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{SECT 0 {EXCHG {PARA 205 "" 0 "" {TEXT 208 112 "Berechnung des magneti
schen Feldvektors A und der Induktion B einer Spule mit Hilfe des Gese
tzes von Biot-Savart" }}{PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 
208 21 "W. Tenten  Sept. 2006" }}}{EXCHG {PARA 206 "> " 0 "" }}{EXCHG 
{PARA 206 "> " 0 "" {MPLTEXT 1 209 8 "restart:" }{MPLTEXT 1 209 28 "wi
th (plots): with (linalg):" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 
209 21 "P := vector([x,y,z]):" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 
1 209 36 "anz:=24: R:=1: wind:=1:  steig:=0.5:" }}}{EXCHG {PARA 205 ""
 0 "" {TEXT 208 48 "Berechnung der einzelnen Vektoren einer Schleife" 
}}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 26 "for t from 0 to wind \+
* anz" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 2 "do" }}{PARA 206 "> " 0 
"" {MPLTEXT 1 209 71 "  v[t]:=vector([x0+t/anz*steig, R*cos(2*Pi/anz*t
), R*sin(2*Pi/anz*t)]);" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 3 "od:" 
}}}{EXCHG {PARA 205 "" 0 "" {TEXT 208 31 "Berechnung des Vektorpotenti
als" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 28 "for f from 0 to \+
wind * anz-1" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 2 "do" }}{PARA 206 
"> " 0 "" {MPLTEXT 1 209 31 "  ds[f]  := evalm(v[f+1]-v[f]):" }}{PARA 
206 "> " 0 "" {MPLTEXT 1 209 26 "  r[f]   := evalm(P-v[f]):" }}{PARA 
206 "> " 0 "" {MPLTEXT 1 209 25 "  rabs[f]:= norm(r[f],2):" }}{PARA 
206 "> " 0 "" {MPLTEXT 1 209 37 "  dsXr[f]:= evalf(ds[f] * 1/rabs[f]):
" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 3 "od:" }}}{EXCHG {PARA 206 "> \+
" 0 "" {MPLTEXT 1 209 43 "A:=evalm(sum(dsXr[von],von=0..wind*anz-1)):"
 }}}{EXCHG {PARA 206 "> " 0 "" }}{EXCHG {PARA 205 "" 0 "" {TEXT 208 
35 "Berechnung vom B-Feld  (= curl(A) )" }}}{EXCHG {PARA 206 "> " 0 ""
 {MPLTEXT 1 209 36 "B[1] := diff(A[3],y) - diff(A[2],z):" }}{PARA 206 
"> " 0 "" {MPLTEXT 1 209 36 "B[2] := diff(A[1],z) - diff(A[3],x):" }}
{PARA 206 "> " 0 "" {MPLTEXT 1 209 36 "B[3] := diff(A[2],x) - diff(A[1
],y):" }}}{EXCHG {PARA 206 "> " 0 "" }}{EXCHG {PARA 205 "" 0 "" {TEXT 
208 25 "Berechnung Betrag A und B" }}}{EXCHG {PARA 206 "> " 0 "" 
{MPLTEXT 1 209 35 "fA:=sqrt(A[1]^2 + A[2]^2 + A[3]^2):" }}{PARA 206 ">
 " 0 "" {MPLTEXT 1 209 35 "fB:=sqrt(B[1]^2 + B[2]^2 + B[3]^2):" }}}
{EXCHG {PARA 206 "> " 0 "" }}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 
209 49 "ti:=time(): x:='x':y:='y':z:='z':x0:='x0':i:='i':" }}}{EXCHG 
{PARA 206 "> " 0 "" {MPLTEXT 1 209 17 "for i from 1 to 5" }}{PARA 206 
"> " 0 "" {MPLTEXT 1 209 2 "do" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 
18 "  x0:=(i-1)*steig:" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 13 "  fAI
[i]:=fA:" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 13 "  fBI[i]:=fB:" }}
{PARA 206 "> " 0 "" {MPLTEXT 1 209 3 "od:" }}}{EXCHG {PARA 206 "> " 0 
"" {MPLTEXT 1 209 26 "fA_sp:=sum(fAI[g],g=1..5):" }}{PARA 206 "> " 0 "
" {MPLTEXT 1 209 26 "fB_sp:=sum(fBI[h],h=1..5):" }}}{EXCHG {PARA 206 "
> " 0 "" }}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 36 "ti:=time(): x
:='x':y:='y':z:='1e-3':" }}}{EXCHG {PARA 206 "> " 0 "" }}{EXCHG {PARA 
206 "> " 0 "" {MPLTEXT 1 209 23 "# B-Feld  plot in Blau " }}}{EXCHG 
{PARA 206 "> " 0 "" {MPLTEXT 1 209 18 "for i from 1 to 20" }}{PARA 
206 "> " 0 "" {MPLTEXT 1 209 2 "do" }}{PARA 206 "> " 0 "" {MPLTEXT 1 
209 67 "  B_plot[i]:=plot3d(fB_sp-(0.2*i),x=-10..10,y=-10..10,view=0..
