í t.u Ll Í ê · c 2018 A alapis.org - Exercises for the Feynman Lectures on Physics - Vol. I,...
Transcript of í t.u Ll Í ê · c 2018 A alapis.org - Exercises for the Feynman Lectures on Physics - Vol. I,...
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Ll ;-*"tü"* T* Í * ,*;t s ê tbt* ?* c*h^ ; " G
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!. ru*, gza^y= h
IAu"'\O +- ' *,.z
== ** t
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'ur)o=-) ?rtl-L
,;= ?+Ü '+('-*ü
?-^ í o ua'*'{1'?tá,,o
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
1
E
o ,**Á
z I nLt"ry
Lt= J- nfI ?u
l" )-L*;
J nt3lz
l.+l / )"'* r/+Y
Iz n I
L3
L
17 , ,rlI 't- fr 1,,! Lt
J L"/'-L rlu
; +: ? h,,.,pt-
P,\ v).tt', J =
/15,5
// wtZÍ'=; \t"
n,q - \ y - I : o T.dÜ
T*yn = f . T.h=Ji;
wq -Ynfi.Od
vvaqh--^P=à =tá ;t
j'-ní
Ít
*gr.0i*;ni)í
/r*lq/,â- -"2h _ ^?
.^1\,?+ )nÉ ftny+tnl
I
*3L \\ 1,ty
(Wl
//
t.
lt
*"*tfr
3J= 4*-
? r*t
@
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
2
1r4*. 2 axL L/ - .,L , z.
í- Y I x'Jx = 7j(*'1,). * * LLJ
o
dy,a: A á"L
L-L
', ? [1r* = ? +r'fr).,f[(*Í +*l]=,.Jz
-!Z
,,2- -!- wt l-'12
4-= * n)*|-r*h ,lí ' .
,=[ ;r'1')o- :*[ n'ào -- 2 i tít' >urt
J:nrt ro
áq --:- n'laàoIrR
'?i {R. n, 't R ' '
de I ,t'àv';jn'f'6' lu)' ''i
* ^
J íI<
»
a)
c)
à)hds á/,
wa.l^4 i
ryn{
7Jo
"rr^,L" a
tl
lu {tn =
Efrr-.'
/ífi,^"u 'I,I'f t',4*r/ I = J' lL
| 5,+',
ll@'' **.ã.inf j nl|--!ntoLno=1, D s^'{ ?4 I, : } t1 L
nc L
,rl ,o ) Frtl ,n'frX--o)F''n* *?rn?/ 3qf
F = tl\l, -, ["-)' n3 | +)' +
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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^.1í(Í.LFn*-^i- * '"-ío'o l, **, )l^- L ^rr*, "*o t','lr.'a n O )
!= ) ,^L'*^LE\'' '' nL'tz \ z/ lz
f1-*À A ;;*z kU "^f* J^ t'"*LL'
Í+ =e)L^L"* ?,"i-u. z4*Lz6tz3
t"w*,r*À, &'àÁ,d'i l^ 1,'-''' )* àan^" 4*Í u'üat
Z **fru*;)*&- q'u' o t
r.ZÍ=1w'L
n.**Á a ''-Jd^ #U l*1"À )^ *^**L;
I-r - r J*Ltn ! *.1"' 16*ti- 3 3
' '' T "''-Í u)' \ u'='oo *"*uo'lu:u
A ,,rÃrr*& *?A, tn^"'**'* -'a e ''*l;' t 'ro'o ' Í4r*' \ u' =
Ç *o' lí
oo'
E,*,,i,ol;{'r- 4,a",l^3., 'J' r do'+rn': 'f tu*f a'í= ta nt'í
tt ,, 4 ,, W, wJ . ! Jrrr,' , i tt nL'(!';'n # *L'*i'"1t ^1"^j
Wl-*à=(r-'') ^Lt*l'6 ^tr'i ?*' : o fr^L'\/*' |'r"'-;L U"
àLly;L't"
I
7';1,]T
//// lltil(\ c.tut t,L-Jtc.,t )^ "**1"^)
p nll" = ) fi,r'n !'I- r'Lié
zaqt,(\o*')u'R"
t."..'-' *e 4a Ca$at t
"r". t* *" 1* c- J<'*t "
[*2 ne1,"'V--R,/éy 1q.+J
