How to earn with AdSense for search
AdSense for search lets you offer your users Google web search directly from your pages. By placing an AdSense for search box on your site, you'll generate earnings from ad clicks made by users on the search results pages.
You won't, however, receive revenue from user searches through your AdSense for Search box. When users perform searches on your site, but choose not to click on the ads on the search results pages, you will not receive any earnings.