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{SECT 0 {EXCHG {PARA 347 "" 0 "" {TEXT 256 77 "SIMULATION DE LA TRAJEC
TOIRE D'UNE PARTICULE CHARGEE DANS UN CHAMP MAGNETIQUE" }}}{EXCHG 
{PARA 348 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 349 "" 
0 "" {TEXT -1 74 "Appliquons le pricipe fondamental de la dynamique \+
\340 une particule charg\351e:" }}{PARA 350 "" 0 "" {XPPEDIT 18 0 "dif
f(p_(t),t) = q;" "6#/-%%diffG6$-%#p_G6#%\"tGF*%\"qG" }{TEXT -1 7 ".V_^
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ions sur les trois axes du rep\350re cart\351sien:" }}}{EXCHG {PARA 
352 "" 1 "" {TEXT -1 7 "Sur x_:" }}}{EXCHG {PARA 353 "> " 0 "" 
{MPLTEXT 1 0 32 "eqd1:=m*diff(vx(t),t)=q*vy(t)*B;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%eqd1G/*&%\"mG\"\"\"-%%diffG6$-%#vxG6#%\"tGF/F(*(%\"q
GF(-%#vyGF.F(%\"BGF(" }}}{EXCHG {PARA 355 "" 0 "" {TEXT -1 7 "Sur y_:
" }}}{EXCHG {PARA 356 "> " 0 "" {MPLTEXT 1 0 33 "eqd2:=m*diff(vy(t),t)
=-q*vx(t)*B;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqd2G/*&%\"mG\"\"\"
-%%diffG6$-%#vyG6#%\"tGF/F(,$*(%\"qGF(-%#vxGF.F(%\"BGF(!\"\"" }}}
{EXCHG {PARA 358 "" 0 "" {TEXT -1 7 "Sur z_:" }}}{EXCHG {PARA 359 "> \+
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{XPPMATH 20 "6#>%%eqd3G/*&%\"mG\"\"\"-%%diffG6$-%#vzG6#%\"tGF/F(\"\"!
" }}}{EXCHG {PARA 361 "" 0 "" {TEXT -1 70 "On prend les conditions ini
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0 "" {MPLTEXT 1 0 53 "eqns := \{eqd1, eqd2, eqd3,vy(0)=0,vx(0)=vo,vz(0
)=vo\}:" }}}{EXCHG {PARA 363 "> " 0 "" {MPLTEXT 1 0 41 "sol := dsolve(
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lG<%/-%#vxG6#%\"tG*&%#voG\"\"\"-%$cosG6#*&*(%\"qGF-%\"BGF-F*F-F-%\"mG!
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{TEXT -1 6 "=q.B/m" }}}{EXCHG {PARA 366 "> " 0 "" {MPLTEXT 1 0 17 "rea
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1 0 17 "eq:=omega0=q*B/m;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/%'
omega0G*&*&%\"qG\"\"\"%\"BGF*F*%\"mG!\"\"" }}}{EXCHG {PARA 369 "> " 0 
"" {MPLTEXT 1 0 22 "assign(isolate(eq,B));" }}}{EXCHG {PARA 370 "> " 
0 "" {MPLTEXT 1 0 4 "sol;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/-%#vzG
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"assign(sol);" }}}{EXCHG {PARA 373 "> " 0 "" {MPLTEXT 1 0 51 "rx:=int(
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{XPPMATH 20 "6#>%#rxG*&*&%#voG\"\"\"-%$sinG6#*&%'omega0GF(%\"tGF(F(F(F
-!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ryG*&*&%#voG\"\"\"-%$cosG
6#*&%'omega0GF(%\"tGF(F(F(F-!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%#rzG*&%#voG\"\"\"%\"tGF'" }}}{EXCHG {PARA 377 "" 0 "" {TEXT -1 36 "On
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{MPLTEXT 1 0 43 "rx:=(t,vo,omega0)->vo*sin(omega0*t)/omega0;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#rxGR6%%\"tG%#voG%'omega0G6\"6$%)operatorG
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{PARA 380 "> " 0 "" {MPLTEXT 1 0 43 "ry:=(t,vo,omega0)->vo*cos(omega0*