fr) e*.ô ú+ *t*a a(.n*, T. ?n,( i: rffeil = 1,1 ss{íf
to^* & l,'* üsta, 1'*nf
r -á Ve ; h1r;'n,",^kY'*'T ' t'1"i-ff
u^^í"" yu "â
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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@k o oiso o A ,wea.-t<* bro " hf vvXau^a ?n o -f^*
4u^s-/ta lr)e rt "' **LL ?* * W ç "Ja'*/^ f'L
r4r»e'ê clb .- .;l^* ' l''l V F--frr<'"4=o'
o v^.^^+,Jp A í'í"i L ulàh' at* ruJ't' oo â'"À"'
f ,.l*^tc,J-{ ,- f{"'* q f 9*' l* a - .;to k i Lh -
t En^â, W, * +o7+ *^ "tL^f t o',\'H ari#
I trl'^ e btutu' '*:,, úu ú 1^.tR
v^1u-4=,,:* t<'ii 4*t or\'* /4'
ea*"y,'"--* à'-!* e úr,'n^ v^;u'0 K=f - n'l e
i = r 1p,-ê ' /c co'-:'o /tlefis}'*'o oa2laaú ^ú NÀ'L
,d04 ctlt4 a'*'h áL tú"L z5 u^&
// /t5. tr tr-7*
V a^^^*
; hga,^e R t4-U-
, 3fiRt 1\L,o z
' ) ''/nn,tnu Ca*a A4 à w
2aa2r_Iti+{,2_= 3firle
t-_ ?x*ri: . 7Xa*»+
l*;Ã/\L4Áê tfl^* ;J;u''Ín, *- Ú '
"* *jo* ^ ?
C,,-á; w"t
/*-l*, IU-+tt';P'
[*. i-lku A *a^^r']n?
ítr, u*ilr,. â, *4"y> :
Ur".W l E,.tF,... ,,, -1 11 , _1o=
n*tLl ç,\'v L=L
E a;*ht ?r.'{ ê
í I t,.z- -J'o''i"-"'
? nq Lr,*',s * I tlXLwo ' nX LP''# = nflt'3ds
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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I@W4) AJ^*"q- h ? A? z L"4;J"*, hrLn^- y'4'§1 lr4{ht'l!*^*'' A*, o lâ'1" ',/*
,Lu*t j'*f
$t;-**-'na l- ?^^ ê u"In "n *-*l- A +t*-'- -à "* **'f*
F** *'' &s;'l* a l*t fr'A* &'^rb**L= e L''o*i " i^*Ã' '
Ü Va"'^-' "*+* W )r!4 j* ud*l^'* 'l 1-"*'o fu e 7*< G 'A" t^
4i bÇ+u'u+ 0'*^;' e*"n*§u'/* N a'o e;'*t ' Va*"a'u-l* /' 'u^u^ 'L'a"*;/'aá'
v^í,lw.''i';''áa'€t'\>"r*t)*+t-'/1"^,ié'..á'rw-!a^;u-*^(44f-"1*;
rA o tu"tv*"'*f' & i'*"A bJ* al;*l* í v- 'à f t^*q f a
à.çat*l^*+'*'*'-7*'E't*J"'u'.'l, ;y**l''ni)L"*in4*;
4,Jàb1ç}-uaf*5,fuà44&l-}1.)t^*,*,t,!.o!**.f^:*l*
4^à.r*-^-?i,,-- 4Á |-u.*^ u:,'* : §a** t- |1.,,* J;. 'hJ*/§$,
// _// _1 ,s;tl
o ebrvt^tÍ'*) & vr{rrr^.. L, f---i'
IZ
lí í,)s,)
l-- /trynt ow l1--/Lf*,rg *ff-f-e*0
hf,^üà4rLd,t
E -55'"5 (?s-- u
t6 , (s; n:) = §r6ni-ai)= l,J,t* {l
Elu*r*^Á^ Aô * {** }^ "!.fl, "*' í"|-(ni-c,
e,j- nj3 3r;q)1
í
at1
(*ii tRrR4
/ I^:r /x P'}^a d'o ü)* J*' t Y e" :
' I r{s4í= á*,(»wní .;,(,tru,6,iur- ç (r*ir:4 à,t.Ào'Ii t;"Tl àh-àt Át
=r=lo,=,!otf ,*:o^,/ I',n'r,qÍc |*!!»::ll"l'Uilq
) =
o o Ro \--'--- JL
àrs í- n;
;Üf'r1 ,\eY
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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*l*o'R=!**'oz -2,!
