TeXgraph# {version 1.99} Cmd Window(-15.142135623731+16.142135623731*i, 16.142135623731-15.142135623731*i, 0.447509225618795+0.447509225618795*i); Margin(0.5, 0.5, 0.5, 0.5); Border(0); [OriginalCoord(1), IdMatrix()]; [theta:=0.8728, phi:=1.309, IdMatrix3D(), ModelView(ortho)]; [GrayScale(0), ComptGraph:=0]; Mac Mcyl = [%1*exp(i*%2), %3]; Msph = %1*[exp(i*%3)*sin(%2), cos(%2)]; xlegend = "$x$"; ylegend = "$y$"; zlegend = "$z$"; text3d1 = "$x$"; text3d2 = "$y$"; text3d3 = "$z$"; labelArc = "$d\theta$"; text3d4 = "$R$"; text3d5 = "$M$"; text3d6 = "$M'$"; text3d7 = "$r$"; text3d8 = "$\theta$"; text3d9 = "$d\theta$"; RepMobSph = [ $A:=%1, SaveAttr(), LineStyle:=solid, Arrows:=1, LabelStyle:=0, Width:=10, $er:=normalize(A), $a:=pxy(A), $erho:=normalize(a), $ephiS:=rot3d(erho, [Origin, vecK], pi/2), $ethetaS:=rot3d(er, [Origin, ephiS], pi/2), Ligne3D( [A,A+er, jump, A,A+ethetaS, jump, A,A+ephiS], 0), LabelSize:=small, Label( Proj3D(A+2*er), "$\vec{u_{r}}$"), Label( Proj3D(A+1.5*ethetaS), "$\vec{u_{\theta}}$"), Label( Proj3D(A+2*ephiS), "$\vec{u_{\varphi}}$"), RestoreAttr() ]; text3d10 = "$O$"; text3d11 = "$H$"; text3d12 = "$\rho$"; text3d13 = "$H'$"; text3d14 = "$d z$"; text3d15 = "$\overrightarrow{B}=B_0\cos(\omega t)\overrightarrow{u}_z$"; text3d16 = "$\overrightarrow{B}$"; Cmd [NbPoints:=100,tMin:=-5,tMax:=5,DotScale:=1+i,LabelSize:=6]; Graph SphChpBMt = [ Ra:=10*sqrt(2), view(-Ra -1,Ra+2,-Ra -1,Ra+2), size(15,1), view3D(-Ra -1,Ra+1,-Ra -1,Ra+1,-Ra -1,Ra+1), {Paramètres de la sphère} Rs:=0.75*Ra,Os:=Msph(0,0,0), {Pt A sur la grande sphère pour définir son rayon} ThetaA:=pi/2, PhiA:=-pi/3, A:=Msph(Rs,ThetaA,PhiA), mOA:=Msph(Rs/2,ThetaA,PhiA), {milieu du segment OA} {M=Mr : Pt sur la sphère pour calculer le moment} Rm:=2*Rs/3,thetaM:=pi/4, phiM:=pi/2, Mr:= Msph(Rm,thetaM,phiM), {moins visible, donc on ne mets que la base mobile sur le pt M'} {mOM:=Msph(Rm/2,thetaM,phiM), milieu du segment OM} {RepMobSph(Mr), base mobile sphérique en M} {} d:=Rm*sin(thetaM), {distance à l'axe z} zM:=Rm*cos(thetaM), {M'=dMr=M+\dM : pour faire la petite bande de courant} DthetaM:=pi/50, Mprime:= Msph(Rm,thetaM+DthetaM,phiM), mOMprime:=Msph(Rm/2,thetaM+DthetaM,phiM), {milieu du segment OM'} RepMobSph(Mprime), {base mobile sphérique en M'} dd:=Rm*sin(thetaM+DthetaM), {distance à l'axe z} {Coord pts pour chp Bext} B1:=M(Rs/2,-Rs/2,-Rs -3), B2:=M(Rs/2,+Rs/2,-Rs -3), B3:=M(Rs/2,-Rs/2,-1), B4:=M(Rs/2,+3*Rs/2,-1), B5:=M(Rs/2,-Rs/2,Rs +1), B6:=M(Rs/2,+Rs/2,Rs +1), N:=3, {longueur vecteur B} {pt pour label champ B} mB2:=B2+N/2*vecK, mB5:=B5+N/2*vecK, Oc:=pz(Mr),{Projeté de M sur Oz} mHM:=(Mr + Oc)/2, {milieu de HM} Ocprime:=pz(Mprime),{Projeté de M' sur Oz} mHHprime:=(Oc+Ocprime)/2, {milieu de