On click run PHP code and paste result in text box?

I have some php code that generates a random password. Next to a text box I have some text which says "click to Generate a random password".

What I am looking to achieve is when the text in double quotes above is clicked that the PHP code is run and the generated random password is then pasted into the text box which is beside the text above in double quotes.

How could do this? I am thinking maybe jQuery but not sure how I would do what I want above.

Solution

Here you are... complete and working example :)
Put files 'index.html' and 'passgenerator.php' into same directory.

index.html

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
    <head>
        <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
        <title></title>
        <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.4.4/jquery.min.js"></script>
        <script type="text/javascript">
            $(document).ready(function(){
                $('#generate').click(function(){
                    $.get('passgenerator.php', function(data) {
                        $('[name=password]').val(data);
                    });
                })
            });
        </script>
    </head>
    <body>
        <form action="">
            <input type="text" name="password">
            <input type="button" id="generate" value="Generate password">
        </form>
    </body>
</html>

passgenerator.php

<?php
echo sha1(uniqid());
?>