To my knowledge google did not specify any maximum or minimum query length. It totally depends on the browser capability. for each browser has some unique number of characters to be allowed for the search query.
Internet Explorer : 2,083 characters
Firefox : 65,536 characters
Opera : 190,000 characters
Safari : 80,000 characters
Chrome : 64 characters
If you try to use URLs longer than this limited characters then you will get a error message.