n *yW$R =-m R a
Ef;*;-,.*"* à v'À^
,|
tu ,0 -- 1 Á /4 0,,,0
/ z/
l= ?r. Rtn ,t et. ! * i
^,1ru'0e
!",r"'lenl f Í*u I"*Í
t= !h#/ f d
t / 'ír1, l*=á*» 2\-t4J,r
t,n. Í "á
2tl6 = r rí$ + {
R".n'?' á"ai'
lv = 14. -l-P
'r'(.fri
JlL== i ,,
8 ^l.,ni )2t"u,.-' )
)-- ^?KIn----relz
t5. t* //
IE7* ,É, .-.^y^ 1",+*Ç,4, * l (, - À r r *)
e*L e^4 t^^1,-ov4 a iLz., ! ^ u,' o ! !,u' "j *-i- / "; p " Ávt
rp*(r;*^T: h
h=n?irÍ",1(!-4 \
c***,toy k *-^w , ^fr(t -, r*) , *f,u= *7( l'üÇ^E l.,-l+r*=9-n ) L"*a-3/L
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
7
't;uq-zÉ=a Í,Á=?à\riá 4u, ô,+
R
//4=?íu'*) ^,;u. l,= Ê+J= on?o=!R __**ru,* o,
I S,zofÍ
c;l u *rl
lâ.[,rnnl lc'l*-nÀi ':
ls " [ * nÊ, ls= ltr -'r'tinnll = to + f1 A"'n'')
o ?* Pa 't'*'["a
t- »,r* A çc '*h *h*YL Ü*
,r*#, lts=tlrnÊ,
Nq bà,4 ),
ht F*le""l*r ^ lluâzL
e ê. hs " &, -l',
stl
hr.r' lrhu
z-- -rtck,A
,11
:r' \n,z---_t,,
hz
í
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
8
lÂ,1I "
tc" h,/, e
' Vi h, Vt'
V=V,
Vn lrz
t- Z
í t,^' - i *i, *.:^i-:-(*.-:r.,ü: = vt = *. *n-,z ,,Í '- l,'i( ' vl)» lr:
) o ,-^.^-*L *yU : c"^^4@\ ) í'* !
rt pt v = l= cb
o^-,{": fa,'r- »=h" V*n^'
rz 1,d" y u". * r,
Ít-
")É
mZÇ>--o
í4="
í cu,* * nI - L.o ) ín* Ç cun "r- l'1 X
.,:í,«-ítr = to
Fcn *K- fl R i-çn= ai-i F'* < R-çiL
,\F R( Ran*-t)*-*---?*
Í+ i1 R
- (n«.9\;-\ e l,t
,, ttr ( na^q'1)x-''' 'a
fl R+
e t/'t ^.
f suh. , !*l^'^4' l'ffiTl<
t11 =
0b) §{ U*-L )" rlken4 Fn, =o
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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2zÍ= L^(zt\.*^t
lz \ / o
-4rtt L"
^rr.r4 t^ = f e[
, t'e i-t^ | t/, ivry,"^,-rÍ1 't/'
J2
a
?/"
^Yo
?;o rl1J
e f *, *=T
)r-l^ 'T =
ô.-* + P.. ;t.Y'^l* § 'á=-2!{*t+w"
u"*aa N a-*,ü , àÜ r)'-íft+u" =o
:t"ytlttt
2,Írro 1 v^x +7 fll=o i )< , -/?w _zL-- íttRtÍU R W / ,'?r-l " 7s
'ã i;, {- **ún= ?/o
;=-/?i.v*tf'
*,à R'
rô t*=4 .
rnl
a-
o
; r t^*tü. -zF.
