[pstricks] Re : Re : Elektrostatic Field

Mon Jan 18 09:51:30 CET 2010

@Juergen Gilg : The idea is excellent, however it is again necessary to improve it.

Here is another method, than it is necessary to improve also!

 \documentclass{article}
\usepackage{pstricks,pst-plot}
\SpecialCoor
\def\FieldLines{%
         /r1 xP xA sub dup mul yP dup mul add sqrt def
         /r2 xP xA add dup mul yP dup mul add sqrt def
%        /V q1 r1 div
%           q2 r2 div
%           add def
%        Ex=-dV/dx
         /Ex q1 xP xA sub mul r1 3 exp div
             q2 xP xA add mul r2 3 exp div
             add def
%        Ey=-dV/dy
         /Ey yP
             q1 r1 3 exp div
             q2 r2 3 exp div
             add mul def
         /NormeE Ex dup mul Ey dup mul add sqrt def
         /dX Ex NormeE div pasX mul def
         /dY Ey NormeE div pasX mul def
}
\begin{document}
\begin{center}
\begin{pspicture*}(-6,-8)(10,8)
% les limites
\pstVerb{/xmin -5 def /xmax 5 def /ymin -5 def /ymax 5 def}%
% le pas d'itération
\pstVerb{/pasX xmax xmin sub 200 div def}%
\pstVerb{/q1 1 def           % les charges
         /q2 -0.5 q1 mul def
         /xA -2.5 def}%
% 15 degrés entre chaque ligne (24*15=360)
\multido{\iA=0+15}{24}{% 24 lignes de champ
\pstVerb{/xStart xA def
         /pasX q1 q1 abs div pasX mul def
         /xP xStart  pasX \iA\space cos mul add def
         /yP 0 pasX \iA\space sin mul add def}%
\parametricplot[plotpoints=2000]{xmin}{xmax}{%
        \FieldLines
        /xP xP dX add def
        /yP yP dY add  def
         xP yP
}
\pstVerb{/xStart xA neg def
         /pasX q2 q2 abs div pasX mul def
         /xP xStart pasX \iA\space cos mul add def
         /yP 0 pasX \iA\space sin mul add def}%
\parametricplot[plotpoints=2000]{xmin}{xmax}{%
        \FieldLines
        /xP xP dX add def
        /yP yP dY add  def
         xP yP
}}
\pscircle[fillstyle=solid](!xA 0){0.2}\pscircle[fillstyle=solid](!xA neg 0){0.2}
\end{pspicture*}
\end{center}

\begin{center}
\begin{pspicture*}(-5,-8)(10,8)
% les limites
\pstVerb{/xmin -5 def /xmax 5 def /ymin -5 def /ymax 5 def}%
% le pas d'itération
\pstVerb{/pasX xmax xmin sub 200 div def}%
\pstVerb{/q1 1 def           % les charges
         /q2 0.5 q1 mul def
         /xA -2.5 def}%
\multido{\iA=0+15}{24}{% 24 lignes de champ
\pstVerb{/xStart xA def
         /pasX q1 q1 abs div pasX mul def
         /xP xStart  pasX \iA\space cos mul add def
         /yP 0 pasX \iA\space sin mul add def}%
\parametricplot[plotpoints=2000]{xmin}{xmax}{%
        \FieldLines
        /xP xP dX add def
        /yP yP dY add  def
         xP yP
}
\pstVerb{/xStart xA neg def
         /pasX q2 q2 abs div pasX mul def
         /xP xStart pasX \iA\space cos mul add def
         /yP 0 pasX \iA\space sin mul add def}%
\parametricplot[plotpoints=2000]{xmin}{xmax}{%
        \FieldLines
        /xP xP dX add def
        /yP yP dY add  def
         xP yP
}}
\pscircle[fillstyle=solid](!xA 0){0.2}\pscircle[fillstyle=solid](!xA neg 0){0.2}
\end{pspicture*}
\end{center}
\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Regards,

M.L.

-----E-mail d'origine-----
De : Juergen Gilg <gilg at acrotex.net>
A : Graphics with PSTricks <pstricks at tug.org>
Envoyé le : Lundi, 18 Janvier 2010 0:08
Sujet : Re: [pstricks] Re :  Elektrostatic Field

  Hello Thomas,

with Manuel's approach and some other idea -- here a possible new wayto get the field lines you presented. The equation for the lines is:

E_x dy = E_y dx

using the  differential equation features of pstricks-add.

