# [pstricks] Re : Elektrostatic Field

Juergen Gilg gilg at acrotex.net
Mon Jan 18 00:08:30 CET 2010

Hello Thomas,

with Manuel's approach and some other idea -- here a possible new way to
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}

\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 to find the lines of the field.
>
> With best regards,
>
> Thomas SÃ¶ll
>
>     ----- Original Message -----
>     *From:* mluque5130 at aol.com <mailto:mluque5130 at aol.com>
>     *To:* pstricks at tug.org <mailto:pstricks at tug.org>
>     *Sent:* Sunday, January 17, 2010 10:31 AM
>     *Subject:* [pstricks] Re : Elektrostatic Field
>
>     This example draws only the vectors at selected points.
>     If nobody gives a complete solution to trace the lines of electric
>     field, 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
>     %        Ex=-dV/dx
>              /Ex q1 xP xA sub mul r1 3 exp div
>                   q2 xP xA add mul r2 3 exp div
>     %        Ey=-dV/dy
>              /Ey yP
>                  q1 r1 3 exp div
>                  q2 r2 3 exp div
>              /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-mail d'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 the the lines of an E-Field from
>     the superposition of two radialsymmetric Charges, 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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