JQuery :: Adding A Click Event To A Variable?

I have a setting where I construct an image reference which I then append somewhere in the DOM, like so for instance:

var one = "<img src = "test.jpg" ";
var two = "/>";
var my_img = one + two;

and then I add it to DOM using after() function. It works fine. However, I also need to add a click event to it. I tried to do this:

my_img.click(function(){
});

and then append it using after(), but it doesn't seem to work. One thing I can think of is append it after a certain ID, then look for it as a child of that ID and add click to it this way. I haven't tried this, but it'll probably work.