Magnetic field of a dipole magnet

For an alternate, more accurate method with pstricks, please see this page.

Edit and compile if you like:

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% Author: Izaak Neutelings (March 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath} % for \dfrac
\usepackage{bm}
\usepackage{tikz,pgfplots}
\tikzset{>=latex} % for LaTeX arrow head
\pgfplotsset{compat=1.13}
\usetikzlibrary{decorations.markings,intersections,calc}
\usepackage{ifthen}
\usepackage{xcolor}
\usepackage{auto-pst-pdf}
\usepackage{pst-magneticfield}
\usepackage[outline]{contour} % glow around text
\colorlet{Bcol}{violet!90}
\colorlet{BcolFL}{violet!90}
\tikzstyle{north}=[thick,top color=red!60,bottom color=red!90,shading angle=20]
\tikzstyle{south}=[thick,top color=blue!60,bottom color=blue!90,shading angle=20]
\contourlength{1.5pt}
\tikzset{
   EFielLineArrow/.style args={#1,#2}{BcolFL,thick,decoration={markings,
          mark=at position #1 with {\arrow[rotate=#2]{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
  \pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed} % for calculation between -1*10^324 and +1*10^324
  \pgfmathsetmacro{\x}{#1/28.45pt}
  \pgfmathsetmacro{\y}{#2/28.45pt}
  \pgfmathsetmacro{\U}{\Q*((\y+\a)^2+(\x)^2)^(3/2)}
  \pgfmathsetmacro{\V}{-(\Q)*((\y-\a)^2+(\x)^2)^(3/2)}
  \pgfkeys{/pgf/fpu=false}
  \pgfmathparse{
    atan2(((\y+\a)*\V + (\y-\a)*\U),((\x)*\V + (\x)*\U))
  }
 
 
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