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<font face="Myriad Pro">Dear all,<br>
<br>
here a little trick to add some arrows... However this can be improved.
I just put in an excerpt of Manuel's example:<br>
<br>
\documentclass{article}<br>
\usepackage{pstricks,pst-plot,pstricks-add}<br>
\SpecialCoor<br>
\def\FieldLines{%<br>
/r1 xP xA sub dup mul yP dup mul add sqrt def<br>
/r2 xP xA add dup mul yP dup mul add sqrt def<br>
/V q1 r1 div<br>
q2 r2 div<br>
add def<br>
% Ex=-dV/dx<br>
/Ex q1 xP xA sub mul r1 3 exp div<br>
q2 xP xA add mul r2 3 exp div<br>
add def<br>
% Ey=-dV/dy<br>
/Ey yP<br>
q1 r1 3 exp div<br>
q2 r2 3 exp div<br>
add mul def<br>
/NormeE Ex dup mul Ey dup mul add sqrt def<br>
/dX Ex NormeE div pasX mul def<br>
/dY Ey NormeE div pasX mul def<br>
}<br>
\begin{document}<br>
\begin{center}<br>
\begin{pspicture*}(-6,-8)(10,8)<br>
% les limites<br>
\pstVerb{/xmin -5 def /xmax 5 def /ymin -5 def /ymax 5 def}%<br>
% le pas d'itération<br>
\pstVerb{/pasX 0.025 def}%<br>
\pstVerb{/q1 1 def % les charges<br>
/q2 -0.5 q1 mul def<br>
/xA -2.5 def}%<br>
% 15 degrés entre chaque ligne (24*15=360)<br>
\multido{\iA=0+24}{15}{% 15 lignes de champ<br>
\pstVerb{/xStart xA def<br>
/pasX q1 q1 abs div 0.05 mul def<br>
/xP xStart pasX \iA\space cos mul add def<br>
/yP 0 pasX \iA\space sin mul add def}%<br>
\parametricplot[plotpoints=2000,linecolor=blue]{xmin}{xmax}{%<br>
\FieldLines<br>
/xP xP dX add def<br>
/yP yP dY add def<br>
xP yP<br>
}<br>
\parametricplot[linecolor=blue,arrows=->,arrowscale=2]{xmax xmin add
2 div 0.2 sub}{xmax xmin add 2 div 0.2 add}{%<br>
\FieldLines<br>
/xP xP dX add def<br>
/yP yP dY add def<br>
xP yP<br>
}}<br>
<br>
\pscircle[fillstyle=solid](!xA 0){0.2}\pscircle[fillstyle=solid](!xA
neg 0){0.2}<br>
\end{pspicture*}<br>
\end{center}<br>
\end{document}<br>
<br>
Regards,<br>
<br>
Juergen<br>
</font><br>
Patrice Mégret wrote:
<blockquote
cite="mid:7D2AE41E6308E846A5077E28FCC186F05724FD2960@EXCHANGE-DB3.fpms.ac.be"
type="cite">
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<div class="Section1">
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">Dear Manuel et al,<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">The solution based on implicit function can be extended
for the equipotential to any number of point charges arbitrarily
placed, but for the field lines thepoint charges should be placed on a
line if you generalize the line equation . If we can find the function
f(x,y)=0 for the E field line with arbitrary geometry, then it should
be possible to use implicit function.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">Probably some care should be taken to avoid division by
zero if the computation grid crosses then charge positions.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">I tested your solution with two charges (Q1=1,Q2=+-0.5,
located at z=+-1) and superpose with mine and it is perfect. (see code
below)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">Concerning the computation time, your solution is very
quick for two charges of same sign but quite slow with two opposite
sign charges (I changed plotpoints to 200 in the parametric plot for
opposite sign charges because with 2000 it is very slow).<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">So probably, for the general case, the field lines should
be computed by your algorithm and the equipotential by implicit
function (that allows also to change the color with the sign, red and
orange in the example below) <o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">I have no idea how to put arrows on the field lines with
my procedure.