However this for sure needs some more cosmetics and refinements --maybe some typing error or whatever.

Try it out:

\documentclass{article}
\usepackage{pstricks-add}

\begin{document}
\begin{pspicture*}(-5,-5)(5,6)
\pstVerb{%
/q1 1 def
/q2 -0.5 q1 mul def
/xA 1.8 def
}

\multido{\rx=-250+10.2}{50}{%
\psplotDiffEqn[%
linewidth=0.25pt,% 
linecolor=red,%
varsteptol=.001,%
method=rk4,%
algebraic,
plotpoints=200%
]{-20}{20}{\rx}{%
(q1*(y[0])/(sqrt((x+xA)^2+(y[0])^2))^3+q2*(y[0])/(sqrt((x-xA)^2+(y[0])^2))^3)%
/%
(q1*(x+xA)/(sqrt((x+xA)^2+(y[0])^2))^3+q2*(x-xA)/(sqrt((x-xA)^2+(y[0])^2))^3)%
}%
}
\pscircle*(!xA 0){0.25}\pscircle*(!xA neg 0){0.25}
\end{pspicture*}
\end{document} 

Regards,

Juergen

Thomas Söll wrote:
ï»¿        
Hallo Manuel,

thank you for your solution. 

Now I have to understand your way tofind the lines of the field.

With best regards,

Thomas SÃ¶ll

-----Original Message ----- 

From:    mluque5130 at aol.com 

To:    pstricks at tug.org 

Sent:Sunday, January 17, 2010 10:31 AM

Subject:[pstricks] Re : Elektrostatic Field

Thisexample draws only the vectors at selected points.
If nobody gives a complete solution to trace the lines of electricfield, I think I can do it in 2 or 3 weeks...

%%%%%%%%%%%%%%%%%%%%%%

\documentclass{article}
\usepackage{pstricks,multido}
\SpecialCoor
\def\fieldlines{% 
         /xP \nx\space def
         /yP \ny\space def
         /r1 xP xA sub dup mul yP dup mul add sqrt def
         /r2 xP xA add dup mul yP dup mul add sqrt def
%        /V q1 r1 div
%           q2 r2 div
%           add def
%        Ex=-dV/dx
         /Ex q1 xP xA sub mul r1 3 exp div
              q2 xP xA add mul r2 3 exp div
              add def
%        Ey=-dV/dy
         /Ey yP 
             q1 r1 3 exp div
             q2 r2 3 exp div
             add mul def
         /NormeE Ex dup mul Ey dup mul add sqrt def
         /uEx Ex NormeE div K mul def
         /uEy Ey NormeE div K mul def
}
\begin{document}

\begin{pspicture}(-5,-5)(5,6)
\multido{\nx=-5+0.5}{22}{%
\multido{\ny=-5+0.5}{22}{%
\pstVerb{/q1 1 def
         /q2 -0.5 q1 mul def
         /K 1 def
         /xA 1.8 def
         \fieldlines}
\rput(\nx,\ny){\psline{->}(0,0)(!uEx uEy)\psdot(0,0)}
}}
\pscircle*(!xA 0){0.25}\pscircle*(!xA neg 0){0.25}
\end{pspicture}

\begin{pspicture}(-5,-5)(5,6)
\multido{\nx=-5+0.5}{22}{%
\multido{\ny=-5+0.5}{22}{%
\pstVerb{/q1 -1 def
         /q2 2 q1 mul def
         /K 1 def
         /xA 2.2 def
         \fieldlines}
\rput(\nx,\ny){\psline{->}(0,0)(!uEx uEy)\psdot(0,0)}
}}
\pscircle*(!xA 0){0.25}\pscircle*(!xA neg 0){0.25}
\end{pspicture}
\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Yours sincerely 

Manuel

-----E-maild'origine-----
De : Thomas SÃ¶ll 1und1 <Thomas.Soell at onlinehome.de>
A : pstricks at tug.org
EnvoyÃ© le : Samedi, 16 Janvier 2010 15:02
Sujet : [pstricks] Elektrostatic Field

Hallo,

is it possible to draw thethe lines of an E-Field from the superposition of two radialsymmetricCharges, as in the picture drawn.

There is one +Q1, the other-0,5*Q1.

Has anyone an idea?

Thanks for helping.

Thomas SÃ¶ll

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-- 
 Jürgen Gilg
 Austr. 59
 70376 Stuttgart
-------------------------------------
 Tel       0711.59 27 88
 e-Mail    gilg at acrotex.net

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