Is it possible to do this from within a class?
$("#" + field).click(this.validate);
“this.validate” is problematic. JavaScript does not have bound methods, so when you pass that reference, it is only pointing to a plain function. When called, ‘this’ will not be correctly set. See ALA for a fairly thorough discussion of the binding loss problem.
Some frameworks provide built-in method-binding functionality; jQuery does not, as it tends to concentrate more on closures than JavaScript objects. In any case, creating a binding wrapper using a closure is pretty simple; Andrey's answer is the usual approach for jQuery users.
The one thing to look out for with closures for event handlers (whether you are using jQuery or not) is that it tends to cause memory leaks in IE. For simple, short-lived web pages you may not care.