Setting the value of a dynamically created text box with jQuery

Using the following code

var newDiv = $(document.createElement("div"));
var newTextBox;

newTextBox = $(document.createElement("input"))
    .attr("type", "text")
    .attr("id", "textbox")
    .attr("name", "textbox");

newTextBox.val("text");
newDiv.append(newTextBox);
alert(newDiv.html());

I get the following

<input name="textbox" id="textbox" type="text">

I get the same thing with

$("#textbox").val("test");

Using

newTextBox = $("<input/>");

Doesn't help either

Where is my value?

EDIT: SOLTUION

So, further up in the stack I was converting the DOM I built to a string and since - like munch mentioned - the dynamic value doesn't get added to the tag, it wasn't showing up.

Thanks for the help