1e-8," }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 38 "             style=con
tour,contours=1," }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 25 "           \+
  color=blue):" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 3 "od:" }}}
{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 15 "(time()-ti)/60;" }}
{PARA 207 "" 1 "" {XPPMATH 20 "6#$\")n;G`!\")" }{TEXT 210 1 " " }
{TEXT 210 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 1 " " }}}
{EXCHG {PARA 205 "" 0 "" {TEXT 208 29 "Vektorpotential plot in gruen" 
}}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 35 "ti:=time(): x:='x':y:
='y':z:='0.1':" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 18 "for i
 from 2 to 22" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 2 "do" }}{PARA 
206 "> " 0 "" {MPLTEXT 1 209 105 "  A_plot[i]:=plot3d(fA_sp-(0.2*i),x=
-10..10,y=-10..10,view=0..1e-4,             style=contour,contours=1,"
 }{MPLTEXT 1 209 27 "\n             color=green):" }{MPLTEXT 1 209 1 "
\n" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 3 "od:" }}}{EXCHG {PARA 206 "
> " 0 "" {MPLTEXT 1 209 15 "(time()-ti)/60;" }}{PARA 207 "" 1 "" 
{XPPMATH 20 "6#$\")m;<@!\")" }{TEXT 210 1 " " }{TEXT 210 1 " " }}}
{EXCHG {PARA 206 "> " 0 "" }}{EXCHG {PARA 205 "" 0 "" {TEXT 208 25 "Le
iterschleife in Schwarz" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 
17 "for i from 1 to 5" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 2 "do" }}
{PARA 206 "> " 0 "" {MPLTEXT 1 209 9 "  k:=i-1;" }}{PARA 206 "> " 0 ""
 {MPLTEXT 1 209 70 "  vL[i]:=vector([(k+t1/48)*steig ,cos(2*Pi/48*t1) \+
,sin(2*Pi/48*t1) ]):" }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 68 "  L_sch
leife[i]:=spacecurve(vL[i],t1=0..24,view=[-1..4,-2..2,-2..2]," }}
{PARA 206 "> " 0 "" {MPLTEXT 1 209 68 "                 axes=normal,la
bels=[X,Y,Z],color=black,thickness=3," }}{PARA 206 "> " 0 "" {MPLTEXT 
1 209 36 "                 tickmarks=[2,2,2]):" }}{PARA 206 "> " 0 "" 
{MPLTEXT 1 209 3 "od:" }}}{EXCHG {PARA 206 "> " 0 "" }}{EXCHG {PARA 
206 "> " 0 "" {MPLTEXT 1 209 13 "# Darstellung" }}}{EXCHG {PARA 206 ">
 " 0 "" }}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 63 "feld:=display3
d(seq(A_plot[i],i=2..22), seq(B_plot[i],i=1..20)," }}{PARA 206 "> " 0 
"" {MPLTEXT 1 209 82 "          seq(L_schleife[i],i=1..5),insequence=f
alse,view=[-10..10,-10..10,-1..1]," }}{PARA 206 "> " 0 "" {MPLTEXT 1 
209 10 "          " }{MPLTEXT 1 209 21 "tickmarks=[10,10,10]," }
{MPLTEXT 1 209 53 "scaling=constrained,orientation=[50,60],grid=[20,20
]," }}{PARA 206 "> " 0 "" {MPLTEXT 1 209 48 "          title=`Spule m.
 5 Windungen Nahfeld`):" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 209 
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