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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">Dear Manuel et al,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">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 &nbsp;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 lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">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 lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">I tested your solution with two charges (Q1=1,Q2=&#43;-0.5, located at z=&#43;-1) and superpose with mine and it is perfect. &nbsp;(see code below)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">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 lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">So probably, for the general case, the field lines should be computed by your algorithm and the equipotential by implicit function (that allows
 also &nbsp;to change the color with the sign, red and orange in the example below) &nbsp;<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">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 lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">Best regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">Patrice<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\documentclass{article}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\usepackage{pstricks,pst-func,pstricks-add}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\begin{document}
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\def\FieldLinesFourElectricCharges{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /r1 xP xA sub dup mul yP yA sub dup mul add sqrt def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /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:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /V q1 r1 div<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; q2 r2 div<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; add<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; q3 r3 div<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; add<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; q4 r4 div<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; add def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ex=-dV/dx<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /Ex q1 xP xA sub mul r1 3 exp div<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">q2 xP xB sub mul r2 3 exp div<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ey=-dV/dy<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /Ey q1 yP yA sub mul r1 3 exp div<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; q2 yP yB sub mul r2 3 exp div
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /NormeE Ex dup mul Ey dup mul add sqrt def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;color:#1F497D">/dX Ex NormeE div pasX mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">/dY Ey NormeE div pasX mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\begin{center}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\begin{pspicture*}(-7,-7)(7,7)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">% les limites<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\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:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">% le nombre de lignes de champ<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%\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:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">% le pas d'itération<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pstVerb{/pasX xmax xmin sub 200 div def}% 0.05<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pstVerb{/q1 1 def&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; % les charges<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /q2 0.5 def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /xA 0 def&nbsp;&nbsp;&nbsp;&nbsp; % leurs positions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yA 1 def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /xB 0 def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yB -1 def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; }%<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\multido{\iA=0&#43;15}{24}{% 24 lignes de champ<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pstVerb{/xStart xA def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yStart yA def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;color:#1F497D">/pasX q1 q1 abs div 0.05 mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">/xP xStart pasX \iA\space cos mul add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yP yStart pasX \iA\space sin mul add def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\parametricplot[plotpoints=2000]{xmin}{xmax}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \FieldLinesFourElectricCharges<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /xP xP dX add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yP yP dY add&nbsp; def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; xP yP<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pstVerb{/xStart xB def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yStart yB def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;color:#1F497D">/pasX q2 q2 abs div 0.05 mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">/xP xStart pasX \iA\space cos mul add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yP yStart pasX \iA\space sin mul add def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\parametricplot[plotpoints=2000]{xmin}{xmax}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \FieldLinesFourElectricCharges<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /xP xP dX add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yP yP dY add&nbsp; def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; xP yP<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pscircle[fillstyle=solid](!xA yA){0.2}\pscircle[fillstyle=solid](!xB yB){0.2}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\begin{psclip}{\psframe[linestyle=none](-5.2,-5.2)(5.2,5.2)}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\multido{\r=0.4&#43;0.2}{3}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\psplotImp[linestyle=dotted,linecolor=red](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">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 lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\multido{\r=1.0&#43;1.0}{3}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\psplotImp[linestyle=dashed,linecolor=red](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">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 lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\multido{\r=0.2&#43;0.4}{5}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\psplotImp[linestyle=solid,linecolor=blue](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">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 lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\multido{\r=-0.2&#43;-0.4}{5}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\psplotImp[linestyle=solid,linecolor=blue](-6,-6)(6,6){%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">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:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\psdots(0,1)(0,-1)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\end{psclip}<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\psaxes{-&gt;}(0,0)(-5.5,-5.5)(5.5,5.5)[$y$,-90][$z$,0]<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\end{pspicture*}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\end{center}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\begin{center}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\begin{pspicture*}(-7,-7)(7,7)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">% les limites<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\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:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">% le nombre de lignes de champ<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%\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:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">% le pas d'itération<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pstVerb{/pasX xmax xmin sub 200 div def}% 0.05<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pstVerb{/q1 1 def&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; % les charges<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /q2 -0.5 def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /xA 0 def&nbsp;&nbsp;&nbsp;&nbsp; % leurs positions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yA 1 def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /xB 0 def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yB -1 def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; }%<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\multido{\iA=0&#43;15}{24}{% 24 lignes de champ<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pstVerb{/xStart xA def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yStart yA def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;color:#1F497D">/pasX q1 q1 abs div 0.05 mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">/xP xStart pasX \iA\space cos mul add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yP yStart pasX \iA\space sin mul add def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\parametricplot[plotpoints=200]{xmin}{xmax}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \FieldLinesFourElectricCharges<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /xP xP dX add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yP yP dY add&nbsp; def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; xP yP<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pstVerb{/xStart xB def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yStart yB def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;color:#1F497D">/pasX q2 q2 abs div 0.05 mul def<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">/xP xStart pasX \iA\space cos mul add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yP yStart pasX \iA\space sin mul add def}%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\parametricplot[plotpoints=200]{xmin}{xmax}{%<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \FieldLinesFourElectricCharges<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /xP xP dX add def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /yP yP dY add&nbsp; def<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; xP yP<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\pscircle[fillstyle=solid](!xA yA){0.2}\pscircle[fillstyle=solid](!xB yB){0.2}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">%\psgrid<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\begin{psclip}{\psframe[linestyle=none](-5.2,-5.2)(5.2,5.2)}<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:&quot;Calibri&quot;,&quot;sans-serif&quot;;
color:#1F497D">\multido{\r=0.4&#43;0.2}{3}{%<o:p></o:p></span></p>
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<p class="MsoNormal"><b><span lang="FR" style="font-size:10.0pt;font-family:&quot;Tahoma&quot;,&quot;sans-serif&quot;">De&nbsp;:</span></b><span lang="FR" style="font-size:10.0pt;font-family:&quot;Tahoma&quot;,&quot;sans-serif&quot;"> pstricks-bounces@tug.org [mailto:pstricks-bounces@tug.org]
<b>De la part de</b> mluque5130@aol.com<br>
<b>Envoyé&nbsp;:</b> lundi 18 janvier 2010 20:11<br>
<b>À&nbsp;:</b> pstricks@tug.org<br>
<b>Objet&nbsp;:</b> [pstricks] Re : Elektrostatic Field<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:&quot;Arial&quot;,&quot;sans-serif&quot;;
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 lang="EN-US" style="font-size:11.0pt;font-family:&quot;Arial&quot;,&quot;sans-serif&quot;;
color:black">Best regards,</span><span lang="EN-US" style="font-size:10.0pt;
font-family:&quot;Arial&quot;,&quot;sans-serif&quot;;color:black"><br>
<br>
</span><span style="font-size:10.0pt;font-family:&quot;Arial&quot;,&quot;sans-serif&quot;;
color:black">Manuel<o:p></o:p></span></p>
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<br>
<hr>
<font face="Verdana" color="Gray" 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
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