Rails 3: Update fields via ajax

application.js

/*
   This part of javascript needs to be included to make 
   a ajax call onchanging the selection value of dropdown.
   Here, application.js is shown just for example. You should 
   load this based on your requirements.
*/

//Use the id of your dropdown instead of "dropdown_id"

$(function($) {
    $("#dropdown_id").change(function() {
        //The controller method from where you want to get the result
        $.ajax({url: '/setval',
        data: 'element_id=' + this.value,
        dataType: 'script'})
    });
});

controller.rb

#This controller method should populate your value
#And assign it in a instance variable.

def setval
    @myval = getValueFromSomeLogic(params[:element_id])
end

setval.js.erb

/*
It will set the value of the text box whose id is
Use the id of your text box instead of "text_box_id"
*/

$('#text_box_id').val('<%= @params %>');