BB-exo2-2016

Exercice'1':'Détermination'des'caractéristiques'de'l’électron'
1.!"#!$%$&'(#!)&*+,)!#$&!-.)-#/&0123!42!)&*+,#!$12!(1*5#(#2&!#2&0#!+#*6!7-89*#$!:10,;12&8-#$!1<!0'=2#!*2!/:8(7!)-#/&0,9*#!
+82$!-#!0)>)0#2&,#-!&#00#$&0#!$*771$)!=8-,-)#23!!".)#/&012!#$&!*2,9*#(#2&!$1*(,$!?!-8!>10/#!)-#/&01$&8&,9*#@!/.#$&!?!+,0#!9*#!$12!
71,+$!#$&!2)=-,=#8A-#3!!
1.1.!42!1A$#05#!9*#!-.)-#/&012!/:80=)!2)=8&,5#(#2&!#$&!+)5,)!5#0$!-#!:8*&@!8&&,0)!780!-8!7-89*#!BC!9*,!#$&!+12/!/:80=)!+#!$,=2#!
1771$)!?!$8!/:80=#!$1,&!71$,&,5#(#2&3!"8!>10/#!)-#/&01$&8&,9*#!#$&!7#07#2+,/*-8,0#!8*!7-89*#!#&!+,0,=)!5#0$!BC3!"#!/:8(7!8!(D(#!
+,0#/&,12!(8,$!#$&!+#!$#2$!1771$)!/80!𝐹!=𝑞𝐸=!−𝑒𝐸!+12/!!𝐸!+,0,=)!5#0$!BE3!!
1.2.!8F!G)&#0(,28&,12!+*!5#/&#*0!8//)-)08&,12!
aG
#2!877-,9*82&!-8!E'(#!-1,!+#!H#I&12!J!
Σ
!
Fext =
!
Fe=d!
p
dt =me
!
aG=q
!
E⇔
!
aG=q
!
E
me
=−e
!
E
me
!
+12&!-#$!/110+122)#$!+82$!-#!7-82!64%!$12&!
!
aG
ax=0=dvx
dt
ay=eE
me
=dvy
dt
!
"
#
#
$
#
#
!
AF!G)&#0(,28&,12!+#$!/110+122)#$!+*!5#/&#*0!5,&#$$#!K!-#$!/12$&82&#$!$12&!+)&#0(,2)#$!?!780&,0!+#$!/12+,&,12$!,2,&,8-#$!?!&!L!M!J!
5M6!L!5M!#&!5M%!L!M3!!
!
!
vG
vx=k1=dx
dt =v0
vy=eE
me
×t+k2=dy
dt
"
#
$
$
%
$
$
⇔
O
!
Gx=v0×t+x0=v0×t
y=eE
2me
×t2+y0=eE
2me
×t2
"
#
$
$
%
$
$
!
/F!G)&#0(,28&,12!+#$!/110+122)#$!+*!5#/&#*0!71$,&,12!K!?!&!L!M@!-8!780&,/*-#!#$&!#2!4!+12/!6M!L!%M!L!M!
1.3.!N9*8&,12!+#!-8!&08O#/&1,0#!J!
t =
x
v
0
$1,&!%P6F!L!
eE
2mev0
2×x2
!
1.4.!QR!L!%Q!L!E@M6CMSE!(!
T!780&,0!+#!-.)9*8&,12!+#!-8!&08O#/&1,0#@!12!7#*&!,$1-#0!-#!087710&!
e
me
J!%Q!L!
eE
2mev0
2×L2⇔e
me
=2ysv0
2
EL2
!L!C@U6CMCC!V3W=SC!3!
42!7#*&!/1(780#0!8*!087710&!#2!*&,-,$82&!-#$!58-#*0$!8+(,$#$!8/&*#--#(#2&!J!
e
me
L!C@XYUUEMC6CMCC!V3W=SC!3!"#$!+#*6!58-#*0$!$12&!
)=8-#$!$,!12!/12$,+'0#!-#!(D(#!21(A0#!+#!/:,>>0#$!$,=2,>,/8&,>$3!!