b)
T*Tn f w** *e fur l. &+" á '
.',, €ri*a L=T )'*' a ^-w ê la+r/r "--A
l'
f #4n"^,,* t<t'4'l
À^-1i*^r,*\wo"r*l^ fr +'T I e^l* l^'z p*Lsl'I.'aX f p-L u*l* a*6'"-finA ' 'Í*u*'
p.sx(+=r).vrT-*"1r e z z.rz r> zlno*-t::*],
T= V^ ! J--!,Í ç#)- ? IL/' 'o ? lfr,
,t+'=r).Vr'l-t'T '? - z ,.rV.- ttl'? vu'
. z .,2 ? r/- 12 '| " ' Fé
?J*-!,Íç#Í - ?;# - *(i) í 'lr-Ç')'Í - 'l13 lt
- lz vo' '13 'a 3'
?n*^ L,a a v-;,";,t"t^ é, ü" x(t='l) '{'iT={t'S? t' *oo
Lrr)*ut t
rAT J-L.#Iar\
e a/*+ã t/* " it 'v,'V 1-Í " 0 K' '
?rr;* , il, * l,'**çnh, 1^. o l^*ç'**n*^k u**"1 /44
hp nr^ nÁ ^n'*^-io ' a' *lí' à (t=o) * a € ú4'^*
x[r*r] *vo-rír, f*'Ê*f tu*T
V", [-íJ u1T'*uâ' ' -f* ?#,yJ" f*
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
10
-zÍ=9qR5
/ Çr=a
íaÍ^x >
.^{õ à yn a? i2 (*.0) * wo
f ** u^+th.*'*h '* fu & * E*l' t=T'
e *(t--t)'o e ic'tv't i
e- Yo -V1T= o , E ü vni neP'la AZ'f '^ff" " L
,o- {*uo=o i {r=§wu«
0 l.te,*r-u JÁ',0, c^r1"1' )'A"'"*-Jt At-'A4 áu{'Y*to,- pa !J' l**
n^4iJir- k **rrrsu*'*L ?e V-'' lJn';t*g ú*" t;*
t -" e,*-- a a u-)*ul* & *-XÁ* ) a4 X)*a,.' r^Áà "n'l
*u',"t ̂ /lo"
"rr&*,áa-çt y . v*l*;7o54 ê^ uea*a *+ tlt '*O" '4,^ V-c.:R. I
E*k- a q: â' aju.lâ .lt"/ +? r- í t*;hu" l'+' o-;> t'*'<
;v*nã* á* **,,fr, » é' /"4*f '?* *'Í á'4r?' v""-'l;'*'a" W'
t- le(.
I
tr .v'\>( =-tÍ\ ) x =l? ) *, !r-t't, 2 tr
:'4 tn14 - -lfr,. & = 3"v.,k ê
'- * {; á='i*tr à(t=')
5 tt+zF
t
á , ar.'
Xt
- l,t, arl,-VXT € í Ye No'l y"
t* r^^*;ur,-;* uâÍ e&fru *\*' àr*o' c'l^ag'í"'" '
v"c'Iá'('í '
t ltt .
&,t/n*r-: .*íT* u,* ril' f o"
e ,,*LgT*Lb M^ 2"-e{*oc'a' tS--"'i k ?u' , *
7Y.í;?"" ) (?-+| {+r+)v6arüo: i V, = **,e''ffí;.-*íT{'*o ) t+ ?
N;L v,lruo n S'R{wat CL'-"fu,
wüT*1?t)/Yw^,""/-\)v ' ^ .^ .i À- T u^-nvo?=o
+ü a ,r,^r**r,Í* ü'*a'-' T'-n to e - HV R u+ Fttt+< Lcw 0
P*t**1r***hu'J^{olanayt*o*-ê{,ÁoVt44r\'1-\'t'^àA"'*fut*JI'"'}"&(r,n o t *r--at *' ff^tr{ /r*L e*"'b'L'^ **{-J )' àJt- p'l'
'**'*fL*' A*}"
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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15, 2Y
r)
ko,l;, ,
i c"-"}**t ? re *"* enú*r*p , lrn*r' hl, R : lrn *+ (f v') n e i1 *c
e mLç4,1*;*h úe,q ; frrf,cl. = frv, *r ínt i'Ê r +v.nR oa'.
2Ê
Qn*
, | .2 *(**l)'
2 \/tuz*JLfrt
Zar - V. zí,,o0.,a+í ?y.70, ) *iloR =[ ,-i r*i]n=t#u".#\à^*-), vr=# **or=
hJ^ R
ô_ Ll
" b* o á,J,-/-t r'{^;, o S*' t{'u.-* a* L*uo^ M,,
\.1".-.:_-/'
I
I
Lrl I
ql
ür*os^un h ,^^"''*rA a-[^l*rl
[tn*t-)u.," lir' tn=fn{ e
-ít
(j,rf.r* f)" = 2 Yn (erf.) u'
tudr44"u J^ t*"*$ '
z
!r;=!r'u' z ?
