Changing page with AJAX using JS

I have the following problem. I want to move the user to another page when a certian condition is met. For example, I have a text input field where a user enters a URL. I want to move the user to this url, without him pressing any kind of submit form. I'm using AJAX to achive this. I have a function that checks for the pattern the user entered, if it is found to be a valid url, the page will change to this url. and if it's not a valid url, it will write error.

I have a <div id='url'></div> that the AJAX updates with error message (on 1st load, before user entered anything) and this message continues until it a valid url was entered. when a valid url was entered, the following will be written to this DIV:

<script type="text/javascript">
window.location.href="http://google.com";   // google.com is just an example
</script>

this doesn't seem to work. but if I put the page change code instead of the error message, it is working.

Why doesn't it work after a valid URL was entered?

I don't see any need for AJAX, just normal javascript. When you find that the entered text is a valid website and you want to load it, just use window.location = "http://google.com"; // google.com is just an example directly - no need to insert it into the document.

Why do you write JS to DIV instead of just calling window.location.href="http://google.com"; ?

For example

$.ajax({
  url: 'answercheck.php',
  success: function( data ) {
    if (data=="correct"){
      window.location.href="http://google.com";
    }
    else
    {
        //show error message
    }
  }
});