Assuming there are no duplicate IDs in the DOM and $parent is a jQuery object containing a single element that is the parent of #myID
var $el = $("#myID");
vs
var $el = $("#myID", $parent); //Faster or slower?
Is there a speed difference between the two of these?
No, it actually makes things slower (or at least, it can), because jQuery has a special path for simple ID selectors and uses
document.getElementById— but only if you don’t give a context. So giving a context will slow things down (or at least, might slow things down), because jQuery won’t be able to take that shortcut. The relevant check is on line 135 of the current uncompressed jQuery release (v1.7.1).