjZ		W.		iN	d< f
g>`
13.12. Iehkdbc dhg^_gkZlhj aZjy^`_gbc ^h j•agbp• ihl_gp•Ze•\ U					d<.
<•^klZgv f•` ieZklbgZfb d	kf Ijhkl•j f•` ieZklbgZfb
aZih\g_gbc _[hg•lhf ^•_e_dljbqgZ ijhgbdg•klv ydh]h ε = 3,0.
<bagZqblb h[¶}fgm ]mklbgm	_g_j]•€	w	pvh]h	dhg^_gkZlhjZ
>` f3)
13.13. GZ f_lZe_\•c dme• jZ^•mkhf R	kf j•\ghf•jgh jhaih^•e_gbc
aZjy^ q gDe Dmey hlhq_gZ rZjhf iZjZn•gm lh\sbghx d					kf.

>•_e_dljbqgZ ijhgbdg•klv iZjZn•gm ε = 2,0 AgZclb _g_j]•x W _e_dljbqgh]h ihey \ rZj• iZjZn•gm fd>`

60