how to cache the javascript file

Hello I am trying make a browser cache experiment. like this

<head>
    <script type="text/javascript" src='<%=Tool.GetFileRefUrl("js_cached.js")%>' ></script>
    <script type="text/javascript">
        var lastFile = fun();
    </script>
    <script src="js_cached.js" type="text/javascript"></script>
    <script type="text/javascript">
        var cacheFile = fun();
    </script>
</head><body>
<form>
<div>

    The cache file is :<script type="text/javascript">
                           document.writeln(cacheFile);
                    </script>
    <br />
    The last file is :<script type="text/javascript">
                          document.writeln(lastFile);
                    </script>    
</div>
</form>
</body>

Tool.GetFileRefUrl("js_cached.js") will return a random js file string every time like "js_cached.js?v=8752162122311"

The first time the fun() runs it returns "A", so the page will show:

The cache file is :A
The last file is :A

Now I changed the file js_cached.js which on the web server and make fun() return "B" and I hope too see the result:

The cache file is :A
The last file is :B

but it actually is:

The cache file is :B
The last file is :B

Is something wrong? Why does the browser not cache the js file? Did I make an incorrect assumption?

the fun is

    function fun() {
    return "A";//after modify it be "B"
}

the Tool.GetFileRefUrl is

public class Tool
{
    public static string GetFileRefUrl(string url)
    {
        var ticks = GetLastWriteTime(url);
        var result = string.Format("{0}?v={1}", url, ticks);
        return result;
    }

    private static long GetLastWriteTime(string fileName)
    {
        var lastWriteTime = File.GetLastWriteTime(HttpContext.Current.Server.MapPath(fileName));
        return lastWriteTime.Ticks;
    }
}

Solution

Finally , I got a way to cache the js file add the page to your browser tab (mark link? well I'm not sure what it is in English, just like My Favorites on IE) Open the link , your will see

The cache file is :A
The last file is :A

modify the js file,and open new tab by mark link

The cache file is :A
The last file is :B

Tks Bergi for your prompt :)