<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">Best regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">Patrice<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\documentclass{article}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\usepackage{pstricks,pst-func,pstricks-add}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\begin{document}
<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\def\FieldLinesFourElectricCharges{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /r1 xP xA sub dup mul yP yA sub dup mul add sqrt
def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /r2 xP xB sub dup mul yP yB sub dup mul add sqrt
def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%
/V q1 r1 div<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%
q2 r2 div<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">% add<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">% q3 r3 div<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">% add<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">% q4 r4 div<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%
add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%
Ex=-dV/dx<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/Ex q1 xP xA sub mul r1 3 exp div<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">q2 xP xB sub mul r2 3 exp div<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">% Ey=-dV/dy<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /Ey q1 yP yA sub mul r1 3 exp div<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> q2 yP yB sub mul r2 3 exp div
<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /NormeE Ex dup mul Ey dup mul add sqrt def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">/dX
Ex NormeE div pasX mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">/dY Ey NormeE div pasX mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\begin{center}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\begin{pspicture*}(-7,-7)(7,7)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">% les limites<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\pstVerb{/xmin -5 def /xmax 5 def /ymin -5 def /ymax 5
def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%
le nombre de lignes de champ<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%\pstVerb{/NL
24 def}% 15 degrés entre chaque ligne (24*15=360)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%
le pas d'itération<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\pstVerb{/pasX
xmax xmin sub 200 div def}% 0.05<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\pstVerb{/q1
1 def % les charges<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/q2 0.5 def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/xA 0 def % leurs positions<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/yA 1 def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/xB 0 def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/yB -1 def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
}%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\multido{\iA=0+15}{24}{%
24 lignes de champ<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\pstVerb{/xStart xA def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yStart yA def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">/pasX
q1 q1 abs div 0.05 mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">/xP xStart pasX \iA\space cos mul add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yP yStart pasX \iA\space sin mul add def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\parametricplot[plotpoints=2000]{xmin}{xmax}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> \FieldLinesFourElectricCharges<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /xP xP dX add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yP yP dY add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> xP yP<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\pstVerb{/xStart xB def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yStart yB def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">/pasX
q2 q2 abs div 0.05 mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">/xP xStart pasX \iA\space cos mul add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yP yStart pasX \iA\space sin mul add def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\parametricplot[plotpoints=2000]{xmin}{xmax}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> \FieldLinesFourElectricCharges<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /xP xP dX add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yP yP dY add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> xP yP<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\pscircle[fillstyle=solid](!xA
yA){0.2}\pscircle[fillstyle=solid](!xB yB){0.2}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\begin{psclip}{\psframe[linestyle=none](-5.2,-5.2)(5.2,5.2)}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=0.4+0.2}{3}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=dotted,linecolor=red](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">x 2 exp y 1 sub 2 exp add sqrt 1 exch div x 2 exp y 1 add
2 exp add sqrt 0.5 exch div add \r\space sub}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=1.0+1.0}{3}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=dashed,linecolor=red](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">x 2 exp y 1 sub 2 exp add sqrt 1 exch div x 2 exp y 1 add
2 exp add sqrt 0.5 exch div add \r\space sub}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=0.2+0.4}{5}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=solid,linecolor=blue](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">y 1 sub x 2 exp y 1 sub 2 exp add sqrt div y 1 add x 2
exp y 1 add 2 exp add sqrt div 0.5 mul add \r\space add}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=-0.2+-0.4}{5}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=solid,linecolor=blue](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">y 1 sub x 2 exp y 1 sub 2 exp add sqrt div y 1 add x 2
exp y 1 add 2 exp add sqrt div 0.5 mul add \r\space add}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\psdots(0,1)(0,-1)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\end{psclip}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\psaxes{->}(0,0)(-5.5,-5.5)(5.5,5.5)[$y$,-90][$z$,0]<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\end{pspicture*}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\end{center}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\begin{center}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\begin{pspicture*}(-7,-7)(7,7)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">% les limites<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\pstVerb{/xmin -5 def /xmax 5 def /ymin -5 def /ymax 5
def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%
le nombre de lignes de champ<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%\pstVerb{/NL
24 def}% 15 degrés entre chaque ligne (24*15=360)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">%
le pas d'itération<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\pstVerb{/pasX
xmax xmin sub 200 div def}% 0.05<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\pstVerb{/q1
1 def % les charges<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/q2 -0.5 def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/xA 0 def % leurs positions<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/yA 1 def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/xB 0 def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
/yB -1 def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
