WordPress path url in js script file

According to the Wordpress documentation, you should use wp_localize_script() in your functions.php file. This will create a Javascript Object in the header, which will be available to your scripts at runtime.

See Codex

Example:

<?php wp_localize_script('mylib', 'WPURLS', array( 'siteurl' => get_option('siteurl') )); ?>

To access this variable within in Javascript, you would simply do:

<script type="text/javascript">    var url = WPURLS.siteurl;</script>

You could avoid hardcoding the full path by setting a JS variable in the header of your template, before wp_head() is called, holding the template URL. Like:

<script type="text/javascript">var templateUrl = '<?= get_bloginfo("template_url"); ?>';</script>

And use that variable to set the background (I realize you know how to do this, I only include these details in case they helps others):

Reset.style.background = " url('"+templateUrl+"/images/searchfield_clear.png') ";

    wp_register_script('custom-js',WP_PLUGIN_URL.'/PLUGIN_NAME/js/custom.js',array(),NULL,true);    wp_enqueue_script('custom-js');    $wnm_custom = array( 'template_url' => get_bloginfo('template_url') );    wp_localize_script( 'custom-js', 'wnm_custom', $wnm_custom );

and in custom.js

alert(wnm_custom.template_url);