!
2.&L’expérience&de&Millikan&
2.1.&Chute&verticale&
2.1.1.&"#!(1*5#(#2&!+#!-8!=1*&&#!#$&!0#/&,-,=2#!*2,>10(#@!12!7#*&!+12/!877-,9*#0!-8!C'0#!-1,!+#!H#I&12!P1*!70,2/,7#!+.,2#0&,#F!9*,!
+,&!9*#!-#$!>10/#$!877-,9*)#$!8*!$%$&'(#!$#!/1(7#2$#2&!J! 𝐹
!"# =𝑓+!𝑃=!0!!
"#$!+#*6!>10/#$!12&!(D(#!+,0#/&,12@!$#2$!1771$)!#&!(D(#!58-#*0!J!𝑓=𝑃!$1,&!6𝜋𝜂𝑟𝑣!!=𝑚𝑔!+12/!𝑣!=!"
!!"#!L! !"# !!"#!L!!!!!!" !×!!"#!
L!!!!!"
!!!
2.1.2.!T!780&,0!+#$!+122)#$!12!7#*&!+)&#0(,2#0!-8!5,&#$$#!/12$&82&#!5C!L! !
!!
=!!,!!×!"!!
!",!
=2,11×10!!!(3$SC!
𝑟=!!!!!
!!"
=!!×!,!!×!"!!×!,!×!"!!
!×!"#×!,!
=1,6×10!!!𝑚=1,6!𝜇𝑚.!"#!08%12!+#!-8!=1*&&#!58*&!C@Z!µ(3!
2.1.3.!G.870'$!-.#670#$$,12!+122)#!?!-8!9*#$&,12!70)/)+#2&#!𝑣!!L!!!!!"
!!@!9*82+!-#!08%12!+,(,2*#@!-8!5,&#$$#!+,(,2*#3!B1*0!9*#!-8!
/:*&#!2#!$1,&!78$!&017!087,+#@!,-!#$&!70)>)08A-#!+#!$)-#/&,122#0!*2#!7#&,&#!=1*&&#-#&&#3!!
2.2.![#(12&)#!+#!-8!=1*&&#-#&&#!
2.2.1.!G.870'$!-.#670#$$,12!𝑣!!L!!!!!"
!!@!?!ρ@!=!#&!η /12$&82&$@!)&82&!+122)!9*#!-#$!=1*&#-#&&#$!12&!+#$!5,&#$$#$!+#!+#$/#2&#!5C!
,+#2&,9*#$@!8-10$!-#*0$!08%12$!$12&!,+#2&,9*#$!J!0C!L!0Y3!!
"#*0$!5,&#$$#$!+#!0#(12&)#!$12&!+,>>)0#2&#$!/80!-#*0$!/:80=#$!9!$12&!+,>>)0#2&#$!J!9C!≠!9Y!
2.2.2.!"8!/:80=#!+#!/#$!=1*&&#-#&&#$!#$&!9*82&,>,)#!!/80!9C!L!S!\#@!9E!L!S!Y#@!9]!L!9Y!L!!S!Z#@!9\!L!S!#!K!&1*&#$!-#$!/:80=#$!$12&!+#$!
(*-&,7-#$!+#!-8!/:80=#!)-)(#2&8,0#!#3!!
2.3.!G82$!-#!+,$71$,&,>!+#!^:1($12@!-#!>8,$/#8*!+.)-#/&012$!#$&!+)5,)!$1*$!-.8/&,12!+#!-8!$#*-#!>10/#!)-#/&01$&8&,9*#!P/:8(7!
𝐸!/12$&82&F!/80!-#!71,+$!#$&!2)=-,=)3!G82$!-#!+,$71$,&,>!+#!_,--,W82@!-#$!=1*&&#$!$12&!,((1A,-,$)#$!#2!>8,$82&!580,#0!-#!/:8(7!
)-#/&0,9*#!O*$9*.?!/#!9*#!-#!71,+$@!70,$!#2!/1(7&#@!/1(7#2$#!-8!>10/#!)-#/&01$&8&,9*#3!