The main idea, is to plot an electric field lines with arrows on it, something like this: enter image description here

My solution is:

\documentclass[tikz, border=1cm]{standalone}
\usepackage{ pgfplots}
\usetikzlibrary{decorations.text, decorations.markings}

    every axis label/.append style={font=\small},

  \draw[red, samples=200, smooth] plot[id=curve, raw gnuplot] function{
    f(x,y) = (0.3 + ((\ea-\eb)/(\ea+2*\eb))/(x**2 + y**2))*y ;
    set xrange [-4:4];
    set yrange [-2:2];
    set view 0,0;
    set isosample 1000,1000;
    set cntrparam levels 50;
    set cont base;
    unset surface;
    splot f(x,y)
  } ;
  \fill[gray!50, draw=blue, thick] (0,0) circle (1.01);

  \clip (0,0) circle (1);
  \foreach \i in {-0.9,-0.675,...,1} {
  \draw[red, decoration={
      mark=at position 0.5 with {\arrow{latex'}}}, postaction={decorate}] (-1,\i) --  (1,\i);

But I have no good idea how to put an arrow in arbitrary position on curve (like I do for middle region lines)

enter image description here

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