How to update part of a web page resource from a field event handler

I'm trying to insert a web page into a crm form where part of that web page is updated from an onChange event handler on a field in the main form.

So my page is roughly laid out as;

The form includes a jQuery library as an available resource.

So the onchange event on "FieldA" should run some jQuery to update "FieldB". Really trivial, or so I thought. As a first pass I just linked a form load event to update FieldB and nothing happened. So I changed it to add a button to my web part and force an update from that, again nothing happens.

A bit of investigation shows that my web part needs to explicitly include the jQuery resource in order to use that even though it is available on the form. Which suggests that it is truly a separate web page almost as though it is being included through the long deprecated frames mechanism in HTML. But however it is is being included the upshot is that my onChange handler can not directly talk to my included web page by simply saying $('#FieldB').html(somedata).

So the question is how do I update data in web page included as a web resource on a CRM form from a field on that form.