HH'} Build3D( bdAxes([0,0],[arrows:=1,color:=firebrick]), bdSphere(Os,Rs,[color:=white,contrast:=0.5, opacity:=0.15, border:=1,twoside:=1,hidden:=0]), bdCercle(Os,Rs,vecK,[color:=darkgray,linestyle:=dashed]), bdSphere(Os,Rm,[color:=blue,contrast:=1, opacity:=0.35, border:=1,twoside:=1]), bdCercle(Os,Rm,vecK,[color:=blue,linestyle:=dashed]), bdDot(A,[dotstyle:=4,dotscale:=1]), bdLine([A,Origin],[color:=black,linestyle:=solid]), bdLabel(mOA,"$R$",[labelpos:=[0.3,i -1],labelsize:=small]), bdLine([Origin,Mr],[color:=blue,width:=10,linestyle:=dotted]), bdLine([Origin,Mprime],[color:=blue,width:=10]), {bdArc(M(2,0,0),Origin,m,3,1,[arrows:=1,labelarc("$\theta$"),normal:=vecK]),} bdLabel(Mr,"$M$",[labelpos:=[0.25,1*i],labelsize:=small]), bdLine([Origin,dMr],[color:=blue,width:=12]), {bdArc(M(2,0,0),Origin,m,3,1,[arrows:=1,labelarc("$\theta$"),normal:=vecK]),} bdLabel(Mprime,"$M'$",[labelpos:=[0.25,0.75*i -2],labelsize:=small]), bdLabel(mOMprime,"$r$",[color:=blue,labelpos:=[0.95,1.5+i],labelsize:=small]), bdArc(Oc,Os,Mr,Rm/3,1,[color:=black,width:=8,arrows:=1,labelsize:=small,labelarc("$\theta$")]), bdArc(Mr,Os,Mprime,Rm/2.35,1,[color:=blue,width:=8,arrows:=0,labelsize:=small]), bdArc(Mr,Os,Mprime,Rm/2.2,1,[color:=blue,width:=8,arrows:=0,labelpos:=[0.25,1*i -1],labelsize:=small,labelarc("$d\theta$")]), bdLabel(Os,"$O$",[labelpos:=[0.3,-0.2+i],labelsize:=small]), bdCercle(Oc,d,vecK,[color:=black,linestyle:=dotted]), bdCercle(Ocprime,dd,vecK,[color:=black,linestyle:=dotted]), bdLine([Oc,Mr],[color:=black,linestyle:=dotted]), bdDot(Oc,[dotstyle:=4,dotscale:=1]), bdLabel(Oc,"$H$",[labelpos:=[0.5,-1+i],labelsize:=small]), bdLabel(mHM,"$\rho$",[labelpos:=[0.3,-1+2*i],labelsize:=small]), bdLine([Ocprime,Mprime],[color:=black,linestyle:=dotted]), bdDot(Ocprime,[dotstyle:=4,dotscale:=1]), bdLabel(Ocprime,"$H'$",[labelpos:=[0.5,-1- i],labelsize:=small]), bdLabel(mHHprime,"$d z$",[labelpos:=[0.5,-1],labelsize:=small]), bdDot([B1,B2,B3,B4,B5,B6],[dotstyle:=cross,dotscale:=2]), {Vecteurs chap Bext} bdLine([B1,B1+N*vecK],[color:=forestgreen,linestyle:=solid,width:=15,arrows:=1,arrowscale:=2,tube:=1]), bdLine([B2,B2+N*vecK],[color:=forestgreen,linestyle:=solid,width:=15,arrows:=1,arrowscale:=2,tube:=1]), bdLine([B3,B3+N*vecK],[color:=forestgreen,linestyle:=solid,width:=15,arrows:=1,arrowscale:=2,tube:=1]), bdLine([B4,B4+N*vecK],[color:=forestgreen,linestyle:=solid,width:=15,arrows:=1,arrowscale:=2,tube:=1]), bdLine([B5,B5+N*vecK],[color:=forestgreen,linestyle:=solid,width:=15,arrows:=1,arrowscale:=2,tube:=1]), bdLine([B6,B6+N*vecK],[color:=forestgreen,linestyle:=solid,width:=15,arrows:=1,arrowscale:=2,tube:=1]), bdLabel(mB2,"$\overrightarrow{B}=B_0\cos(\omega t)\overrightarrow{u}_z$",[color:=forestgreen,labelpos:=[1.95,1],labelsize:=small]), bdLabel(mB5,"$\overrightarrow{B}$",[color:=forestgreen,labelpos:=[0.5,-1],labelsize:=small]), ), Display3D() ];