# How to draw magnetic lines of force in coil with Tikz?

I'm trying to draw the magnetic lines of force in a coil that should looks like this picture using the tikz package. I've tried to use a foreach loop with controls but (maybe I'm placing the controls wrongly) I don't get ellipse like lines of force... The code I used is this one:

\begin{tikzpicture}
\tikzstyle arrowstyle=[scale=2] %Arrow size
\draw[thick, black, postaction={decorate,decoration={markings,mark=at position .42 with {\arrow[arrowstyle]{stealth}}}}] (0,0) ellipse (1 and 2);
\foreach \x in {0,0.5,...,5}
\draw (-3,\x) .. controls (0,0) and (0,0) .. (3,\x);
\end{tikzpicture}


I think lines must be a part of an ellipse but I don't know how to place the inner point of these ellipses.

There are better ways, polar plots e.g., but you can start with something like this:

\documentclass[tikz,border=5pt]{standalone}
\usetikzlibrary{arrows.meta,decorations.markings}

\begin{document}

\begin{tikzpicture}
\tikzstyle arrowstyle=[scale=2] %Arrow size
\draw[thick, black, postaction={decorate,decoration={markings,mark=at position .42 with {\arrow[arrowstyle]{stealth}}}}] (0,0) ellipse (1 and 2);
\path[clip] (-2,-2.7) rectangle (2,2.7);
\foreach \y in {15,30,...,75} {
\draw (0,{2*tan(\y)+1.5*cos(\y)}) ellipse ({1.5*tan(\y)} and {2*tan(\y)});
\draw (0,{-2*tan(\y)-1.5*cos(\y)}) ellipse ({1.5*tan(\y)} and {2*tan(\y)});
}
\draw (-3,0) -- (3,0);
\end{tikzpicture}

\end{document}