! I L{r'*J*e') J'i a'^'(n nt) w'z \r t
l^ '- 2 uR
1.4
"l@
'/ r;-tr*fu na.y * t,1(rulollt*;-R
W r,,l.rl^- h;â *&l a ',.,*t 'l' a"-S^Jln' '?- r^í' FS *^Tl* '
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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@1N,"L 'fÂlr*" ozo'
rla^r^*, ea'u+< fud a ' Y- e
It-.- x,i \fi j =P'. x' i' r S' i'
^ *^* lÀcad rr\ Jz-"* j' *Y l*
F{^, r,Trrt,v
Cll"* kL * o.-.ár*oL- a' lloe ,1"< { o ,çLh*'u *;'k-l
à)4ú* 1*",".ht. xt it+y, ir, #= i' i' ri' i' r;' !rl'#
Y' )' L' *'J' i' r O' #' ri' # * x' à! ri'# r *' # r'1"#
'{*^'#rl#d;,- 4e 4i, - d3;, -_ u i,Ê3 _-+er-at ár-aro v
1'it à+ d l4! i'\ - 4!- lI Ü = - ,'L'7' àt ao\arn/- àt à+ àt
#.* #,#(,,)=_ #í,.-DL'd' j' da 4 "Í - Lí'\=-F'7í ts \ àt /
àe de dit ,..iràt lt Jt
, t/.. ar.Jrr-J*
'-frtu# -rr^o) l'
*,-v "'l) i'Í+
lot u'x' " Fi
+ h^rt)'= í
# =X,.r,-$, jt rtil, *' * i' *rJ' (-' i') * *|'"'') r l' ("'l') :
= i, i, *J, j,n , ,$'i'-!'L'1 - t"(x';'*Y i')
= (,i ' - z^, i '- ,' ^) i ' * ( 'r't
n zut;' ' *' l)i''t
(oo 7,-,i' l'-l* W #,- # e'r''rin't l' ^E = - ü'
â1 ríx T
r^fu a LurÁ*, i)r'lÜ* â í' * ^ u i')'-fi*oa;ru^o)i'+(
.-" (,)=*rr::)ü), e.i@ 'r'-t* (i)"(:', :,'),:?
f. ^ § n
1 a**)i' + (- í* *' e - 7l * o) i' {* i' - tn 2 ui'- "' *') i' r(* J"-
u z u )
F*u€+Tsa^,a.*í/-ya2*v,***.x,1*1,=Çu€rt*,+r^^2i.r;ifina*# +FXt^n0 = ti'+ *2 u*í-^ i!' ) -)''= -ixbanÇl^t'1t\z**''
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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0*l-J, .
F-er *-,-' á *lt''*' u')
"*r'1"*-4.e' ',^,P lvtht e
* eáJíJl
-l "l
1 ln) x tL'
,\: :' :'\t
\-,i, o \
2+uJ=un
[àue\ =alrri I
.(- " \' L' r' ;' i')
l4va\I
-t
_
lat /n
J r^rX Vn
,r[ - r j' ;'+ tux'r1 =\ ; :' i'\= '"'x'i'-''v'i'
L I \-"lt ''txt o
I
oj,j' - t *J' í'* z* i'it- w x' ;'-*" J'J'
,,iL-Etx') l'+(i'*' w*'t-"J') à'
'- r.r., ri') nf)(o* o;L*u i') §'
í,ru^t\'tt +t'ít ** * 4 a*ali'
,? t - w u xt * Ç'* Çx báni A"4#*a*tcuj t+ w' uxt'íl
,* r'J' >,,í,, ,{§*t+í'fc*a 'êhN i<t+**'l' -'í
j' *'[l-o ul-I
\' olI
â " r lla- - x'l,l-
d
t",=(.x
= É,.(uti
= (xu#+
i' - 2 o 't+zmr*''
t,trxwTt' , " \,
ln't
e pL+4;ff* Áç rarq I
!=r,âü=rrí-ii
Çx tu+ * B tq*^# *- *
*Çrl*§ r ít t*0 'Y\ 1
&n*rn @
- {àU + axú- l a, /n' *é)| é-i
ffiA\ r; rç-fr =(#)rt ürxv4 +I':xv4 * tn v w xh"
'llln Vr tn
= ldlr-l * z i n7, oL *i, 'ilar tn
Ú' " x' n' *ü' j'ár'
c©2018 Afialapis.org - Exercises for the Feynman Lectures on Physics - Vol. I, Cap. 15
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