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\"F*F*F*" }}}{EXCHG {PARA 382 "> " 0 "" {MPLTEXT 1 0 24 "rz:=(t,vo,ome
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{MPLTEXT 1 0 15 "omega1:=e*B/mi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
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{XPPEDIT 18 0 "omega;" "6#%&omegaG" }{TEXT -1 1 "/" }{XPPEDIT 18 0 "ga
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{EXCHG {PARA 408 "" 0 "" {TEXT -1 122 "Si l'on consid\350re le plan or
thogonal \340 z_, le mouvement est circulaire de rayon R. Ce dernier e
st appell\351 rayon de Larmor." }}{PARA 409 "" 0 "" {XPPEDIT 18 0 "rx \+
:= vo/omega0*sin(omega0*t);" "6#>%#rxG*(%#voG\"\"\"%'omega0G!\"\"-%$si
nG6#*&F(F'%\"tGF'F'" }{XPPEDIT 18 0 "ry := vo*cos(omega0*t)/omega0;" "
6#>%#ryG*(%#voG\"\"\"-%$cosG6#*&%'omega0GF'%\"tGF'F'F,!\"\"" }{TEXT 
-1 7 " \nDonc " }{XPPEDIT 18 0 "rx^2+ry^2 = R^2;" "6#/,&*$%#rxG\"\"#\"
\"\"*$%#ryGF'F(*$%\"RGF'" }}{PARA 410 "" 0 "" {TEXT -1 19 "Par identif
ication " }{XPPEDIT 18 0 "R = m*vo/e/B;" "6#/%\"RG**%\"mG\"\"\"%#voGF'
%\"eG!\"\"%\"BGF*" }}}{EXCHG {PARA 411 "> " 0 "" {MPLTEXT 1 0 20 "R:=(
m,vo)->m*vo/e/B;" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"RGR6$%\"mG%#voG6\"6$%)operatorG%&arrowGF)*&*&9$\"\"\"9%F0F0*&%\"eGF0
%\"BGF0!\"\"F)F)F)" }}}{EXCHG {PARA 413 "" 0 "" {TEXT -1 22 "Applicati
on num\351rique:" }}}{EXCHG {PARA 414 "" 0 "" {TEXT -1 16 "Pour un \+
\351lectron" }}}{EXCHG {PARA 415 "> " 0 "" {MPLTEXT 1 0 9 "R(me,ve);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++]7.a!#9" }}}{EXCHG {PARA 417 "
" 0 "" {TEXT -1 11 "Pour un ion" }}}{EXCHG {PARA 418 "> " 0 "" 
{MPLTEXT 1 0 9 "R(mi,vi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nmmmK
!#7" }}}{EXCHG {PARA 420 "> " 0 "" {MPLTEXT 1 0 18 "R(mi,vi)/R(me,ve);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+TR)e/'!\")" }}}{EXCHG {PARA 
422 "" 0 "" {TEXT -1 89 "Les rayon de Larmor d'un ion est donc environ
 50 fois plus grand que celui d'un  \351lectron" }}{PARA 423 "" 0 "" 
{TEXT -1 82 "La fr\351quence de giration autour des lignes de champ es
t diff\351rente selon l'esp\350ce:" }}}{EXCHG {PARA 440 "" 0 "" {TEXT 
-1 16 "Pour un \351lectron" }}}{EXCHG {PARA 441 "> " 0 "" {MPLTEXT 1 
0 29 "f1:=omega1/(2*Pi):\nevalf(f1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#$\"+#H[Yx%!\"#" }}}{EXCHG {PARA 443 "" 0 "" {TEXT -1 11 "Pour un ion
" }}}{EXCHG {PARA 428 "> " 0 "" {MPLTEXT 1 0 29 "f2:=omega2/(2*Pi):\ne
valf(f2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+,s**y;\"\"#" }}}
{EXCHG {PARA 432 "> " 0 "" {MPLTEXT 1 0 6 "f2/f1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+<N[;N!\"'" }}}{EXCHG {PARA 435 "" 0 "" {TEXT -1 89 
"Les \351lectrons tournent donc \340 une fr\351quence environ 3000 foi
s sup\351rieure \340 celle des ions" }}}}{MARK "38 1 0" 2 }{VIEWOPTS 
1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }