TikZpictures as wide as columns in the figure environment inside of the multicol environment?

Question

I have been writing a document that has a bunch of geometric figures in it. Each geometric figure is accompanied by some remarks. The remarks always immediately precede (i.e., appear above) the figure they concern. I have used \begin{figure}[H] <remarks, in English> <geometric figure> \end{figure} in order to force each geometric figure always to appear on the same page as my remarks about them, because I prefer that style. If it is important, my figures are written in the tikzpicture environment.

Recently, I decided that the document would look better in a two-column format, so I used multicols. So we've got tikzpicture inside of figure inside of multicol. My question is: How can I make each geometric figure conform to the width of the column it appears in? How does one do that for a particular figure? And how does one do it globally?

In case it matters, my code looks something like this, though for brevity's sake I have included only one of my geometric figures:

\documentclass{article}
\usepackage{tikz}
\usepackage{float}
\usepackage{multicol}
-----------------------
\begin{document}
\begin{multicols}{2}
\begin{figure}[H]
Below are two concentric circular arcs, blah blah blah...\
\begin{tikzpicture}[scale=.75, >=Stealth]
    \draw [gray, very thin] (-4, -4) grid (4, 4);
    \draw [<->, blue, semithick] (-4.5, 0) -- (4.5, 0);
    \draw [<->, blue, semithick] (0, -4.5) -- (0, 4.5);
    \draw [red] (4, 0) arc [start angle=0, end angle=230, radius=4];
    \draw [purple] (.5, 0) arc [start angle=0, end angle=315, radius=.5];
\end{tikzpicture}
\end{figure}
\end{multicols}
\end{document}

Thank you!

Answer 1

A bit rude solution, but it works ...

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\usepackage{float}
\usepackage{multicol}
\newlength\picwidth
\usepackage{lipsum}
\begin{document}
\begin{multicols}{2}
\lipsum[1]
\begin{figure}[H]
\centering
\setlength\picwidth{9cm} % max. width of image
\begin{tikzpicture}[scale=\linewidth/\picwidth, % ratio column width/image width
                    >=Stealth]
    \draw [gray, very thin] (-4, -4) grid (4, 4);
    \draw [<->, blue, semithick] (-4.5, 0) -- (4.5, 0);
    \draw [<->, blue, semithick] (0, -4.5) -- (0, 4.5);
    \draw [red] (4, 0) arc [start angle=0, end angle=230, radius=4];
    \draw [purple] (.5, 0) arc [start angle=0, end angle=315, radius=.5];
\end{tikzpicture}
\end{figure}
\lipsum[2-4]
\end{multicols}
\end{document}