Image charge of a sphere

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% Author: Izaak Neutelings (March 2021)
% page 8 https://archive.org/details/StaticAndDynamicElectricity
% https://tex.stackexchange.com/questions/56353/extract-x-y-coordinate-of-an-arbitrary-point-on-curve-in-tikz
% https://tex.stackexchange.com/questions/412899/tikz-calculate-and-store-the-euclidian-distance-between-two-coordinates
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath} % for \dfrac
\usepackage{mathabx} % for \Earth
\usepackage{bm} % \bm
\usepackage{physics}
\usetikzlibrary{3d}
\usepackage{tikz,pgfplots}
\usepackage[outline]{contour} % glow around text
\usepackage{ifthen}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}
\usetikzlibrary{decorations.markings}
\tikzset{>=latex} % for LaTeX arrow head
\pgfplotsset{compat=1.13}
\contourlength{1.2spt}
\usepackage{xcolor}
\colorlet{Ecol}{orange!90!black}
\colorlet{EcolFL}{orange!80!black}
\tikzstyle{charge+}=[very thin,top color=red!50,bottom color=red!90!black,shading angle=20]
\tikzstyle{charge-}=[very thin,top color=blue!50,bottom color=blue!80,shading angle=20]
\tikzset{EFieldLine/.style={thick,EcolFL,decoration={markings,mark=at position #1 with {\arrow{latex}}},
                                 postaction={decorate}},
         EFieldLine/.default=0.5,
         EFielLineArrow/.style args = {#1}{EcolFL,decoration={markings,
          mark=at position 0.5 with {\arrow[rotate=#1]{latex}}},
          postaction={decorate}}
}
\makeatletter
  \newcommand{\xy}[3]{% % FIND X, Y
    \tikz@scan@one@point\pgfutil@firstofone#1\relax
    \edef#2{\the\pgf@x}%
    \edef#3{\the\pgf@y}%
  }
\makeatother
\newcommand{\EFielLineArrow}[2]{ % ELECTRIC FIELD LINE ARROW
 
 
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