Is ext js compatible with .jsp, java backend?
In short, yes, but see the following article, in terms for ease of use integration (tag library) wise:
http://raibledesigns.com/rd/entry/ext_js_tag_library
and the referenced article:
http://blog.james-carr.org/2008/01/22/making-extjs-more-accessible-to-java-developers/
Ext JS is a javascript library. It exists at the client side of the browser. So it doesn't matter whether you use PHP, JSP or ASP.Net, as long as a browser supports javascript, ExtJS will work there.
Perhaps a better way of understanding your lack of knowledge is to ask why or what is so special about javascript they would mean a java backend would not work...
Google "json"...
I strongly recommend taking a look at Grails. It lives in the java world, and plays extremely nice together with ExtJS. For example, you probably will have to generate and parse a lot of JSON between server and ExtJS client, and Grails does that as if it was a language built-in.