}%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\multido{\iA=0+15}{24}{%
24 lignes de champ<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\pstVerb{/xStart xA def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yStart yA def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">/pasX
q1 q1 abs div 0.05 mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">/xP xStart pasX \iA\space cos mul add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yP yStart pasX \iA\space sin mul add def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\parametricplot[plotpoints=200]{xmin}{xmax}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> \FieldLinesFourElectricCharges<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /xP xP dX add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yP yP dY add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> xP yP<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\pstVerb{/xStart xB def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yStart yB def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">/pasX
q2 q2 abs div 0.05 mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">
</span><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">/xP xStart pasX \iA\space cos mul add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yP yStart pasX \iA\space sin mul add def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\parametricplot[plotpoints=200]{xmin}{xmax}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> \FieldLinesFourElectricCharges<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /xP xP dX add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> /yP yP dY add def<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> xP yP<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\pscircle[fillstyle=solid](!xA
yA){0.2}\pscircle[fillstyle=solid](!xB yB){0.2}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">%\psgrid<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\begin{psclip}{\psframe[linestyle=none](-5.2,-5.2)(5.2,5.2)}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=0.4+0.2}{3}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=dashed,linecolor=red](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">x 2 exp y 1 sub 2 exp add sqrt 1 exch div x 2 exp y 1 add
2 exp add sqrt 0.5 exch div sub \r\space sub}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=0.04+0.04}{3}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=dashed,linecolor=red](-8,-8)(8,8){%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">x 2 exp y 1 sub 2 exp add sqrt 1 exch div x 2 exp y 1 add
2 exp add sqrt 0.5 exch div sub \r\space sub}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=-0.4+-0.2}{3}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=dashed,linecolor=orange](-6,-6)(6,6){<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">x 2 exp y 1 sub 2 exp add sqrt 1 exch div x 2 exp y 1 add
2 exp add sqrt 0.5 exch div sub \r\space sub}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=-0.04+-0.04}{3}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=dashed,linecolor=orange](-6,-6)(6,6){<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">x 2 exp y 1 sub 2 exp add sqrt 1 exch div x 2 exp y 1 add
2 exp add sqrt 0.5 exch div sub \r\space sub}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=0.0+0.08}{10}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=solid,linecolor=blue](-6,-6)(6,6){<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">y 1 sub x 2 exp y 1 sub 2 exp add sqrt div y 1 add x 2
exp y 1 add 2 exp add sqrt div 0.5 mul sub \r\space add}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\multido{\r=-0.02+-0.06}{10}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\psplotImp[linestyle=solid,linecolor=blue](-6,-6)(6,6){<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">y 1 sub x 2 exp y 1 sub 2 exp add sqrt div y 1 add x 2
exp y 1 add 2 exp add sqrt div 0.5 mul sub \r\space add}}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\psdots(0,1)(0,-1)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\end{psclip}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);">\psaxes{->}(0,0)(-5.5,-5.5)(5.5,5.5)[$y$,-90][$z$,0]<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\end{pspicture*}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\end{center}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US">\end{document}<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"
lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size: 11pt; font-family: "Calibri","sans-serif"; color: rgb(31, 73, 125);"><o:p> </o:p></span></p>
<div
style="border-style: solid none none; border-color: rgb(181, 196, 223) -moz-use-text-color -moz-use-text-color; border-width: 1pt medium medium; padding: 3pt 0cm 0cm;">
<p class="MsoNormal"><b><span
style="font-size: 10pt; font-family: "Tahoma","sans-serif";" lang="FR">De :</span></b><span
style="font-size: 10pt; font-family: "Tahoma","sans-serif";" lang="FR">
<a class="moz-txt-link-abbreviated" href="mailto:pstricks-bounces@tug.org">pstricks-bounces@tug.org</a> [<a class="moz-txt-link-freetext" href="mailto:pstricks-bounces@tug.org">mailto:pstricks-bounces@tug.org</a>]
<b>De la part de</b> <a class="moz-txt-link-abbreviated" href="mailto:mluque5130@aol.com">mluque5130@aol.com</a><br>
<b>Envoyé :</b> lundi 18 janvier 2010 20:11<br>
<b>À :</b> <a class="moz-txt-link-abbreviated" href="mailto:pstricks@tug.org">pstricks@tug.org</a><br>
<b>Objet :</b> [pstricks] Re : Elektrostatic Field<o:p></o:p></span></p>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p class="MsoNormal"><span
style="font-size: 10pt; font-family: "Arial","sans-serif"; color: black;">The
solution of Patrice is very good! I think Patrick has won the challenge
of tracing field lines and equipotential ... for now ...<br>
How to add arrows to the field lines?<br>
<br>
Thanks to Herbert for the improved code.<br>
<br>
</span><span
style="font-size: 11pt; font-family: "Arial","sans-serif"; color: black;"
lang="EN-US">Best regards,</span><span
style="font-size: 10pt; font-family: "Arial","sans-serif"; color: black;"
lang="EN-US"><br>
<br>
</span><span
style="font-size: 10pt; font-family: "Arial","sans-serif"; color: black;">Manuel<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size: 10pt; font-family: "Arial","sans-serif"; color: black;"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size: 10pt; font-family: "Arial","sans-serif"; color: black;"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size: 10pt; font-family: "Arial","sans-serif"; color: black;"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size: 10pt; font-family: "Helvetica","sans-serif"; color: black;"><o:p> </o:p></span></p>
</div>
</div>
<br>
<hr>
<font color="Gray" face="Verdana" size="2">Important notification: In
the context of the creation of the University of Mons, FPMs email
address policy is changing from '@fpms.ac.be' to '@umons.ac.be' (or
@student.fpms.ac.be to @student.umons.ac.be), please update your
contact list accordingly.<br>
<br>
Note importante: Dans le cadre de la création de l'Université de Mons,
la stratégie d'adresse de courrier électronique de la FPMs change de
'@fpms.ac.be' à '@umons.ac.be' (ou @student.fpms.ac.be to
@student.umons.ac.be), merci de mettre à jour votre liste d'adresses en
conséquence.<br>
</font>
<pre wrap="">
<hr size="4" width="90%">
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</blockquote>
<br>
<pre class="moz-signature" cols="65">--
Jürgen Gilg
Austr. 59
70376 Stuttgart
-------------------------------------
Tel 0711.59 27 88
e-Mail <a class="moz-txt-link-abbreviated" href="mailto:gilg@acrotex.net">gilg@acrotex.net</a>
</pre>
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